# A Performance Analysis Model for Corporate Human Resource Management Based on Extenics Theory

Authors: Mingyan Li; Tiantian Gao; Jianxue Wang; Huanyu Wang
Journal: Discrete Dynamics in Nature and Society
 (2022)

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## Abstract

There are several problems with the performance analysis of corporate human resource management (HRM), namely, the incomplete index system and the difficulty in decision-making under multiple fuzzy factors. To solve these problems, this paper improves the method for corporate HRM performance analysis (HRMPA). First, a novel corporate HRMPA index system was established under the principle of comprehensiveness. Next, the fuzzy closeness of corporate HRMPA was calculated based on fuzzy theory, and the extenics correlation coefficient of corporate HRMPA was computed with the aid of the extenics theory. Then, fuzzy extenics factors were introduced to create an integrated corporate HRMPA model. The proposed model was proved valid and feasible through case analysis. The research results shed new light on the theories of HRMPA and enjoy great applicable value in engineering.


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## Body

## 1. Introduction

Alongside with physical and financial resources, human resource plays a critical role in corporate operation and development [1–3]. In the pursuit of sustainable development, it is increasingly important to manage these human factors that constrain corporate development. As a result, corporate human resource management (HRM) has attracted much attention from entrepreneurs and researchers. By analyzing the performance of corporate HRM, it is possible to identify and resolve the problems and weaknesses in corporate development, making the enterprise more competitive [4–7].So far, many scholars have explored corporate HRM and analyzed the HRM performance, producing constructive results. For example, Tooranloo et al. [8] integrated fuzzy analytic hierarchy process (FAHP) with type-2 fuzzy decision-making trail and evaluation laboratory (DEMATEL) to examine the successful factors of sustainable HRM. Renkema et al. [9] discussed the application of multilevel thinking in HRM research. Gao [10] establishes a matter-element model to evaluate the effectiveness of inclusive HRM. Zeng [11] expounded on how to manage enterprise human resource performance in the era of big data. Shao and Guo [12] evaluated the human resource of grid enterprises, using the fuzzy technique for order of preference by similarity to ideal solution (TOPSIS). Azadeh and Zarrin [13] developed a novel intelligent framework that evaluates and analyzes human resource productivity from the angles of flexible engineering, incentives, ergonomics, as well as health, safety, and environment (HSE). Čech et al. [14] deliberated on the HRM situation of manufacturing enterprises in China. Sun [15] evaluated the strategic level of corporate HRM by analytic hierarchy analysis (AHP) and gray correlation analysis (GCA). Through data envelopment analysis (DEA), Yang [16] assessed the corporate HRM efficiency in a comprehensive manner. Li et al. [17] evaluated the performance of corporate HRM based on the balanced scorecard (BSC)-matter-element model.However, it should be noted that corporate HRM is a systematic project. Besides the influence of corporate human factors, corporate HRM must focus on the correlation of corporate human resource with internal and external factors of corporate development and try to disclose the implicit effects of these factors on corporate HRM. Otherwise, it is impossible to reasonably evaluate corporate HRM performance, not to mention supporting the rapid and healthy corporate development.Therefore, this paper fully integrates extenics theory [18, 19], fuzzy system theory [20, 21], and AHP to create a new index system for corporate HRM performance analysis (HRMPA) and develop an improved model for corporate HRMPA.The remainder of this paper is organized as follows: Section2 introduces the relevant concepts and their definitions; Section 3 sets up the new index system for corporate HRMPA; Sections 4 and 5 discuss the fuzzy analysis and extenics analysis of corporate HRM performance, respectively; Section 6 proposes the improved model for corporate HRMPA; Section 7 verifies the proposed model through case analysis; Section 8 puts forward the conclusions.


