# Decision-Making Method of Qualitative and Quantitative Comprehensive Evaluation of Talents Based on Probability Hesitation Fuzzy Language

Authors: Xueer Ji; Lei Wang; Huifeng Xue; Yufeng Gao
Journal: Mathematical Problems in Engineering
 (2021)

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## Abstract

A scientific, reasonable, and novel talent evaluation index system is the foundation of talent training and selection. Based on the novel “Man-Machine-Environment System Engineering” (hereinafter referred to as MMESE) theory, this paper proposes a novel talent evaluation index system that considers the ontological attributes and the external environment of the object comprehensively for talent evaluation, which could help the evaluator obtain more accurate evaluation results. Since the comprehensive evaluation of MMESE talents is a complex decision-making problem that is both qualitative and quantitative, a corresponding decision-making method that integrates qualitative and quantitative approaches is proposed here based on probabilistic language entropy and the possibility of superior order relationships. First, the weights of quantitative and qualitative attributes are calculated based on entropy theory and probabilistic fuzzy language. Second, the standard weight vectors of qualitative and quantitative attributes are obtained by adjusting the weight integration coefficients, and the change intervals of the pros and cons between the objects to be evaluated are calculated. Third, the pros and cons of the objects to be evaluated are compared to obtain the possibility degree matrix that describes the priority relationships among the objects, and a ranking vector is derived from the possibility degree matrix to reflect the rankings of the objects’ pros and cons. Finally, this system and the decision-making methods have been verified as scientific and effective.


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## Body

## 1. Introduction

The world is experiencing a serious shortage of talents in the twenty-first century. Aside from the uneven economic development levels, the main reason for such a shortage is the lack of a scientific and comprehensive mechanism for talent training and selection. Therefore, the research on talent evaluation index systems and talent evaluation methods is of great significance to the formulation of strategic plans for talent training and the emergence of global talents. Particularly, a scientific and reasonable talent evaluation index system is the foundation of talent training and selection, and such a system has been studied extensively for the affecting factors. Tian et al. [1] focused on the connotation, characteristics, and growth rules of talents and studied the impact of the integration of external environments (e.g., social, group, cultural, educational, and natural) and internal factors (e.g., physiology, psychology, and intelligence) on talent growth. Qiu [2] built an evaluation system that is both qualitative and quantitative to evaluate college students for potential international applied talents in the context of internationalization. Li [3] improved the evaluation system for the education results of higher vocational students with a quality and ability evaluation index system specially designed for these students. Nan et al. [4] proposed an innovation-oriented talent evaluation system for greater achievements of the innovation-driven development strategy. From the perspective of the human resources value chain, Shang and Wang [5] created an evaluation index system for the talent ecosystem, in which three first-level indicators, namely, talent competence, organizational ability, and regional environment, are evaluated. These research findings have greatly promoted the fairness and righteousness of the talent evaluation and selection process.As for the talent evaluation methods, studies have been focused on the competitive evaluation method, analytic hierarchy process, and fuzzy evaluation method, and so on. For example, Jia et al. [6] used the competitive evaluation method to design index weights and evaluation models for advanced talents in scientific and technological fields. Labi et al. [7] recommended using AHP in four evaluation steps when selecting employees. Metin and Deha Er [8] proposed a fuzzy comprehensive multistage multicriteria evaluation model for management and academic talents. Lazarevic [9] proposed a fuzzy two-level model to minimize subjective judgment in employee selection. Drigas et al. [10] used the neurofuzzy technique to investigate and evaluate unemployed people or those working in specific positions.Talent evaluation involves various internal and external factors and complex component systems, especially under the context of rapid social and economic developments. Vague and uncertain information generated during the evaluation process is difficult to handle with the currently available quantitative evaluation models. In 1981, a comprehensive edge technology named Science-Man-Machine-Environment System Engineering (SMMESE) [11] was born, which provided an important theoretical foundation to build talent evaluation index systems in complex environments. In 1990, based on SMMESE, Qian and his colleagues put forward the “integrated method from qualitative evaluation to quantitative evaluation” [12], which is effective for talent evaluation. The core of Qian’s method is to organically integrate quantitative data and expert experience, knowledge, and subjective judgments. However, as the talent evaluation index system becomes more complex, decision-making experts are constrained by their knowledge structure and levels, making the quantification of complex qualitative indicators difficult.To tackle such a problem, experts have begun to use language terms as the way to express information, such as Zadeh’s [13] fuzzy language method proposed in 1975. In Zadeh’s method, qualitative decisions are represented as language variables such as “good” or “bad,” and this method enhances the feasibility and flexibility of decision expressions. Studies in numerous fields have testified the reliability of this method, and this method has been extensively studied for extensions into fuzzy decision-making methods. For example, Ali et al. [14] built an MADM decision model based on the q-rung orthopair fuzzy bipolar soft sets. Ali et al. [15] studied the fuzzy bipolar soft expert-based decision-making method and implemented it in a COVID-19 situation.However, the fuzzy language method only uses single linguistic terms to give value to linguistic variables, which could be insufficient and inaccurate to reflect the real expert opinions. For this reason, Rodriguez et al. [16] proposed the concept of hesitant fuzzy linguistic term set (HFLTS), in which text-free grammars and conversion functions are used to transform the expert’s decision languages into operable hesitant fuzzy language sets. Following that, HFLTS has been applied in various decision-making methods for language information. Xu and Gou [17] proposed the concepts of hesitation fuzzy entropy and hesitation fuzzy cross-entropy and applied them to multicriteria decision-making problems. HFLTS provides possible language terms for decision-making experts, and these language terms are assumed to have equivalent importance in decision-making. However, in actual decision-making problems, since all experts have their preferences, the importance of different language terms is often varied. Therefore, Pang et al. [18] extended HFLTS to probability linguistic term set (PLTS) to reflect such variations, which allows experts to assign probabilities for multiple linguistic terms. Wang and Xue [19] proposed a comprehensive decision-making method that incorporates quantitative data and linguistic probabilities based on a comprehensive integrated discussion method.In summary, the available literature has provided many references for the construction of talent evaluation index systems and evaluation methods, but there are still several shortcomings. Firstly, a talent evaluation index system is primarily a systematic analysis of human factors and the external environment, but previous methods failed to consider the impact of “machines” on talent training in the information era. Secondly, the lack of scientificity in talent evaluation methods makes them difficult to perform comprehensive, quantitative, and qualitative evaluations in a complex environment. Thirdly, available evaluation models have found it difficult to accurately express the qualitative indicators in the talent indicator system, and therefore the fuzziness of these indicators is not represented in the evaluation results.To solve these deficiencies, the internal and external factors affecting talent growth are comprehensively analyzed based on the theory of MMESE in this paper. Following that, an MMESE talent evaluation index system is created to comprehensively expand the connotation of the talent evaluation index system. In addition, the theories of comprehensive integration methods, probabilistic language fuzzy entropy, and superior order relationship are employed in this paper for the comprehensive evaluation of fuzzy quantitative and qualitative indicators in talent evaluation. Finally, a qualitative and quantitative indicator is proposed to the MMESE talent evaluation index system to verify its effectiveness and scientificity.


## 2. The MMESE Talent Evaluation Index System

### 2.1. Theory of Construction

In the big data era, external devices have brought us massive information and changed the ways people use to acquire knowledge. Biology and machines tend to integrate into the new era, and the cutting-edge brain-computer interface technology has become a strategic hot spot in many countries. The contradiction between the explosive growth of human knowledge and the slow development of biological brains has become more prominent than it has ever been. Moreover, the growth models of talents across times and regions change with the local informatization level, resulting in more significant limitations of the traditional talent evaluation index system. Therefore, a scientific and rational talent evaluation index system for the big data era is needed to address the influences of machine development, as well as economic, political, social network, and other external factors, on talent growth.Particularly, MMESE believes that the interactions among man, machine, and environment make up not a simple cycle but a spiral growth process [20]. Electronic computers have shifted the role of humans from a direct operator to a decision-maker, leading to significant enhancement, partial replacement, and great expansions of the functions of human mental work. In this way, human beings are assigned to more advanced and smart activities. MMESE theory is an important foundation of talent evaluation indicators. Besides, within the vigorous development of science and technology, almost all cutting-edge scientific research and technological work are controlled by computers. Consequently, talent emergence is experiencing a boom, and traditional talent evaluation index systems need corresponding changes.In this paper, the coupling relationships between human and machine, human and environment, and machine and environment are analyzed under three complex systems. Additionally, an MMESE talent evaluation index system that involves both qualitative and quantitative factors is proposed. Particularly, MMESE does not merely study the performance of human, machine, and environment; it also involves special considerations about the coupling relationship between the three elements and the methods to coordinate them to build an MMSES talent evaluation index system. There are seven aspects in the MMESE theory (Figure1).Figure 1
Schematic diagram of the MMESE theory.


### 2.2. Factor Analysis of the MMESE Talent Evaluation Index System

The talent evaluation index system in the MMESE theory is a dynamic, open, and multilevel model involving both qualitative and quantitative indicators. Specifically, personal ability, physical and mental health, moral quality, family environment, social environment, and innovation ability are some of the most-mentioned indicators [20–23]. Based on the available research results related to talent evaluation index elements, this paper combines the MMESE theory with these elements and divides the factors involved into three levels: human (B1), machine (B2), and environment (B3). When selecting the indices, the principles of pertinence, systematization, completeness, practicability, and foresight were strictly followed, and the indices selected in the first round were screened for better performance of the MMESE talent evaluation system.


#### 2.2.1. Factors of the B1 Layer

In theB1 layer “Human,” talents are evaluated from four aspects, namely, health level (C1), psychological quality (C2), education level (C3), and innovation ability (C4).C1 is focused on health risk assessments, and talents with relatively stable physical fitness are given good evaluations because they are considered to be able to engage in long-term, stable, and continuous growth. Since 1980, the life expectancy worldwide has increased by 10 years to 74.8 years in 2015. However, the annual death toll has also risen from 48 million in 1990 to nearly 56 million in 2015. Specifically, chronic diseases are still one of the major health problems for humans. According to the 2016 World Health Organization (WHO) report, there are more than 6 billion subhealthy people in the world, accounting for 85% of the total population [24]. Unhealthy conditions can make people feel burnt out or unresponsive, leading to lower vitality and adaptability. Moreover, many people are frequently finding themselves in a state of work anxiety, irritability, and helplessness, and these conditions will bring serious undesired impacts to talent development. Therefore, the indicators in the C1 aspect are used as quantitative parameters for personal health analysis. Health risk assessment [25] is a tool that describes and evaluates the possibility of an individual suffering or dying from a specific disease at a specific time in the future. It is indeed a quantitative assessment of the individual’s health status and the risk of future illness and death for him/her.TheC2 aspect is focused on mental health. WHO defines health to be more than the absence of disease and weakness. It also includes the physical, psychological, and social integrity of an individual. In 2001, WHO further defined mental health as a state of health or happiness in which individuals can realize themselves, cope with the pressures of daily life, work productively, and contribute to the society in which they live [26]. Some scholars believe that mental health is essential for an individual’s overall health, and it is a continuous psychological state in which the individual shows good vitality, positive inner experience, satisfactory social adaptation, and effective production capability, thereby giving full play to his/her physical and mental potentials [27]. Therefore, the main evaluation criteria in C2 are self-harmony, interpersonal harmony, and social harmony.TheC3 aspect addresses education. A person’s knowledge level is reflected in his/her academic qualifications and knowledge structures. School education is designed to cultivate people with particular plans in designated institutions, and schools are the foundation of talent growth. Therefore, the C3 aspects consider the highest education level of the individual.TheC4 aspect considers the individual’s innovation ability. In 1950, JP Guilford (1950) delivered a famous speech entitled “Creativity” at the American Psychology Annual Conference, calling for joint research on creative issues. From then on, the research on the quality of innovative talents has flourished till now. Here in this paper, the innovation ability refers to the talents’ ability to propose new ideas, theories, methods, and inventions with economic, social, or ecological value in practical activities.With the analysis above, the detailed indicators of the “Human” layer in the MMESE talent evaluation index system are obtained (Table1).Table 1
MMESE talent growth factor index system (Human layer).
Target levelCriterion levelSubtarget levelAttributeIndex levelMMESE talent evaluation index systemHuman (B1)Health level (C1)Qualitative—Psychological quality (C2)QuantitativeSelf-harmony, interpersonal harmony, and social harmonyEducation level (C3)QualitativeThe highest level of education currently received by the individualInnovation ability (C4)QuantitativeThe ability to continuously provide new ideas, new theories, new methods, and new inventions


#### 2.2.2. Factors of theB2 Layer

In theB2 layer “Machine,” talents are evaluated from two aspects, namely, daily information downloads (C5) and computer application capabilities (C6).TheC5 aspect reflects the amount of information acquired. According to the Statistical Report on China’s Internet Development Status released by China Internet Network Information Center (CNNIC), as of December 2020, China holds 980 million Internet users (70.4% of its total population). Moreover, there are 342 million online education users and 460 million online literature users, accounting for 34.6% and 46.5% of all the netizens, respectively. The average weekly online time per capita is 26.2 hours; meanwhile, the average monthly mobile phone traffic for an individual in China is 7.2 G, which is 1.2 times the global average. In summary, Internet has become an important source for people to receive knowledge and information.TheC6 aspect focuses on how well an individual masters computer skills. In most industries, computers have become the primary tool to improve the efficiencies in industrial production, operation, and management and to reduce the operational risks and costs. Parameters in the C6 aspect reflect a person’s capability of working with computers, for example, to what extent an individual masters common office software and network applications.With the analysis above, the detailed indicators of the “Machine” layer in the MMESE talent evaluation index system are obtained (Table2).Table 2
MMESE talent growth factor index system (Machine layer).
Target levelCriterion levelSubtarget levelAttributeIndex levelMMESE talent evaluation index systemMachine (B2)Daily information downloads (C5)QualitativeThe amount of information downloaded by individuals on the Internet every dayComputer application capabilities (C6)QuantitativeIncluding the use of common office software, network applications, and handling simple problems


#### 2.2.3. Factors of theB3 Layer

In theB3 layer “Environment,” talents are evaluated from four aspects, which consist of the economic environment (C7), the policy environment (C8), the network environment (C9), and the family environment (C10).TheC7 aspect addresses the economic factors. The economy casts varied effects on talent development. Specifically, the changes in the local consumption structure and residents’ income could affect local investment in talent training. In this paper, GDP indicators are chosen to represent the impact of the economic environment on talents.TheC8 aspect is devoted to the relevant policies. Regional policies can either restrict or promote talent development, and talent growth and development are inseparable from the principles of national and regional policies. Favorable policies can support talent growth by inspiring work enthusiasm in the local population or creating favorable social conditions for talent growth. In this paper, policies and laws about talent introduction, talent incentives, and talent protection are selected to describe the policy environment.TheC9 aspect focuses on the computer network, which directly affects the way people obtain information. People in different regions have significantly different experiences in enjoying the convenience, diversity, and timeliness of knowledge acquisition via the Internet. The network development level, a factor neglected in traditional talent growth index frameworks, is dynamic, innovative, and forward-looking. In this paper, local data download speed is chosen to define the network quality.TheC10 aspect investigates the family factors. Families are the birthplaces and cradles of talents, and they are the space for individual growth and life, bringing fundamental impacts to the development of individual talents. Specifically, the literacy of family members is an important factor that affects individual development, which is therefore chosen as the parameter for C10.With the analysis above, the detailed indicators of the “Machine” layer in the MMESE talent evaluation index system are obtained (Table3).Table 3
MMESE talent growth factor index system (Environment layer).
Target levelCriterion levelSubtarget levelAttributeIndex levelMMESE talent evaluation index systemEnvironment (B3)Economic environment (C7)Qualitative—Policy environment (C8)Quantitative—Network environment (C9)QualitativeRegional network speedFamily environment (C4)QualitativeEducational status of immediate family membersIn a word, the MMESE talent evaluation index system involves the impacts from the development of human intelligence, the machines, and the external environment on talents. Both humans and computers have their strengths and weaknesses. Computers are more effective in massive, repetitive, and programmed work, while humans are more productive in tasks that require advanced and creative thinking. When selecting new talent indicators to improve a talent evaluation system, the three major layers of MMESE should be studied in depth.


## 2.1. Theory of Construction

In the big data era, external devices have brought us massive information and changed the ways people use to acquire knowledge. Biology and machines tend to integrate into the new era, and the cutting-edge brain-computer interface technology has become a strategic hot spot in many countries. The contradiction between the explosive growth of human knowledge and the slow development of biological brains has become more prominent than it has ever been. Moreover, the growth models of talents across times and regions change with the local informatization level, resulting in more significant limitations of the traditional talent evaluation index system. Therefore, a scientific and rational talent evaluation index system for the big data era is needed to address the influences of machine development, as well as economic, political, social network, and other external factors, on talent growth.Particularly, MMESE believes that the interactions among man, machine, and environment make up not a simple cycle but a spiral growth process [20]. Electronic computers have shifted the role of humans from a direct operator to a decision-maker, leading to significant enhancement, partial replacement, and great expansions of the functions of human mental work. In this way, human beings are assigned to more advanced and smart activities. MMESE theory is an important foundation of talent evaluation indicators. Besides, within the vigorous development of science and technology, almost all cutting-edge scientific research and technological work are controlled by computers. Consequently, talent emergence is experiencing a boom, and traditional talent evaluation index systems need corresponding changes.In this paper, the coupling relationships between human and machine, human and environment, and machine and environment are analyzed under three complex systems. Additionally, an MMESE talent evaluation index system that involves both qualitative and quantitative factors is proposed. Particularly, MMESE does not merely study the performance of human, machine, and environment; it also involves special considerations about the coupling relationship between the three elements and the methods to coordinate them to build an MMSES talent evaluation index system. There are seven aspects in the MMESE theory (Figure1).Figure 1
Schematic diagram of the MMESE theory.


## 2.2. Factor Analysis of the MMESE Talent Evaluation Index System

The talent evaluation index system in the MMESE theory is a dynamic, open, and multilevel model involving both qualitative and quantitative indicators. Specifically, personal ability, physical and mental health, moral quality, family environment, social environment, and innovation ability are some of the most-mentioned indicators [20–23]. Based on the available research results related to talent evaluation index elements, this paper combines the MMESE theory with these elements and divides the factors involved into three levels: human (B1), machine (B2), and environment (B3). When selecting the indices, the principles of pertinence, systematization, completeness, practicability, and foresight were strictly followed, and the indices selected in the first round were screened for better performance of the MMESE talent evaluation system.