## 2. Basic Concepts and Definitions

Relying on formal and intelligent models, extenics, as a transdisciplinary science, studies the possibility of expanding design objects and the rules and methods to expand and innovate things and, on this basis, presents solutions to contradictions.The key theoretical supports of extenics are matter element and extension set. Their application prospects are wide in engineering. First, the design object is formally modeled as a matter-element model. After obtaining the name and feature of the matter-element model, as well as the eigenvalue corresponding to the feature, an orderly tripe is obtained for performance analysis. Second, the extensible distance and extenics correlation function in the extension set theory can quantify the transformation of the object from quantitative change to qualitative change, making the performance analysis more realistic.Definition 1.
HRMPA matter element.
During the HRMPA, each object of performance analysis can be described as an ordered tripleR = (N, C, V), where N, C, and V are the name of matter element, the feature of matter element, and the value of the feature, respectively. If HRMPA matter-element R has n features, then its matter-element model can be expressed as follows:(1)R=N,C,V=Nc1v1⋮⋮civi⋮⋮cnvn.
The dimensionality of variable N equals the number of features ofR and depends on the object being described. R is the name of the matter element. The value of R is determined by the number N of features of the matter element.Definition 2.
HRMPA classic domain matter element.
Letm be the number of levels for HRMPA results. Suppose the value of feature ci of the i-th matter element at level j is vij=viaj,vibjviaj≤vibj. Then, the HRMPA classic domain matter-element Rj corresponding to the i-th matter element at level j can be expressed as follows:(2)Rj=Nj,C,V=Njc1v1aj,v1bj⋮⋮civiaj,vibj⋮⋮cnvnaj,vnbj.Definition 3.
HRMPA nodal domain matter element.
The HRMPA nodal domain matter elementRo that corresponds to Rj can be defined as follows:(3)RΟ=NΟ,C,V=NΟc1v1aΟ,v1bΟ⋮⋮civiaΟ,vibΟ⋮⋮cnvnaΟ,vnbΟ.where(4)viaΟ=min1≤j≤mviaj,vibΟ=max1≤j≤mvibj.Definition 4.
HRMPA extension distance.
During the HRMPA, if the matter-element model of objectP of performance analysis is RP, and the value of feature ci of the i-th matter element is viP, then the extension distance between the model and HRMPA classic domain matter element Rj on matter-element feature ci can be defined as follows:(5)ρij=viP−viaj+vibj2−vibj−viaj2.
The extension distance between the model and HRMPA nodal domain matter-elementRo on matter-element feature ci can be defined as follows:(6)ρiΟ=viP−viaΟ+vibΟ2−vibΟ−viaΟ2.


## 3. HRMPA Index System

### 3.1. Principles of Index Selection

To make HRMPA results scientific, rational, and reliable, the HRMPA indices were selected based on the following principles:(1)
Scientific principle: the HRMPA indices should have clear scientific meanings and reasonably reflect the essential problems of HRMPA(2)
Systematic principle: the HRMPA indices should be strictly logical, and systematically demonstrate the internal logic and external relevance of HRMPA(3)
Integrity principle: the HRMPA indices should thoroughly and holistically manifest how HRMPA is affected by various factors in different aspects(4)
Objective principle: the HRMPA indices should objectively and truthfully reveal the actual situation of the enterprise, such that the corporate development and management could be analyzed without being disturbed by subjective views or personal preferences(5)
Transformable principle: the HRMPA indices should be quantifiable, or the index values should be transformable, such that the indices could be processed effectively to estimate the corporate HRM level in an accurate manner(6)
Hierarchical principle: the HRMPA indices should form a reasonable hierarchy with clear layers, such that corporate HRMPA, which is complicated by various constraints and influencing factors, could be evaluated clearlyThe basis for hierarchical evaluation is setting up a clear, hierarchical evaluation index system based on the correlations between superior and subordinate indices. The hierarchy of these two types of indices facilitates the breakdown of evaluation indices and the analysis and processing of evaluation values.