### 2.2.1. Factors of the B1 Layer

In theB1 layer “Human,” talents are evaluated from four aspects, namely, health level (C1), psychological quality (C2), education level (C3), and innovation ability (C4).C1 is focused on health risk assessments, and talents with relatively stable physical fitness are given good evaluations because they are considered to be able to engage in long-term, stable, and continuous growth. Since 1980, the life expectancy worldwide has increased by 10 years to 74.8 years in 2015. However, the annual death toll has also risen from 48 million in 1990 to nearly 56 million in 2015. Specifically, chronic diseases are still one of the major health problems for humans. According to the 2016 World Health Organization (WHO) report, there are more than 6 billion subhealthy people in the world, accounting for 85% of the total population [24]. Unhealthy conditions can make people feel burnt out or unresponsive, leading to lower vitality and adaptability. Moreover, many people are frequently finding themselves in a state of work anxiety, irritability, and helplessness, and these conditions will bring serious undesired impacts to talent development. Therefore, the indicators in the C1 aspect are used as quantitative parameters for personal health analysis. Health risk assessment [25] is a tool that describes and evaluates the possibility of an individual suffering or dying from a specific disease at a specific time in the future. It is indeed a quantitative assessment of the individual’s health status and the risk of future illness and death for him/her.TheC2 aspect is focused on mental health. WHO defines health to be more than the absence of disease and weakness. It also includes the physical, psychological, and social integrity of an individual. In 2001, WHO further defined mental health as a state of health or happiness in which individuals can realize themselves, cope with the pressures of daily life, work productively, and contribute to the society in which they live [26]. Some scholars believe that mental health is essential for an individual’s overall health, and it is a continuous psychological state in which the individual shows good vitality, positive inner experience, satisfactory social adaptation, and effective production capability, thereby giving full play to his/her physical and mental potentials [27]. Therefore, the main evaluation criteria in C2 are self-harmony, interpersonal harmony, and social harmony.TheC3 aspect addresses education. A person’s knowledge level is reflected in his/her academic qualifications and knowledge structures. School education is designed to cultivate people with particular plans in designated institutions, and schools are the foundation of talent growth. Therefore, the C3 aspects consider the highest education level of the individual.TheC4 aspect considers the individual’s innovation ability. In 1950, JP Guilford (1950) delivered a famous speech entitled “Creativity” at the American Psychology Annual Conference, calling for joint research on creative issues. From then on, the research on the quality of innovative talents has flourished till now. Here in this paper, the innovation ability refers to the talents’ ability to propose new ideas, theories, methods, and inventions with economic, social, or ecological value in practical activities.With the analysis above, the detailed indicators of the “Human” layer in the MMESE talent evaluation index system are obtained (Table1).Table 1
MMESE talent growth factor index system (Human layer).
Target levelCriterion levelSubtarget levelAttributeIndex levelMMESE talent evaluation index systemHuman (B1)Health level (C1)Qualitative—Psychological quality (C2)QuantitativeSelf-harmony, interpersonal harmony, and social harmonyEducation level (C3)QualitativeThe highest level of education currently received by the individualInnovation ability (C4)QuantitativeThe ability to continuously provide new ideas, new theories, new methods, and new inventions


### 2.2.2. Factors of theB2 Layer

In theB2 layer “Machine,” talents are evaluated from two aspects, namely, daily information downloads (C5) and computer application capabilities (C6).TheC5 aspect reflects the amount of information acquired. According to the Statistical Report on China’s Internet Development Status released by China Internet Network Information Center (CNNIC), as of December 2020, China holds 980 million Internet users (70.4% of its total population). Moreover, there are 342 million online education users and 460 million online literature users, accounting for 34.6% and 46.5% of all the netizens, respectively. The average weekly online time per capita is 26.2 hours; meanwhile, the average monthly mobile phone traffic for an individual in China is 7.2 G, which is 1.2 times the global average. In summary, Internet has become an important source for people to receive knowledge and information.TheC6 aspect focuses on how well an individual masters computer skills. In most industries, computers have become the primary tool to improve the efficiencies in industrial production, operation, and management and to reduce the operational risks and costs. Parameters in the C6 aspect reflect a person’s capability of working with computers, for example, to what extent an individual masters common office software and network applications.With the analysis above, the detailed indicators of the “Machine” layer in the MMESE talent evaluation index system are obtained (Table2).Table 2
MMESE talent growth factor index system (Machine layer).
Target levelCriterion levelSubtarget levelAttributeIndex levelMMESE talent evaluation index systemMachine (B2)Daily information downloads (C5)QualitativeThe amount of information downloaded by individuals on the Internet every dayComputer application capabilities (C6)QuantitativeIncluding the use of common office software, network applications, and handling simple problems


### 2.2.3. Factors of theB3 Layer

In theB3 layer “Environment,” talents are evaluated from four aspects, which consist of the economic environment (C7), the policy environment (C8), the network environment (C9), and the family environment (C10).TheC7 aspect addresses the economic factors. The economy casts varied effects on talent development. Specifically, the changes in the local consumption structure and residents’ income could affect local investment in talent training. In this paper, GDP indicators are chosen to represent the impact of the economic environment on talents.TheC8 aspect is devoted to the relevant policies. Regional policies can either restrict or promote talent development, and talent growth and development are inseparable from the principles of national and regional policies. Favorable policies can support talent growth by inspiring work enthusiasm in the local population or creating favorable social conditions for talent growth. In this paper, policies and laws about talent introduction, talent incentives, and talent protection are selected to describe the policy environment.TheC9 aspect focuses on the computer network, which directly affects the way people obtain information. People in different regions have significantly different experiences in enjoying the convenience, diversity, and timeliness of knowledge acquisition via the Internet. The network development level, a factor neglected in traditional talent growth index frameworks, is dynamic, innovative, and forward-looking. In this paper, local data download speed is chosen to define the network quality.TheC10 aspect investigates the family factors. Families are the birthplaces and cradles of talents, and they are the space for individual growth and life, bringing fundamental impacts to the development of individual talents. Specifically, the literacy of family members is an important factor that affects individual development, which is therefore chosen as the parameter for C10.With the analysis above, the detailed indicators of the “Machine” layer in the MMESE talent evaluation index system are obtained (Table3).Table 3
MMESE talent growth factor index system (Environment layer).
Target levelCriterion levelSubtarget levelAttributeIndex levelMMESE talent evaluation index systemEnvironment (B3)Economic environment (C7)Qualitative—Policy environment (C8)Quantitative—Network environment (C9)QualitativeRegional network speedFamily environment (C4)QualitativeEducational status of immediate family membersIn a word, the MMESE talent evaluation index system involves the impacts from the development of human intelligence, the machines, and the external environment on talents. Both humans and computers have their strengths and weaknesses. Computers are more effective in massive, repetitive, and programmed work, while humans are more productive in tasks that require advanced and creative thinking. When selecting new talent indicators to improve a talent evaluation system, the three major layers of MMESE should be studied in depth.


## 2.2.1. Factors of the B1 Layer

In theB1 layer “Human,” talents are evaluated from four aspects, namely, health level (C1), psychological quality (C2), education level (C3), and innovation ability (C4).C1 is focused on health risk assessments, and talents with relatively stable physical fitness are given good evaluations because they are considered to be able to engage in long-term, stable, and continuous growth. Since 1980, the life expectancy worldwide has increased by 10 years to 74.8 years in 2015. However, the annual death toll has also risen from 48 million in 1990 to nearly 56 million in 2015. Specifically, chronic diseases are still one of the major health problems for humans. According to the 2016 World Health Organization (WHO) report, there are more than 6 billion subhealthy people in the world, accounting for 85% of the total population [24]. Unhealthy conditions can make people feel burnt out or unresponsive, leading to lower vitality and adaptability. Moreover, many people are frequently finding themselves in a state of work anxiety, irritability, and helplessness, and these conditions will bring serious undesired impacts to talent development. Therefore, the indicators in the C1 aspect are used as quantitative parameters for personal health analysis. Health risk assessment [25] is a tool that describes and evaluates the possibility of an individual suffering or dying from a specific disease at a specific time in the future. It is indeed a quantitative assessment of the individual’s health status and the risk of future illness and death for him/her.TheC2 aspect is focused on mental health. WHO defines health to be more than the absence of disease and weakness. It also includes the physical, psychological, and social integrity of an individual. In 2001, WHO further defined mental health as a state of health or happiness in which individuals can realize themselves, cope with the pressures of daily life, work productively, and contribute to the society in which they live [26]. Some scholars believe that mental health is essential for an individual’s overall health, and it is a continuous psychological state in which the individual shows good vitality, positive inner experience, satisfactory social adaptation, and effective production capability, thereby giving full play to his/her physical and mental potentials [27]. Therefore, the main evaluation criteria in C2 are self-harmony, interpersonal harmony, and social harmony.TheC3 aspect addresses education. A person’s knowledge level is reflected in his/her academic qualifications and knowledge structures. School education is designed to cultivate people with particular plans in designated institutions, and schools are the foundation of talent growth. Therefore, the C3 aspects consider the highest education level of the individual.TheC4 aspect considers the individual’s innovation ability. In 1950, JP Guilford (1950) delivered a famous speech entitled “Creativity” at the American Psychology Annual Conference, calling for joint research on creative issues. From then on, the research on the quality of innovative talents has flourished till now. Here in this paper, the innovation ability refers to the talents’ ability to propose new ideas, theories, methods, and inventions with economic, social, or ecological value in practical activities.With the analysis above, the detailed indicators of the “Human” layer in the MMESE talent evaluation index system are obtained (Table1).Table 1
MMESE talent growth factor index system (Human layer).
Target levelCriterion levelSubtarget levelAttributeIndex levelMMESE talent evaluation index systemHuman (B1)Health level (C1)Qualitative—Psychological quality (C2)QuantitativeSelf-harmony, interpersonal harmony, and social harmonyEducation level (C3)QualitativeThe highest level of education currently received by the individualInnovation ability (C4)QuantitativeThe ability to continuously provide new ideas, new theories, new methods, and new inventions


## 2.2.2. Factors of theB2 Layer

In theB2 layer “Machine,” talents are evaluated from two aspects, namely, daily information downloads (C5) and computer application capabilities (C6).TheC5 aspect reflects the amount of information acquired. According to the Statistical Report on China’s Internet Development Status released by China Internet Network Information Center (CNNIC), as of December 2020, China holds 980 million Internet users (70.4% of its total population). Moreover, there are 342 million online education users and 460 million online literature users, accounting for 34.6% and 46.5% of all the netizens, respectively. The average weekly online time per capita is 26.2 hours; meanwhile, the average monthly mobile phone traffic for an individual in China is 7.2 G, which is 1.2 times the global average. In summary, Internet has become an important source for people to receive knowledge and information.TheC6 aspect focuses on how well an individual masters computer skills. In most industries, computers have become the primary tool to improve the efficiencies in industrial production, operation, and management and to reduce the operational risks and costs. Parameters in the C6 aspect reflect a person’s capability of working with computers, for example, to what extent an individual masters common office software and network applications.With the analysis above, the detailed indicators of the “Machine” layer in the MMESE talent evaluation index system are obtained (Table2).Table 2
MMESE talent growth factor index system (Machine layer).
Target levelCriterion levelSubtarget levelAttributeIndex levelMMESE talent evaluation index systemMachine (B2)Daily information downloads (C5)QualitativeThe amount of information downloaded by individuals on the Internet every dayComputer application capabilities (C6)QuantitativeIncluding the use of common office software, network applications, and handling simple problems


## 2.2.3. Factors of theB3 Layer

In theB3 layer “Environment,” talents are evaluated from four aspects, which consist of the economic environment (C7), the policy environment (C8), the network environment (C9), and the family environment (C10).TheC7 aspect addresses the economic factors. The economy casts varied effects on talent development. Specifically, the changes in the local consumption structure and residents’ income could affect local investment in talent training. In this paper, GDP indicators are chosen to represent the impact of the economic environment on talents.TheC8 aspect is devoted to the relevant policies. Regional policies can either restrict or promote talent development, and talent growth and development are inseparable from the principles of national and regional policies. Favorable policies can support talent growth by inspiring work enthusiasm in the local population or creating favorable social conditions for talent growth. In this paper, policies and laws about talent introduction, talent incentives, and talent protection are selected to describe the policy environment.TheC9 aspect focuses on the computer network, which directly affects the way people obtain information. People in different regions have significantly different experiences in enjoying the convenience, diversity, and timeliness of knowledge acquisition via the Internet. The network development level, a factor neglected in traditional talent growth index frameworks, is dynamic, innovative, and forward-looking. In this paper, local data download speed is chosen to define the network quality.TheC10 aspect investigates the family factors. Families are the birthplaces and cradles of talents, and they are the space for individual growth and life, bringing fundamental impacts to the development of individual talents. Specifically, the literacy of family members is an important factor that affects individual development, which is therefore chosen as the parameter for C10.With the analysis above, the detailed indicators of the “Machine” layer in the MMESE talent evaluation index system are obtained (Table3).Table 3
MMESE talent growth factor index system (Environment layer).
Target levelCriterion levelSubtarget levelAttributeIndex levelMMESE talent evaluation index systemEnvironment (B3)Economic environment (C7)Qualitative—Policy environment (C8)Quantitative—Network environment (C9)QualitativeRegional network speedFamily environment (C4)QualitativeEducational status of immediate family membersIn a word, the MMESE talent evaluation index system involves the impacts from the development of human intelligence, the machines, and the external environment on talents. Both humans and computers have their strengths and weaknesses. Computers are more effective in massive, repetitive, and programmed work, while humans are more productive in tasks that require advanced and creative thinking. When selecting new talent indicators to improve a talent evaluation system, the three major layers of MMESE should be studied in depth.


## 3. Relevant Theories of Qualitative Index Weight Calculation Based on Probabilistic Language

The comprehensive evaluation of a talent growth factor index system is a highly complex and uncertain decision-making problem, and its quantitative calculation is extremely difficult, making a reasonable and simplified model necessary to solve such a problem. Compared with traditional evaluation methods, hesitant fuzzy linguistic decision-making methods are very applicable when processing complex problems. Extensive studies have been performed on (group) decision-making based on hesitant fuzzy linguistic term sets. In this paper, the probabilistic language entropy theory is improved for the qualitative talent evaluation, and the weight calculation strategy for the qualitative criteria in probabilistic languages based on the entropy theory is proposed.


### 3.1. Probabilistic Language Term Set

The probabilistic language term set is expanded based on the hesitant fuzzy language term set. Decision-makers can provide multiple linguistic terms to state their opinions and their corresponding probability information to represent their comprehensive and accurate preferences.Definition 1 (see [18]).
Assume thatS=st|t=−τ,…,−1,0,1,…τ is a limited and completely ordered discrete language term set. As a result, it is a probabilistic language term set that can be expressed as(1)hs=sϕlpl|sϕl∈S,pl≥0,l=1,2,…,#hs,∑l=1#hspl≤1,where sϕl represents the language term in the language term set S, pl represents the probability of sϕl, and #hs is the number of language terms in hs.
If∑l=1#hspl=1, then we say that hs has complete probability distribution information; if ∑l=1#hspl<1, then some language term information in hs is unknown. In actual decision-making processes, because the experience and knowledge of experts are limited, incomplete information in hs is common. Besides, the probability information in hs could even be completely unknown if all the experts could not give the corresponding language terms.
If the language term information inhs is incomplete, then it would need normalization. Specifically, if a language term sl is not present in hs, it should not appear in the probability language term set after normalization, either. Based on this idea, unknown probability information 1−∑l=1#hspl is evenly distributed to each language term in hs.Definition 2.
(see [28]). hs=sϕlpl|sϕl∈S,pl≥0,l=1,2,…,#hs,∑l=1#hspl≤1 is a set of probability language terms on a language term set S, and if ∑l=1#hspl<1, the normalized set of probability language terms h˜s becomes(2)h˜s=sϕlpl|sϕl∈S,pl≥0,l=1,2,…,#hs,∑l=1#hspl=1,where pl˜=pl/∑l=1#hspl,l=1,2,…,#hs.


### 3.2. Comparison of the Probabilistic Language Term Sets

Symbolic distance, as a measure of information in fuzzy theory and fuzzy decision-making, is used to study the rankings of fuzzy numbers. Since fuzzy language term sets are simple and convenient to compare based on symbolic operations, this paper proposes a comparison strategy for probabilistic language term sets based on symbolic operations.Definition 3.
(see [28]). Assume hs=sϕlpl|sϕl∈S,pl≥0,l=1,2,…,#hs,∑l=1#hspl≤1 is a probabilistic language term set on a language term set S=st|t=−τ,…,−1,0,1,…τ, #hs is the number of language terms in hs, and the function Ist can transform language terms st into corresponding subscript values tt=−τ,…,−1,0,1,…τ. Then, the expectation of hs can be defined as(3)ehs=∑l=1#hsIsϕlpl.
Furthermore, the variance ofhs is defined as(4)vhs=∑l=1#hsIsϕl−ehs2pl.
For any two probabilistic language term setshs1 and hs2,(5)hs1=sϕl1pl1|sϕl1∈S,pl1≥0,l=1,2,…,#hs1,∑l=1#hs1pl1≤1;hs2=sϕl2pl2|sϕl2∈S,pl2≥0,l=1,2,…,#hs2,∑l=1#hs2pl2≤1,they can be compared based on their expectations and variances:(1)
Ifehs1>ehs2, then hs1 is greater than hs2, which is recorded as hs1≻hs2.(2)
Ifehs1<ehs2, then hs1 is smaller than hs2, which is recorded as hs1≺hs2.(3)
Ifehs1=ehs2, the variances vhs1 and vhs2 should be calculated. If vhs1>vhs2, then hs1≺hs2; if vhs1<vhs2, then hs1≻hs2; if vhs1=vhs2, hs1 is equivalent to hs2, which is recorded as hs1∼hs2.


### 3.3. Probability Language Entropy

Probability language term sets are an extension of hesitant fuzzy language term sets, so probability language entropy, which is defined below, is also an extension of hesitant fuzzy language entropy and the probability language terminologies.Definition 5.
(see [29]). S=st|t=−τ,…,−1,0,1,…τ is a set of language terms, hs=sϕlpl|sϕl∈S,l=1,2,…,#hs, hs1=sϕl1pl1|sϕl1∈S,l=1,2,…,#hs1, and hs2=sϕl2pl2|sϕl2∈S,l=1,2,…,#hs2 are three sets of probability language terms on S, #hs=#hs1=#hs2=L, and function Ist can convert language terms St into the corresponding subscript values tt=−τ,…,−1,0,1,…τ. Then, a probability language entropy Ehs must satisfy the following conditions:(1)
0≤Ehs≤1(2)
When and only whenhs=S−τ1 or hs=Sτ1, Ehs=0(3)
When and only when#hs=2,pϕ1=pϕ2=0.5,Isϕ1+Isϕ2=0,Ehs=1(4)
For∀l=1,2,…,L, if or Isϕ11≤Isϕ12≤0, and pl1=pl2, then Ehs1≥Ehs2(5)
Ehs=Ehsc, while hsc=s−ϕlpl||sϕl∈S,pl≥0,l=1,2,…,#hs
Based on these conditions, for anyhs=sϕlpl|sϕl∈S,pl≥0,l=1,2,…,#hs,∑l=1#hspl≤1 on S=st|t=−τ,…,−1,0,1,…τ, #hs=L, Ehs of hs can be expressed as(6)Ehs=−12Lln2∑l=1Lpllnpl+1−plln1−pl+Isϕl+IsϕL−l+1+2τ4τlnIsϕl+IsϕL−l+1+2τ4τ+2τ−Isϕl−IsϕL−l+14τln2τ−Isϕl−IsϕL−l+14τ.


## 3.1. Probabilistic Language Term Set

The probabilistic language term set is expanded based on the hesitant fuzzy language term set. Decision-makers can provide multiple linguistic terms to state their opinions and their corresponding probability information to represent their comprehensive and accurate preferences.Definition 1 (see [18]).
Assume thatS=st|t=−τ,…,−1,0,1,…τ is a limited and completely ordered discrete language term set. As a result, it is a probabilistic language term set that can be expressed as(1)hs=sϕlpl|sϕl∈S,pl≥0,l=1,2,…,#hs,∑l=1#hspl≤1,where sϕl represents the language term in the language term set S, pl represents the probability of sϕl, and #hs is the number of language terms in hs.
If∑l=1#hspl=1, then we say that hs has complete probability distribution information; if ∑l=1#hspl<1, then some language term information in hs is unknown. In actual decision-making processes, because the experience and knowledge of experts are limited, incomplete information in hs is common. Besides, the probability information in hs could even be completely unknown if all the experts could not give the corresponding language terms.
If the language term information inhs is incomplete, then it would need normalization. Specifically, if a language term sl is not present in hs, it should not appear in the probability language term set after normalization, either. Based on this idea, unknown probability information 1−∑l=1#hspl is evenly distributed to each language term in hs.Definition 2.
(see [28]). hs=sϕlpl|sϕl∈S,pl≥0,l=1,2,…,#hs,∑l=1#hspl≤1 is a set of probability language terms on a language term set S, and if ∑l=1#hspl<1, the normalized set of probability language terms h˜s becomes(2)h˜s=sϕlpl|sϕl∈S,pl≥0,l=1,2,…,#hs,∑l=1#hspl=1,where pl˜=pl/∑l=1#hspl,l=1,2,…,#hs.