### 3.2. Hierarchical Structure of the Index System

Corporate human resource, as an important part of corporate resources, directly drives the corporate development. Corporate HRM is a complex and systematic project. During the implementation, corporate HRM is often constrained and affected by various factors. In corporate HRMPA, these factors must be analyzed systematically and used to formulate the evaluation standard for corporate HRMPA. The standard provides the criteria and guidance for the selection of corporate HRMPA indices. These factors specifically refer to the impactors of corporate human resource management, including the internal factors and external factors of corporate development, and their correlations with corporate human resources. The specific contents are reflected in our evaluation index system for HRMPA.Considering the effects of corporate human resource on corporate development, corporate HRM is directly affected by organizational structure and system, culture and development environment, market development condition, talent training and management, development planning, and corporate intellectual property rights. The direct effects of these factors will eventually be reflected in corporate benefit.Specifically, the organizational structure and system guarantees corporate HRM. A good organizational structure and system makes corporate HRM more productive. Culture and development environment refers to the corporate culture and internal/external conditions of corporate development. It is a strong internal driver of corporate HRM. Market development condition reflects the effect of growing market competitiveness on corporate HRM, which is a strong external driver of corporate HRM. Talent training and management, development planning, and intellectual property protection influence the process of corporate HRM, especially the implementing steps. These three factors are important supports to corporate HRM. Corporate benefit, as the result of corporate HRM, directly mirrors corporate HRM performance and provides important guidance for implementing corporate HRM.Through the above analysis, several criteria were established for corporate HRMPA, namely, organizational structure and system (Z1), culture and development environment (Z2), market development condition (Z3), development planning (Z4), talent training and management (Z5), corporate benefit (Z6), and intellectual property protection (Z7). The weights of different standards are mainly determined by consulting experts in the relevant fields and then analyzed through AHP, a popular tool for index weighting. If feature ci is positive, then the eigenvalue of the k-th HRMPA object on that feature is the RMPA index under that criterion. In other words, the corporate HRMPA index system was designed under the hierarchical structure in Figure 1.Figure 1
Hierarchical structure of the corporate HRMPA index system.


### 3.3. Establishment of the Index System

Under the principles of index selection and HRMPA criteria, the indices were selected under each criterion.The criterion organizational structure and system (Z1) mainly demonstrates how much corporate HRM performance is affected by the key functional departments and positions and corporate rules and regulations, as well as the rationality of these influencing factors. The following indices were selected under this criterion: division of functional departments (C11), setting of functional positions (C12), staffing (C13), personnel system (C14), performance management system (C15), and talent incentive and development system (C16).The criterion culture and development environment (Z2) mainly demonstrates whether corporate HRM is promoted by the corporate culture and internal/external conditions of corporate development. The following indices were selected under this criterion: corporate values (C21), cultural brand and image (C22), employee satisfaction (C23), internal development environment (C24), and external development environment (C25).The criterion market development condition (Z3) mainly demonstrates whether the market development condition could effectively support product development and whether the HRM could promote corporate market competitiveness. The following indices were selected under this criterion: marketing strategy planning (C31), market share of brand product (C32), brand development ability (C33), and consumer satisfaction (C34).The criterion development planning (Z4) mainly demonstrates whether development goals and strategies are sustainable. The following indices were selected under this criterion: management and leadership (C41), human resource planning (C42), innovation (C43), goal setting and implementation (C44), and operation, management, and planning (C45).The criterion talent training and management (Z5) mainly demonstrates how much corporate HRM values talents, especially the backbone talents. The following indices were selected under this criterion: professional brain drain (C51), talent team building (C52), recruitment and talent introduction (C53), employee training and development (C54), compensation incentives and performance management (C55), and working enthusiasm (C56).The criterion corporate benefit (Z6) mainly demonstrates how much corporate HRM benefits corporate development. The following indices were selected under this criterion: average market growth rate (C61), social service satisfaction (C62), average profit growth rate (C63), average revenue growth rate (C64), brand product development efficiency (C65), product development and listing cycle (C66), and research and development capacity (C67).The criterion intellectual property protection (Z7) mainly demonstrates the knowledge reserve and research ability during corporate HRM. The following indices were selected under this criterion: number of research projects as a proportion of the industrial total (C71), number of technical patents as a proportion of the industrial total (C72), number of academic papers and books as a proportion of the industrial total (C73), formulation of industrial norms and standards (C74), and transformation of research results (C75).On this basis, the corporate HRMPA index system was constructed as shown in Figure2.Figure 2
Corporate HRMPA index system.