## 3.2. Comparison of the Probabilistic Language Term Sets

Symbolic distance, as a measure of information in fuzzy theory and fuzzy decision-making, is used to study the rankings of fuzzy numbers. Since fuzzy language term sets are simple and convenient to compare based on symbolic operations, this paper proposes a comparison strategy for probabilistic language term sets based on symbolic operations.Definition 3.
(see [28]). Assume hs=sϕlpl|sϕl∈S,pl≥0,l=1,2,…,#hs,∑l=1#hspl≤1 is a probabilistic language term set on a language term set S=st|t=−τ,…,−1,0,1,…τ, #hs is the number of language terms in hs, and the function Ist can transform language terms st into corresponding subscript values tt=−τ,…,−1,0,1,…τ. Then, the expectation of hs can be defined as(3)ehs=∑l=1#hsIsϕlpl.
Furthermore, the variance ofhs is defined as(4)vhs=∑l=1#hsIsϕl−ehs2pl.
For any two probabilistic language term setshs1 and hs2,(5)hs1=sϕl1pl1|sϕl1∈S,pl1≥0,l=1,2,…,#hs1,∑l=1#hs1pl1≤1;hs2=sϕl2pl2|sϕl2∈S,pl2≥0,l=1,2,…,#hs2,∑l=1#hs2pl2≤1,they can be compared based on their expectations and variances:(1)
Ifehs1>ehs2, then hs1 is greater than hs2, which is recorded as hs1≻hs2.(2)
Ifehs1<ehs2, then hs1 is smaller than hs2, which is recorded as hs1≺hs2.(3)
Ifehs1=ehs2, the variances vhs1 and vhs2 should be calculated. If vhs1>vhs2, then hs1≺hs2; if vhs1<vhs2, then hs1≻hs2; if vhs1=vhs2, hs1 is equivalent to hs2, which is recorded as hs1∼hs2.


## 3.3. Probability Language Entropy

Probability language term sets are an extension of hesitant fuzzy language term sets, so probability language entropy, which is defined below, is also an extension of hesitant fuzzy language entropy and the probability language terminologies.Definition 5.
(see [29]). S=st|t=−τ,…,−1,0,1,…τ is a set of language terms, hs=sϕlpl|sϕl∈S,l=1,2,…,#hs, hs1=sϕl1pl1|sϕl1∈S,l=1,2,…,#hs1, and hs2=sϕl2pl2|sϕl2∈S,l=1,2,…,#hs2 are three sets of probability language terms on S, #hs=#hs1=#hs2=L, and function Ist can convert language terms St into the corresponding subscript values tt=−τ,…,−1,0,1,…τ. Then, a probability language entropy Ehs must satisfy the following conditions:(1)
0≤Ehs≤1(2)
When and only whenhs=S−τ1 or hs=Sτ1, Ehs=0(3)
When and only when#hs=2,pϕ1=pϕ2=0.5,Isϕ1+Isϕ2=0,Ehs=1(4)
For∀l=1,2,…,L, if or Isϕ11≤Isϕ12≤0, and pl1=pl2, then Ehs1≥Ehs2(5)
Ehs=Ehsc, while hsc=s−ϕlpl||sϕl∈S,pl≥0,l=1,2,…,#hs
Based on these conditions, for anyhs=sϕlpl|sϕl∈S,pl≥0,l=1,2,…,#hs,∑l=1#hspl≤1 on S=st|t=−τ,…,−1,0,1,…τ, #hs=L, Ehs of hs can be expressed as(6)Ehs=−12Lln2∑l=1Lpllnpl+1−plln1−pl+Isϕl+IsϕL−l+1+2τ4τlnIsϕl+IsϕL−l+1+2τ4τ+2τ−Isϕl−IsϕL−l+14τln2τ−Isϕl−IsϕL−l+14τ.


## 4. The Comprehensive, Integrated, Qualitative, and Quantitative Decision-Making Model

### 4.1. Problem Description

To solve multiattribute complex decision-making problems, experts need to consider the qualitative and quantitative properties of the objects and sort out the pros and cons of all the possible alternatives. Specifically, quantitative attributes are generally expressed as specific values, while qualitative attributes are evaluated by the experts’ language evaluations based on their empirical knowledge. In actual decision-making process, such language evaluations are summarized into a set of probability language terms, and because expert knowledge is limited, attribute weights are often inaccurate or even completely unknown. Therefore, a multicriteria decision-making problem involving both qualitative and quantitative attributes can be described as follows.Assume an alternative setA=A1,A2,…,Am. Its decision criteria contain quantitative Cz=C1z,C2z,…,Cnzz and qualitative Cq=C1q,C2q,…,Cnqq property sets, and the corresponding criterion attribute weight sets are wz=w1z,w1z,…,wnzz and wq=w1q,w1q,…,wnqq, respectively. The criterion attribute weight sets must satisfy ∑j=1nzwjz+∑k=1nqwkq=1, and all guidelines are considered preferred. Then, consider a property value matrix X=xijm×nzi=1,2,…,m;j=1,2,…,nz under Cz, in which xij represents the property value of Ai on the quantitative attribute Cjz. Subsequently, a probability language decision matrix H=hsikm×nqi=1,2,…,m;k=1,2,…,nq could be obtained by summarizing the expert decision information under Cq, in which hsik represents the probability language term set of Ai on Ckq.In this paper, the weights of all criteria attributes are assigned as completely unknown to avoid inaccurate weights in the decision-making process. Consequently, a qualitative attribute weight setwz=w1z,w1z,…,wnzz and a quantitative attributes weight set wq=w1q,w1q,…,wnqq must be obtained via reasonable calculations. In addition, all criteria attributes must be integrated to obtain the final decisions for complex decision-making problems. This paper proposes a comprehensive and integrated decision-making method based on probabilistic hesitation language entropy, cross-entropy, and the possibility of priority relationship, and this method could provide qualitative and quantitative solutions to complex decision-making problems in talent evaluation.


### 4.2. Property Weight Calculations Based on Entropy

The entropy weight method obtains the entropy information and calculates the attribute weights simply based on the data of each decision attribute, thereby evading the subjectivity of attribute weight assignments. In this paper, the entropy weight method is applied to calculate the quantitative attribute weights following a previous report [30], and the calculated results would be incorporated with the probabilistic language entropy theory to obtain the qualitative attribute weights. The specific calculation process of quantitative attribute weights has been elaborated in literature [31], which will not be repeated here.For the weight calculation of qualitative attributes, the probability language entropyEhsik is calculated following formula (5), and the total entropy E^k=∑i=1mEhsik of all the qualitative attributes Ckq is obtained by accumulation. According to the entropy theory, smaller overall entropy numbers correspond to larger attribute weights. Therefore, we have the calculation formula for qualitative attribute weights:(7)wkq=∑k=1k=nqE^k∑k=1k=nq∑k=1k=nqE^k/E^k.


### 4.3. Alternative Sorting Based on the Possibility of Precedence Relationship

In a multicriteria decision-making problem, the criterion attribute values of each alternative should be integrated for comprehensive ranking. However, the relationship between the pros and cons of the alternatives can be determined by comparing their attribute values in single criteria. Specifically, Gou et al. [30] proposed an alternative queuing method (AQM) based on the outranking method, which processes the priority relationships with a directed relationship graph and a 0-1 matrix. In this paper, a ranking method for alternatives is proposed based on the possibility of priority relationships [31,32].First, the directed relationship graph and the 0-1 matrix of the optimal order relationship among the alternatives must be explained. For two alternativesAi and Aj, if Ai≻Aj (Ai better than Aj), their directed relationship can be expressed as Ai⟶Aj in the graph; if Ai=Aj (the priorities of Ai and Aj are equal), their directed relationship can be expressed as Ai∪Aj in the graph. Finally, if the advantages and disadvantages of Ai and Aj are not comparable, their relationship shall not be represented in the directed relationship graph. Similarly, a 0-1 matrix can be applied to describe the relationships. Assume that the 0-1 matrix is M. If Ai≻Aj, make Mij=1, Mij=0; if Ai=Aj, make Mij=Mji=1; if the pros and cons of Ai and Aj are not comparable, then make Mij=Mji=0. In particular, the priority relationship of the alternatives in the 0-1 matrix is expressed as 1; in other words, the elements on the main diagonal always satisfy Mij=Mji=1 in the 0-1 matrix.The priority relationship between four sample alternativesA1,A2,A3,A4 under a single criterion can be represented by the directed graph (Figure 2).Figure 2
The directed graph of alternative plans.The order of priority relationships in Figure2 is used for illustration. The probability of association among Ai and Aj is matrix P which is used to indicate the credibility of the situation that Ai is associated with Aj. The four alternatives A1,A2,A3,A4 are compared in pairs to get four possibility matrices (Ps) that describe their mutual priority relationships:(8)P=A1A2A3A4A1A2A3A4p11p12p13p14p21p22p23p24p31p32p33p34p41p42p43p44.An elementpiji,j=1,2,3,4 in a possibility degree matrix P must satisfy the following properties:(1)
0≤pij≤1(2)
pij+pji=1, especially, pii=0.5i,j=1,2,3,4In a possibility degree matrixP=Pijm×mi,j=1,2,…,m that reflects the priority relationships among m alternatives, the possible degree information of all m alternatives is mutually compared, and P is a fuzzy complementary judgment matrix. Then, the problem of ranking the pros and cons of the m alternatives turns into a problem of finding the ranking vector of P, which has been solved in a previous report [31]:(9)vi=1mm−1∑j=1mpij+m2−1,i=1,2,…,m.The ranking vectorV=v1,v2,…,vmT of the possibility degree matrix P=Pijm×m can be obtained by formula (10), and the pros and cons of the m alternatives can be ranked by the numerical values of the elements in V.