## 3.1. Principles of Index Selection

To make HRMPA results scientific, rational, and reliable, the HRMPA indices were selected based on the following principles:(1)
Scientific principle: the HRMPA indices should have clear scientific meanings and reasonably reflect the essential problems of HRMPA(2)
Systematic principle: the HRMPA indices should be strictly logical, and systematically demonstrate the internal logic and external relevance of HRMPA(3)
Integrity principle: the HRMPA indices should thoroughly and holistically manifest how HRMPA is affected by various factors in different aspects(4)
Objective principle: the HRMPA indices should objectively and truthfully reveal the actual situation of the enterprise, such that the corporate development and management could be analyzed without being disturbed by subjective views or personal preferences(5)
Transformable principle: the HRMPA indices should be quantifiable, or the index values should be transformable, such that the indices could be processed effectively to estimate the corporate HRM level in an accurate manner(6)
Hierarchical principle: the HRMPA indices should form a reasonable hierarchy with clear layers, such that corporate HRMPA, which is complicated by various constraints and influencing factors, could be evaluated clearlyThe basis for hierarchical evaluation is setting up a clear, hierarchical evaluation index system based on the correlations between superior and subordinate indices. The hierarchy of these two types of indices facilitates the breakdown of evaluation indices and the analysis and processing of evaluation values.


## 3.2. Hierarchical Structure of the Index System

Corporate human resource, as an important part of corporate resources, directly drives the corporate development. Corporate HRM is a complex and systematic project. During the implementation, corporate HRM is often constrained and affected by various factors. In corporate HRMPA, these factors must be analyzed systematically and used to formulate the evaluation standard for corporate HRMPA. The standard provides the criteria and guidance for the selection of corporate HRMPA indices. These factors specifically refer to the impactors of corporate human resource management, including the internal factors and external factors of corporate development, and their correlations with corporate human resources. The specific contents are reflected in our evaluation index system for HRMPA.Considering the effects of corporate human resource on corporate development, corporate HRM is directly affected by organizational structure and system, culture and development environment, market development condition, talent training and management, development planning, and corporate intellectual property rights. The direct effects of these factors will eventually be reflected in corporate benefit.Specifically, the organizational structure and system guarantees corporate HRM. A good organizational structure and system makes corporate HRM more productive. Culture and development environment refers to the corporate culture and internal/external conditions of corporate development. It is a strong internal driver of corporate HRM. Market development condition reflects the effect of growing market competitiveness on corporate HRM, which is a strong external driver of corporate HRM. Talent training and management, development planning, and intellectual property protection influence the process of corporate HRM, especially the implementing steps. These three factors are important supports to corporate HRM. Corporate benefit, as the result of corporate HRM, directly mirrors corporate HRM performance and provides important guidance for implementing corporate HRM.Through the above analysis, several criteria were established for corporate HRMPA, namely, organizational structure and system (Z1), culture and development environment (Z2), market development condition (Z3), development planning (Z4), talent training and management (Z5), corporate benefit (Z6), and intellectual property protection (Z7). The weights of different standards are mainly determined by consulting experts in the relevant fields and then analyzed through AHP, a popular tool for index weighting. If feature ci is positive, then the eigenvalue of the k-th HRMPA object on that feature is the RMPA index under that criterion. In other words, the corporate HRMPA index system was designed under the hierarchical structure in Figure 1.Figure 1
Hierarchical structure of the corporate HRMPA index system.