### 4.4. Comprehensive, Integrated, Qualitative, and Quantitative Decision-Making

To solve multicriteria decision-making problems with both qualitative and quantitative attributes, entropy weight, probabilistic language entropy, cross-entropy, and priority ordering methods are integrated to propose a comprehensive 3-part decision-making method.(1)
Calculate the quantitative attribute weight setwz and the qualitative attribute weight set wq.(2)
Choose an appropriate weight integration coefficientδδ>0 so that ∑wz/∑wq=δ. Then the standard weight set becomes(10)w=w1,w2,…,wnz,wnz+1,wnz+2,…,,wnz+nq,where wi=wzi/1+δ,i=1,2,…,nz, wnz+j=δwqj/1+δ,j=1,2,…,nq, and nz and nq are the quantitative attributes and their quantities, respectively.Since the weights of qualitative and quantitative attributes are calculated via different methods, they are not directly comparable. Besides,δδ>0 is a factor that directly affects the conversion of the standard weight set w=w¯z,w¯q. Meanwhile, since the importance of each attribute in actual decision-making processes cannot be too wide, the differences in importance among attributes will generally not exceed 10 times. Therefore, if the decision-maker does not have a clear preference on the importance of attributes, δ values may be selected within 0.1≤δ≤10 (when 0.1≤δ<1, quantitative attributes are more stressed; when 1<δ≤10, then qualitative attributes are more stressed). Following that, calculate the change interval Ri−,Ri+ of the overall pros and cons Ri of scheme Ai, where Ri− and Ri+ represent the minimum and maximum values of Ri across the alternatives, respectively. Compare the change intervals of Ri of all alternatives Aii,j=1,2,…,m in pairs to obtain the possibility degree matrix P=Pijm×mi,j=1,2,…,m that describes the priority relationships across all alternatives and obtain the comprehensive rankings of the alternatives with the ranking method in Section 4.3.The overall steps of the proposed method are as follows:Step 1: calculate the quantitative attribute weight setwz and the qualitative attribute weight set wq according to Section 4.2, and ∑wz=1,∑wq=1.Step 2: set the value interval ofδ as δ∈0.1,10, and take δ=0.1 as the initial weight integration coefficient.Step 3: inputδ, and calculate the standard weight set w=w¯z,w¯q.Step 4: under each criterion attributeCj (when j=1,2,…,nz, it refers to the quantitative attributes; when j=nz+1,nz+2,…,nz+nq, it refers to the qualitative attributes), compare the alternatives in pairs and establish a directed graph or 0-1 matrix for them. For quantitative attributes, the values of the attributes may be compared directly to determine the pros and cons of the alternatives. For qualitative attributes, the pros and cons of the alternatives may be compared following the probabilistic language term set method in Section 2.2. The 0-1 matrices are constructed following the procedure and definitions in Section 4.3.Step 5: based on the prioritized matrixMj obtained in step 4, for alternatives Ai,Aki,k=1,2,…,m, the cumulative weight of all the criterion attributes that satisfy Ai≻Ak is recorded as the overall benefit weight w≻i,k; similarly, the cumulative weight of all the criterion attributes that satisfy Ai≺Ak is recorded as the overall disadvantage weight w≺i,k, and the cumulative weight of all the criterion attributes that satisfy Ai＝Ak is recorded as the overall indifference weight w=i,k.Step 6: construct alternative plans for the indicators for the measurement ofAi,Aki,k=1,2,…,m’s pros and cons degree:(11)Rik=w≻i,k+μw≈i,kw≻i,k+1−μw≈i,k,where0≤μ≤1 indicates the influence degree of the alternatives and the indifference situation on the pros and cons. Larger Rik suggests higher superiority of Ai over Ak.Step 7: calculate the averageRik of the alternatives Ai,Ak and the overall pros and cons Ri of the alternative Ai:(12)Ri=1m∑k=1mRik.Step 8: update the maximum and minimum values inRi−,Ri+ for all alternatives Ai, and let δ=δ+0.01. If δ>10, go to step 9; otherwise, go to step 3.Step 9: compare the intervalRi−,Ri+ of each pair according to formula (13), and obtain the probability piji,j=1,2,…,m of plan Ai being superior over Aj [33, 34]:(13)pij=minLi+Lj,maxRi+−Rj−,0Li+Lj,whereLi=Ri+−Rj−,Lj=Rj+−Rj−.Step 10: build the possible degree matrixP=pijm×n based on the piji,j=1,2,…,m numbers obtained for all alternatives, and rank the alternatives with the ranking method in Section 4.3.


## 4.1. Problem Description

To solve multiattribute complex decision-making problems, experts need to consider the qualitative and quantitative properties of the objects and sort out the pros and cons of all the possible alternatives. Specifically, quantitative attributes are generally expressed as specific values, while qualitative attributes are evaluated by the experts’ language evaluations based on their empirical knowledge. In actual decision-making process, such language evaluations are summarized into a set of probability language terms, and because expert knowledge is limited, attribute weights are often inaccurate or even completely unknown. Therefore, a multicriteria decision-making problem involving both qualitative and quantitative attributes can be described as follows.Assume an alternative setA=A1,A2,…,Am. Its decision criteria contain quantitative Cz=C1z,C2z,…,Cnzz and qualitative Cq=C1q,C2q,…,Cnqq property sets, and the corresponding criterion attribute weight sets are wz=w1z,w1z,…,wnzz and wq=w1q,w1q,…,wnqq, respectively. The criterion attribute weight sets must satisfy ∑j=1nzwjz+∑k=1nqwkq=1, and all guidelines are considered preferred. Then, consider a property value matrix X=xijm×nzi=1,2,…,m;j=1,2,…,nz under Cz, in which xij represents the property value of Ai on the quantitative attribute Cjz. Subsequently, a probability language decision matrix H=hsikm×nqi=1,2,…,m;k=1,2,…,nq could be obtained by summarizing the expert decision information under Cq, in which hsik represents the probability language term set of Ai on Ckq.In this paper, the weights of all criteria attributes are assigned as completely unknown to avoid inaccurate weights in the decision-making process. Consequently, a qualitative attribute weight setwz=w1z,w1z,…,wnzz and a quantitative attributes weight set wq=w1q,w1q,…,wnqq must be obtained via reasonable calculations. In addition, all criteria attributes must be integrated to obtain the final decisions for complex decision-making problems. This paper proposes a comprehensive and integrated decision-making method based on probabilistic hesitation language entropy, cross-entropy, and the possibility of priority relationship, and this method could provide qualitative and quantitative solutions to complex decision-making problems in talent evaluation.


## 4.2. Property Weight Calculations Based on Entropy

The entropy weight method obtains the entropy information and calculates the attribute weights simply based on the data of each decision attribute, thereby evading the subjectivity of attribute weight assignments. In this paper, the entropy weight method is applied to calculate the quantitative attribute weights following a previous report [30], and the calculated results would be incorporated with the probabilistic language entropy theory to obtain the qualitative attribute weights. The specific calculation process of quantitative attribute weights has been elaborated in literature [31], which will not be repeated here.For the weight calculation of qualitative attributes, the probability language entropyEhsik is calculated following formula (5), and the total entropy E^k=∑i=1mEhsik of all the qualitative attributes Ckq is obtained by accumulation. According to the entropy theory, smaller overall entropy numbers correspond to larger attribute weights. Therefore, we have the calculation formula for qualitative attribute weights:(7)wkq=∑k=1k=nqE^k∑k=1k=nq∑k=1k=nqE^k/E^k.


## 4.3. Alternative Sorting Based on the Possibility of Precedence Relationship

In a multicriteria decision-making problem, the criterion attribute values of each alternative should be integrated for comprehensive ranking. However, the relationship between the pros and cons of the alternatives can be determined by comparing their attribute values in single criteria. Specifically, Gou et al. [30] proposed an alternative queuing method (AQM) based on the outranking method, which processes the priority relationships with a directed relationship graph and a 0-1 matrix. In this paper, a ranking method for alternatives is proposed based on the possibility of priority relationships [31,32].First, the directed relationship graph and the 0-1 matrix of the optimal order relationship among the alternatives must be explained. For two alternativesAi and Aj, if Ai≻Aj (Ai better than Aj), their directed relationship can be expressed as Ai⟶Aj in the graph; if Ai=Aj (the priorities of Ai and Aj are equal), their directed relationship can be expressed as Ai∪Aj in the graph. Finally, if the advantages and disadvantages of Ai and Aj are not comparable, their relationship shall not be represented in the directed relationship graph. Similarly, a 0-1 matrix can be applied to describe the relationships. Assume that the 0-1 matrix is M. If Ai≻Aj, make Mij=1, Mij=0; if Ai=Aj, make Mij=Mji=1; if the pros and cons of Ai and Aj are not comparable, then make Mij=Mji=0. In particular, the priority relationship of the alternatives in the 0-1 matrix is expressed as 1; in other words, the elements on the main diagonal always satisfy Mij=Mji=1 in the 0-1 matrix.The priority relationship between four sample alternativesA1,A2,A3,A4 under a single criterion can be represented by the directed graph (Figure 2).Figure 2
The directed graph of alternative plans.The order of priority relationships in Figure2 is used for illustration. The probability of association among Ai and Aj is matrix P which is used to indicate the credibility of the situation that Ai is associated with Aj. The four alternatives A1,A2,A3,A4 are compared in pairs to get four possibility matrices (Ps) that describe their mutual priority relationships:(8)P=A1A2A3A4A1A2A3A4p11p12p13p14p21p22p23p24p31p32p33p34p41p42p43p44.An elementpiji,j=1,2,3,4 in a possibility degree matrix P must satisfy the following properties:(1)
0≤pij≤1(2)
pij+pji=1, especially, pii=0.5i,j=1,2,3,4In a possibility degree matrixP=Pijm×mi,j=1,2,…,m that reflects the priority relationships among m alternatives, the possible degree information of all m alternatives is mutually compared, and P is a fuzzy complementary judgment matrix. Then, the problem of ranking the pros and cons of the m alternatives turns into a problem of finding the ranking vector of P, which has been solved in a previous report [31]:(9)vi=1mm−1∑j=1mpij+m2−1,i=1,2,…,m.The ranking vectorV=v1,v2,…,vmT of the possibility degree matrix P=Pijm×m can be obtained by formula (10), and the pros and cons of the m alternatives can be ranked by the numerical values of the elements in V.