## 3.3. Establishment of the Index System

Under the principles of index selection and HRMPA criteria, the indices were selected under each criterion.The criterion organizational structure and system (Z1) mainly demonstrates how much corporate HRM performance is affected by the key functional departments and positions and corporate rules and regulations, as well as the rationality of these influencing factors. The following indices were selected under this criterion: division of functional departments (C11), setting of functional positions (C12), staffing (C13), personnel system (C14), performance management system (C15), and talent incentive and development system (C16).The criterion culture and development environment (Z2) mainly demonstrates whether corporate HRM is promoted by the corporate culture and internal/external conditions of corporate development. The following indices were selected under this criterion: corporate values (C21), cultural brand and image (C22), employee satisfaction (C23), internal development environment (C24), and external development environment (C25).The criterion market development condition (Z3) mainly demonstrates whether the market development condition could effectively support product development and whether the HRM could promote corporate market competitiveness. The following indices were selected under this criterion: marketing strategy planning (C31), market share of brand product (C32), brand development ability (C33), and consumer satisfaction (C34).The criterion development planning (Z4) mainly demonstrates whether development goals and strategies are sustainable. The following indices were selected under this criterion: management and leadership (C41), human resource planning (C42), innovation (C43), goal setting and implementation (C44), and operation, management, and planning (C45).The criterion talent training and management (Z5) mainly demonstrates how much corporate HRM values talents, especially the backbone talents. The following indices were selected under this criterion: professional brain drain (C51), talent team building (C52), recruitment and talent introduction (C53), employee training and development (C54), compensation incentives and performance management (C55), and working enthusiasm (C56).The criterion corporate benefit (Z6) mainly demonstrates how much corporate HRM benefits corporate development. The following indices were selected under this criterion: average market growth rate (C61), social service satisfaction (C62), average profit growth rate (C63), average revenue growth rate (C64), brand product development efficiency (C65), product development and listing cycle (C66), and research and development capacity (C67).The criterion intellectual property protection (Z7) mainly demonstrates the knowledge reserve and research ability during corporate HRM. The following indices were selected under this criterion: number of research projects as a proportion of the industrial total (C71), number of technical patents as a proportion of the industrial total (C72), number of academic papers and books as a proportion of the industrial total (C73), formulation of industrial norms and standards (C74), and transformation of research results (C75).On this basis, the corporate HRMPA index system was constructed as shown in Figure2.Figure 2
Corporate HRMPA index system.


## 4. Fuzzy Corporate HRMPA

### 4.1. Normalization of HRMPA Indices

Based on the corporate HRMPA index system, the HRMPA matter elements were constructed under each criterion. The obtained HRMPA matter elements have various kinds of features. Some features are described qualitatively by language, and some are quantified as numbers. Moreover, different kinds of matter-element feature usually differ in dimensions. To unify the evaluation standard for corporate HRMPA, the matter-element features were normalized as follows.If a feature is qualified by language, then it was assigned a value by the fuzzy membership function or against the 0–1 scale. If a feature is quantified by a number, then it was processed in two different cases.If the featureci is a positive feature, then the eigenvalue of the k-th HRMPA object on that feature is vikP=vikLP,vikRP, vikLP≤vikRP. Then, the feature can be normalized as follows:(7)uikP=uikLP,uikRP,uikLP=vikLP−viaΟvibΟ−viaΟ,uikRP=vikRP−viaΟvibΟ−viaΟ.vikLP and vikRP are the values of object k relative to the left and right sides of the initial interval of matter-element feature ci, respectively; viaΟ and vibΟ are the minimum and maximum values of all objects relative to the left and right sides of the interval of matter-element feature ci, respectively; uikLP and uikRP be the values of object k relative to the left and right sides of the normalized interval of matter-element feature ci, respectively.If the featureci is a reverse feature, then the eigenvalue of the k-th HRMPA object on that feature is vikP=vikLP,vikRP, vikLP≤vikRP. Then, the feature can be normalized as follows:(8)uikP=uikLP,uikRP,uikLP=vibΟ−vikRPvibΟ−viaΟ,uikRP=vibΟ−vikLPvibΟ−viaΟ.


### 4.2. Calculation Model of Fuzzy Closeness

Through normalization, all HRMPA matter-element features can be evaluated by a unified standard. Considering the fuzziness of HRMPA matter-element features, the fuzzy distance between thek-th HRMPA matter-element Rk(P) and HRMPA classic domain matter-element Rj on matter-element feature ci can be constructed as [22–24] follows:(9)dijkP=uiaj−uikLPq+uibj−uikRPq2q,where uij=uiaj,uibj is the normalized eigenvalue of matter-element feature ci of HRMPA classic domain matter-element Rj (uiaj≤uibj).Ifq = 1, then dijkP is the Hamming distance between HRMPA matter-element Rk(P) and HRMPA classic domain matter-element Rj on matter-element feature ci; If q = 2, then dijkP is the Euclidean distance between HRMPA matter-element Rk(P) and HRMPA classic domain matter-element Rj on matter-element feature ci.Similarly, the fuzzy distance between thek-th HRMPA matter-element Rk(P) and HRMPA nodal domain matter-element Ro on matter-element feature ci can be constructed as follows:(10)diΟkP=uiaΟ−uikLPq+uibΟ−uikRPq2q,where uiΟ=uiaΟ,uibΟ is the normalized eigenvalue of matter-element feature ci of HRMPA nodal domain matter-element Ro (uiaΟ≤uibΟ).Thus, the fuzzy closenessκijkP between the k-th HRMPA matter-element Rk(P) and HRMPA classic domain matter-element Rj and that κiΟkP between the k-th HRMPA matter-element Rk(P) and HRMPA nodal domain matter-element Ro on matter-element feature ci can be, respectively, expressed as follows:(11)κijkP=1−dijkP,κiΟkP=1−diΟkP.


## 4.1. Normalization of HRMPA Indices

Based on the corporate HRMPA index system, the HRMPA matter elements were constructed under each criterion. The obtained HRMPA matter elements have various kinds of features. Some features are described qualitatively by language, and some are quantified as numbers. Moreover, different kinds of matter-element feature usually differ in dimensions. To unify the evaluation standard for corporate HRMPA, the matter-element features were normalized as follows.If a feature is qualified by language, then it was assigned a value by the fuzzy membership function or against the 0–1 scale. If a feature is quantified by a number, then it was processed in two different cases.If the featureci is a positive feature, then the eigenvalue of the k-th HRMPA object on that feature is vikP=vikLP,vikRP, vikLP≤vikRP. Then, the feature can be normalized as follows:(7)uikP=uikLP,uikRP,uikLP=vikLP−viaΟvibΟ−viaΟ,uikRP=vikRP−viaΟvibΟ−viaΟ.vikLP and vikRP are the values of object k relative to the left and right sides of the initial interval of matter-element feature ci, respectively; viaΟ and vibΟ are the minimum and maximum values of all objects relative to the left and right sides of the interval of matter-element feature ci, respectively; uikLP and uikRP be the values of object k relative to the left and right sides of the normalized interval of matter-element feature ci, respectively.If the featureci is a reverse feature, then the eigenvalue of the k-th HRMPA object on that feature is vikP=vikLP,vikRP, vikLP≤vikRP. Then, the feature can be normalized as follows:(8)uikP=uikLP,uikRP,uikLP=vibΟ−vikRPvibΟ−viaΟ,uikRP=vibΟ−vikLPvibΟ−viaΟ.