## 4.4. Comprehensive, Integrated, Qualitative, and Quantitative Decision-Making

To solve multicriteria decision-making problems with both qualitative and quantitative attributes, entropy weight, probabilistic language entropy, cross-entropy, and priority ordering methods are integrated to propose a comprehensive 3-part decision-making method.(1)
Calculate the quantitative attribute weight setwz and the qualitative attribute weight set wq.(2)
Choose an appropriate weight integration coefficientδδ>0 so that ∑wz/∑wq=δ. Then the standard weight set becomes(10)w=w1,w2,…,wnz,wnz+1,wnz+2,…,,wnz+nq,where wi=wzi/1+δ,i=1,2,…,nz, wnz+j=δwqj/1+δ,j=1,2,…,nq, and nz and nq are the quantitative attributes and their quantities, respectively.Since the weights of qualitative and quantitative attributes are calculated via different methods, they are not directly comparable. Besides,δδ>0 is a factor that directly affects the conversion of the standard weight set w=w¯z,w¯q. Meanwhile, since the importance of each attribute in actual decision-making processes cannot be too wide, the differences in importance among attributes will generally not exceed 10 times. Therefore, if the decision-maker does not have a clear preference on the importance of attributes, δ values may be selected within 0.1≤δ≤10 (when 0.1≤δ<1, quantitative attributes are more stressed; when 1<δ≤10, then qualitative attributes are more stressed). Following that, calculate the change interval Ri−,Ri+ of the overall pros and cons Ri of scheme Ai, where Ri− and Ri+ represent the minimum and maximum values of Ri across the alternatives, respectively. Compare the change intervals of Ri of all alternatives Aii,j=1,2,…,m in pairs to obtain the possibility degree matrix P=Pijm×mi,j=1,2,…,m that describes the priority relationships across all alternatives and obtain the comprehensive rankings of the alternatives with the ranking method in Section 4.3.The overall steps of the proposed method are as follows:Step 1: calculate the quantitative attribute weight setwz and the qualitative attribute weight set wq according to Section 4.2, and ∑wz=1,∑wq=1.Step 2: set the value interval ofδ as δ∈0.1,10, and take δ=0.1 as the initial weight integration coefficient.Step 3: inputδ, and calculate the standard weight set w=w¯z,w¯q.Step 4: under each criterion attributeCj (when j=1,2,…,nz, it refers to the quantitative attributes; when j=nz+1,nz+2,…,nz+nq, it refers to the qualitative attributes), compare the alternatives in pairs and establish a directed graph or 0-1 matrix for them. For quantitative attributes, the values of the attributes may be compared directly to determine the pros and cons of the alternatives. For qualitative attributes, the pros and cons of the alternatives may be compared following the probabilistic language term set method in Section 2.2. The 0-1 matrices are constructed following the procedure and definitions in Section 4.3.Step 5: based on the prioritized matrixMj obtained in step 4, for alternatives Ai,Aki,k=1,2,…,m, the cumulative weight of all the criterion attributes that satisfy Ai≻Ak is recorded as the overall benefit weight w≻i,k; similarly, the cumulative weight of all the criterion attributes that satisfy Ai≺Ak is recorded as the overall disadvantage weight w≺i,k, and the cumulative weight of all the criterion attributes that satisfy Ai＝Ak is recorded as the overall indifference weight w=i,k.Step 6: construct alternative plans for the indicators for the measurement ofAi,Aki,k=1,2,…,m’s pros and cons degree:(11)Rik=w≻i,k+μw≈i,kw≻i,k+1−μw≈i,k,where0≤μ≤1 indicates the influence degree of the alternatives and the indifference situation on the pros and cons. Larger Rik suggests higher superiority of Ai over Ak.Step 7: calculate the averageRik of the alternatives Ai,Ak and the overall pros and cons Ri of the alternative Ai:(12)Ri=1m∑k=1mRik.Step 8: update the maximum and minimum values inRi−,Ri+ for all alternatives Ai, and let δ=δ+0.01. If δ>10, go to step 9; otherwise, go to step 3.Step 9: compare the intervalRi−,Ri+ of each pair according to formula (13), and obtain the probability piji,j=1,2,…,m of plan Ai being superior over Aj [33, 34]:(13)pij=minLi+Lj,maxRi+−Rj−,0Li+Lj,whereLi=Ri+−Rj−,Lj=Rj+−Rj−.Step 10: build the possible degree matrixP=pijm×n based on the piji,j=1,2,…,m numbers obtained for all alternatives, and rank the alternatives with the ranking method in Section 4.3.


## 5. Case Analysis of the Proposed Method

### 5.1. Case Description

In this study, the qualitative and quantitative parameters of three personsA1, A2, and A3 were comprehensively evaluated with the proposed method, and their pros and cons were ranked. The language term set S=s−3=extreme poor,s−2=very bad,s−1=poor,s0=fair,s1=good,s2=very good,s3=excellent was used to evaluate the persons.C1 results in Table 4 were obtained based on personal health risk assessments following common medical procedures, and the overall personal health risk W was calculated by dividing the health risk values. Under normal circumstances, W is divided into seven levels, described in a set W=W−3=no risk,W−2=very low risk,W−1=low risk,W0=general risk,W1=medium risk,W2=high risk,W3=major risk. C3 and C10 results are based on the highest education levels of the individuals and their immediate family members. According to Regulations of the People’s Republic of China on Academic Degrees, the results can be described by any element in the following set: E=E3=doctorate,E2=master′s degree,E1=undergraduate,E0=university,E−1=senior high school,E−2=junior high school,E−3=primary school. C5 results were obtained based on the average daily network usage. C7 data reflect the local per capita GDP at the individual’s residence, and C9 data were obtained based on the individual’s local area network. With these data, the quantitative index data of the three talents evaluated were obtained (Table 4).Table 4
Quantitative attribute value matrix for comprehensive talent evaluation.
C1C3C5GBC7 (ten thousand/yuan)C9 (Mbps)C10A1W2E11.58.7847.44E−1A2W−2E32.516.4997.66E1A3W0E016.6248.96E−2Table5 shows the qualitative judgment information of 5 experts in terms of the indicators in C2, C4, C6, and C8 aspects on the 3 talents evaluated.Table 5
Language decision matrix provided by decision experts.
C2C4C6C8Expert 1A1S2S0S1S2A2S0S3S2S2A3S3S1S−2S0Expert 2A1S1S−1S0S2A2S−1S2S3S3A3S2S−2S−3S0Expert 3A1S1S1S2S1A2S−2S2S1S2A3S2S1S−2S−1Expert 4A1S3S−1S2S2A2S−1S2S2S3A3S2S1S−1S1Expert 5A1S2S2S−1S2A2S−2S3S3S2A3S2S0S−1S0The information in Table5 was processed to obtain the language terms and their corresponding probability values (Table 6 and 7).Table 6
Linguistic terms and their corresponding probability valuesC2,C4 after summary of expert decision information.
C2C4A1S10.4,S20.4,S30.2S−10.4,S00.2,S10.2,S20.2A2S−20.4,S−10.4,S00.2S20.6,S30.4A3S20.8,S30.2S−20.2,S00.2,S10.6Table 7
Comparison of results from different decision-making methods.
Decision methodDecision indexAlternative ranking resultsOptimal alternative[35]C1,C3,C5,C7,C9,C10A1≻A2≻A3A3[19]C2,C4,C6,C8A2≻A1≻A3A2[20]C1,C2,C3,C4,C5,C6,C7,C8,C9,C10A2≻A1≻A3A2Paper methodC1,C2,C3,C4,C5,C6,C7,C8,C9,C10A2≻1A1≻1A3A2The analysis of the cases above followed the methods discussed in this paper, and the specific process is described as follows:Step 1: calculate the weight sets of quantitative indicatorsC1,C3,C5,C7,C9,C10 by the entropy weights wz=0.1502,0.1598,0.1717,0.2157,0.1428 according to formulas (8) and (9). Similarly, calculate the weight sets of qualitative indicators C2,C4,C6,C8 by the entropy weights wq=0.2609,0.2443,0.2939,0.2008.Steps 2 to 8: set the parameterμ=0.6 and the value interval of the weight integration coefficient δ=0.1,10. Subsequently, update the values of δ with a step width of 0.01, and calculate the changes in the pros and cons of the qualitative and quantitative evaluation of talents Rii=1,2,3 as described in Figure 3.In order to visually display the distribution ofRii=1,2,3 as δ changes, a box plot is depicted (Figure 4).Ri−,Ri+ of the qualitative and quantitative evaluation and talent rankings are obtained as follows for the three evaluated personnel:(14)R−,R+=1.5809,1.7874;R−,R+=2.4639,3.4846;R−,R+=0.6575,0.7268.Steps 9 to 10: compare the overallRii=1,2,3 for all the talents in pairs, and obtain the probability matrix P that describes the priority relationship of talent ranking with formula (13):(15)P=0.50110.51000.5.According to formula (10), the ranking vector V of P was calculated to be(16)V=0.3333,0.5000,0.1667T.Judging from the elements inV, the final qualitative and qualitative comprehensive evaluation result for the three talents was A2≻A1≻A3. Additionally, with the possibility degree matrix P, a comprehensive ranking including the possibility degree of the optimal order relationship revealed that all probabilities of superiority were 1, and the evaluation result remained A2≻1A1≻1A3.Figure 3
The changes of the weight integration coefficientδ and the overall pros and cons of each person’s ranking.Figure 4
The distribution box plot of the overall pros and cons of talent ranking.