## 4.2. Calculation Model of Fuzzy Closeness

Through normalization, all HRMPA matter-element features can be evaluated by a unified standard. Considering the fuzziness of HRMPA matter-element features, the fuzzy distance between thek-th HRMPA matter-element Rk(P) and HRMPA classic domain matter-element Rj on matter-element feature ci can be constructed as [22–24] follows:(9)dijkP=uiaj−uikLPq+uibj−uikRPq2q,where uij=uiaj,uibj is the normalized eigenvalue of matter-element feature ci of HRMPA classic domain matter-element Rj (uiaj≤uibj).Ifq = 1, then dijkP is the Hamming distance between HRMPA matter-element Rk(P) and HRMPA classic domain matter-element Rj on matter-element feature ci; If q = 2, then dijkP is the Euclidean distance between HRMPA matter-element Rk(P) and HRMPA classic domain matter-element Rj on matter-element feature ci.Similarly, the fuzzy distance between thek-th HRMPA matter-element Rk(P) and HRMPA nodal domain matter-element Ro on matter-element feature ci can be constructed as follows:(10)diΟkP=uiaΟ−uikLPq+uibΟ−uikRPq2q,where uiΟ=uiaΟ,uibΟ is the normalized eigenvalue of matter-element feature ci of HRMPA nodal domain matter-element Ro (uiaΟ≤uibΟ).Thus, the fuzzy closenessκijkP between the k-th HRMPA matter-element Rk(P) and HRMPA classic domain matter-element Rj and that κiΟkP between the k-th HRMPA matter-element Rk(P) and HRMPA nodal domain matter-element Ro on matter-element feature ci can be, respectively, expressed as follows:(11)κijkP=1−dijkP,κiΟkP=1−diΟkP.


## 5. Extenics Corporate HRMPA

After obtaining the eigenvalues of HRMPA matter-elementRk(P) on all matter-element features, the extenics corporate HRMPA was carried out based on extenics theory. According to Definition 4, if the eigenvalue uik(P) of HRMPA matter-element Rk(P) on matter-element feature ci is an exact value, then the extension distance between HRMPA matter-element Rk(P) and HRMPA classic domain matter-element Rj on matter-element feature ci can be expressed as follows [25, 26]:(12)ρijkP=uikP−uiaj+uibj/2−uibj−uiaj2.If the eigenvalueuik(P) of HRMPA matter-element Rk(P) on matter-element feature ci is a fuzzy value, that is, uikP=uikLP,uikRP, uikLP≤uikRP, then the extension distance between HRMPA matter-element Rk(P) and HRMPA classic domain matter-element Rj on matter-element feature ci can be expressed as follows:(13)ρijkP=uikRP−uiaj+uibj/2+uikLP−uiaj+uibj/2−uibj−uiaj2.Similarly, if the eigenvalueuik(P) of HRMPA matter-element Rk(P) on matter-element feature ci is an exact value, then the extension distance between HRMPA matter-element Rk(P) and HRMPA nodal domain matter-element Ro on matter-element feature ci can be expressed as follows:(14)ρiΟkP=uikP−uiaΟ+uibΟ2−uibΟ−uiaΟ2.If the eigenvalueuik(P) of HRMPA matter-element Rk(P) on matter-element feature ci is a fuzzy value, that is, uikP=uikLP,uikRP, uikLP≤uikRP, then the extension distance between HRMPA matter-element Rk(P) and HRMPA nodal domain matter-element Ro on matter-element feature ci can be expressed as follows:(15)ρiΟkP=uikRP−uiaΟ+uibΟ/2+uikLP−uiaΟ+uibΟ/2−uibΟ−uiaΟ2.Therefore, the extenics correlation coefficient between HRMPA matter-elementRk(P) and HRMPA nodal domain matter-element Ro on matter-element feature ci can be expressed as follows:(16)KijkP=−ρijkPuibj−uiajuikP∈uij,ρijkPρiΟkP−ρijkPuikP∉uij.