### 5.2. Method Comparison

In this section, the method proposed in this paper was compared with those that use either qualitative or quantitative indicators alone for talent evaluation with a comprehensive entropy-based evaluation strategy [33], and the quantitative indicators in Section 5.1 were used as the samples. More specifically, the maximum deviation-based decision method described in literature [19] was used to sort out the alternatives in the qualitative indicators of the 5.1 case, and a previously reported method [20] and the method proposed in this paper were used to sort the evaluation objects through all the quantitative and qualitative indicators. The comparative analysis of talent rankings is described in Table 7.From Table7, it could be concluded that the decision-making results from quantitative indicators alone are quite different from those from other methods. More precisely, the decision-making results from quantitative indicators are more sensitive to the influence of simple data and information. On the other hand, the comprehensive talent evaluation is a complex process, which asks for comprehensive consideration of the internal and external factors in talent growth, but the decision-making results from quantitative data alone are more one-sided, making them inaccurate. For decision-making using qualitative indicators alone, the produced results obtained via the maximum deviation method are identical to those obtained via averaging the qualitative and quantitative integrated weights, suggesting that experts can use their own experience and knowledge comprehensively during complex problem decision-making to produce more comprehensive judgments.Even so, the decision-making method in this paper can not only get the rankings of alternatives without predefining qualitative and quantitative weight integration coefficients but also obtain the possibility of the priority relationship between two alternatives, which is an intuitive reflection of the relationship between the alternatives. Meanwhile, since the comprehensive talent evaluation method proposed in this paper considers the comprehensive influence of quantitative and qualitative attributes on the talent evaluation results, the evaluation process is more reasonable and applicable to heterogeneous index data.


## 5.1. Case Description

In this study, the qualitative and quantitative parameters of three personsA1, A2, and A3 were comprehensively evaluated with the proposed method, and their pros and cons were ranked. The language term set S=s−3=extreme poor,s−2=very bad,s−1=poor,s0=fair,s1=good,s2=very good,s3=excellent was used to evaluate the persons.C1 results in Table 4 were obtained based on personal health risk assessments following common medical procedures, and the overall personal health risk W was calculated by dividing the health risk values. Under normal circumstances, W is divided into seven levels, described in a set W=W−3=no risk,W−2=very low risk,W−1=low risk,W0=general risk,W1=medium risk,W2=high risk,W3=major risk. C3 and C10 results are based on the highest education levels of the individuals and their immediate family members. According to Regulations of the People’s Republic of China on Academic Degrees, the results can be described by any element in the following set: E=E3=doctorate,E2=master′s degree,E1=undergraduate,E0=university,E−1=senior high school,E−2=junior high school,E−3=primary school. C5 results were obtained based on the average daily network usage. C7 data reflect the local per capita GDP at the individual’s residence, and C9 data were obtained based on the individual’s local area network. With these data, the quantitative index data of the three talents evaluated were obtained (Table 4).Table 4
Quantitative attribute value matrix for comprehensive talent evaluation.
C1C3C5GBC7 (ten thousand/yuan)C9 (Mbps)C10A1W2E11.58.7847.44E−1A2W−2E32.516.4997.66E1A3W0E016.6248.96E−2Table5 shows the qualitative judgment information of 5 experts in terms of the indicators in C2, C4, C6, and C8 aspects on the 3 talents evaluated.Table 5
Language decision matrix provided by decision experts.
C2C4C6C8Expert 1A1S2S0S1S2A2S0S3S2S2A3S3S1S−2S0Expert 2A1S1S−1S0S2A2S−1S2S3S3A3S2S−2S−3S0Expert 3A1S1S1S2S1A2S−2S2S1S2A3S2S1S−2S−1Expert 4A1S3S−1S2S2A2S−1S2S2S3A3S2S1S−1S1Expert 5A1S2S2S−1S2A2S−2S3S3S2A3S2S0S−1S0The information in Table5 was processed to obtain the language terms and their corresponding probability values (Table 6 and 7).Table 6
Linguistic terms and their corresponding probability valuesC2,C4 after summary of expert decision information.
C2C4A1S10.4,S20.4,S30.2S−10.4,S00.2,S10.2,S20.2A2S−20.4,S−10.4,S00.2S20.6,S30.4A3S20.8,S30.2S−20.2,S00.2,S10.6Table 7
Comparison of results from different decision-making methods.
Decision methodDecision indexAlternative ranking resultsOptimal alternative[35]C1,C3,C5,C7,C9,C10A1≻A2≻A3A3[19]C2,C4,C6,C8A2≻A1≻A3A2[20]C1,C2,C3,C4,C5,C6,C7,C8,C9,C10A2≻A1≻A3A2Paper methodC1,C2,C3,C4,C5,C6,C7,C8,C9,C10A2≻1A1≻1A3A2The analysis of the cases above followed the methods discussed in this paper, and the specific process is described as follows:Step 1: calculate the weight sets of quantitative indicatorsC1,C3,C5,C7,C9,C10 by the entropy weights wz=0.1502,0.1598,0.1717,0.2157,0.1428 according to formulas (8) and (9). Similarly, calculate the weight sets of qualitative indicators C2,C4,C6,C8 by the entropy weights wq=0.2609,0.2443,0.2939,0.2008.Steps 2 to 8: set the parameterμ=0.6 and the value interval of the weight integration coefficient δ=0.1,10. Subsequently, update the values of δ with a step width of 0.01, and calculate the changes in the pros and cons of the qualitative and quantitative evaluation of talents Rii=1,2,3 as described in Figure 3.In order to visually display the distribution ofRii=1,2,3 as δ changes, a box plot is depicted (Figure 4).Ri−,Ri+ of the qualitative and quantitative evaluation and talent rankings are obtained as follows for the three evaluated personnel:(14)R−,R+=1.5809,1.7874;R−,R+=2.4639,3.4846;R−,R+=0.6575,0.7268.Steps 9 to 10: compare the overallRii=1,2,3 for all the talents in pairs, and obtain the probability matrix P that describes the priority relationship of talent ranking with formula (13):(15)P=0.50110.51000.5.According to formula (10), the ranking vector V of P was calculated to be(16)V=0.3333,0.5000,0.1667T.Judging from the elements inV, the final qualitative and qualitative comprehensive evaluation result for the three talents was A2≻A1≻A3. Additionally, with the possibility degree matrix P, a comprehensive ranking including the possibility degree of the optimal order relationship revealed that all probabilities of superiority were 1, and the evaluation result remained A2≻1A1≻1A3.Figure 3
The changes of the weight integration coefficientδ and the overall pros and cons of each person’s ranking.Figure 4
The distribution box plot of the overall pros and cons of talent ranking.


## 5.2. Method Comparison

In this section, the method proposed in this paper was compared with those that use either qualitative or quantitative indicators alone for talent evaluation with a comprehensive entropy-based evaluation strategy [33], and the quantitative indicators in Section 5.1 were used as the samples. More specifically, the maximum deviation-based decision method described in literature [19] was used to sort out the alternatives in the qualitative indicators of the 5.1 case, and a previously reported method [20] and the method proposed in this paper were used to sort the evaluation objects through all the quantitative and qualitative indicators. The comparative analysis of talent rankings is described in Table 7.From Table7, it could be concluded that the decision-making results from quantitative indicators alone are quite different from those from other methods. More precisely, the decision-making results from quantitative indicators are more sensitive to the influence of simple data and information. On the other hand, the comprehensive talent evaluation is a complex process, which asks for comprehensive consideration of the internal and external factors in talent growth, but the decision-making results from quantitative data alone are more one-sided, making them inaccurate. For decision-making using qualitative indicators alone, the produced results obtained via the maximum deviation method are identical to those obtained via averaging the qualitative and quantitative integrated weights, suggesting that experts can use their own experience and knowledge comprehensively during complex problem decision-making to produce more comprehensive judgments.Even so, the decision-making method in this paper can not only get the rankings of alternatives without predefining qualitative and quantitative weight integration coefficients but also obtain the possibility of the priority relationship between two alternatives, which is an intuitive reflection of the relationship between the alternatives. Meanwhile, since the comprehensive talent evaluation method proposed in this paper considers the comprehensive influence of quantitative and qualitative attributes on the talent evaluation results, the evaluation process is more reasonable and applicable to heterogeneous index data.


## 6. Conclusion

A comprehensive qualitative and quantitative talent evaluation index system is proposed in this paper for talent evaluation in complex environments. The proposed system is based on the “human-machine-environment” system engineering theory, the probabilistic language entropy, and priority relationships. There are three main research conclusions:(1)
The coupling relationships between human and machine, human and environment, and environment and machine were analyzed to establish a talent evaluation index system that integrates MMESE qualitative and quantitative factors. The system not only reflects the use of machines in the information age to promote talent growth but also reflects the impact of the external environment on talents. The proposed system is more favorable than previously available talent evaluation index systems because it considers both qualitative and quantitative aspects instead of just one.(2)
Theories related to probabilistic language terminology were applied to qualitative indicators of talents as assessed by experts. These theories can reflect the vagueness and uncertainty of experts’ knowledge-based empirical judgments more accurately so that more accurate expert evaluation results could be obtained.(3)
The entropy theory was used to calculate the attribute weights of qualitative criteria, and by integrating the theory with the possibility matrix of the priority relationships, a comprehensive integrated decision-making method that involves both qualitative and quantitative factors in talent evaluation is proposed to consider statistical data indicators and expert knowledge for more promising and accurate talent evaluation. The talent evaluation results obtained from the method are more consistent with the real-world situation. The validity of the decision-making method in this paper is verified with the examples and the comparative analysis of the available methods.In a word, the MMESE talent evaluation index system and comprehensive evaluation method proposed in this paper can provide scientific and accurate solutions for talent evaluation and selection. This method can be extended to policy evaluation, program selection, and consultation decision-making, all of which involve complex environments.



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*Source: 8903427-2021-12-21.xml*