## 6. Implementation of the HRMPA Model

### 6.1. AHP-Based Weighting of Matter-Element Features

The AHP is a simple, flexible, and practical method for multicriteria decision-making, offering a desirable tool to reliably quantify qualitative problems. Through the AHP, the weights of matter elements can be determined quickly and accurately [27–30].Several experts were invited to make pairwise comparisons of HRMPA matter-element features and rate the relative importance of each feature to the other in the pair against a 9-point scale. Letaij be the importance of matter-element feature ci relative to cj, and aij = 1/aji be the importance of matter-element feature cj relative to ci. The possible values of aij and the corresponding meanings are listed in Table 1.Table 1
The 9-point scale for pairwise comparison.
aijMeaning1ci and cj are equally important3ci is slightly more important than cj5ci is moderately more important than cj7ci is strongly more important than cj9ci is extremely more important than cj2, 4, 6, 8Intermediate states between adjacent levelsReciprocalsImportance ofcj relative to ciTable1 lists a total of 9 states. Among them, state 1 means equal importance; state 3 means slight importance; state 5 means relative importance; state 7 means strong importance; state 9 means extremely strong importance; states 2, 4, 6, and 8 are between states 1 and 3, 3 and 5, 5 and 7, and 7 and 9, respectively.Based on the pairwise comparison, the judgement matrixA of matter-element features can be obtained as follows:(17)A=a11⋯a1j⋯a1n⋮⋮⋮⋮⋮ai1⋯aij⋯ain⋮⋮⋮⋮⋮an1⋯anj⋯ann.According to the judgement matrixA, the maximum eigenvalue λmaxA and the corresponding eigenvector WA were obtained. The AHP is a decision-making method that quantifies and qualifies the elements related to the decision-making process, after breaking down them into the layers of goals, criteria, and alternatives. The process of AHP involves constructing the judgement matrix and solving its maximum eigenvalue. However, it is difficult to construct a consistent matrix, when the order of the matrix is being judged. Besides, the judgement matrix should not deviate from the consistent condition too much. Therefore, it is necessary to test whether the judgement matrix is sufficiently consistent. Then, the consistency index CI(A) of the judgement matrix A can be obtained as follows:(18)CIA=λmaxA−nn−1.Then, the table of average random consistency indicesRI was looked up based on the number n of HRMPA matter-element features. The specific results are shown in Table 2.Table 2
Correspondence betweenRI and n.
n12345RI000.580.901.12n678910RI1.241.321.411.451.49Based on theRI value, the consistency ratio CR(A) corresponding to the judgement matrix A can be obtained as follows:(19)CRA=CIARIA.Then, the judgement matrixA was subjected to a consistency test. If CR(A) < 0.1, then the judgement matrix A meets the consistency requirement. Thus, the weight wi of matter-element feature ci can be obtained as follows:(20)wi=∑j=1naij∑i=1n∑j=1naij.


### 6.2. Construction of the Integrated Model

Considering the effects of the weights of different matter-element features, the integrated weighted fuzzy closenessκjk∗P between HRMPA matter-element Rk(P) and HRMPA classic domain matter-element Rj on the matter-element features of the same level can be established as follows:(21)κjk∗P=∑i=1nwi∗κijkP=∑i=1nwi∗1−dijkP.Similarly, the integrated weighted extenics correlation coefficientτjk∗P between HRMPA matter-element Rk(P) and HRMPA classic domain matter-element Rj on the matter-element features of the same level can be established as follows:(22)τjkP=∑i=1nwi∗KijkP.The uncertainty of HRMPA matter-element features may affect the corporate HRMPA results. On this basis, the authors set up the integrated performance analysis model between HRMPA matter-elementRk(P) and HRMPA classic domain matter-element Rj. In other words, the integrated correlation θjkP between Rk(P) and Rj can be expressed as follows:(23)θjkP=α∗κjk∗P+β∗τjk∗P,where α and β (α = 1−β) are fuzzy extenics factors.


### 6.3. Determination of Fuzzy Extenics Factors

According to fuzzy system theory, in the physical sense, the calculation model of HRMPA fuzzy closeness focuses on the external attributes of matter-element features, that is, evaluates how much the uncertain external attributes of each fuzzy index affect corporate HRMPA, while the internal attributes are clear.According to extenics theory, in the physical sense, the calculation model of HRMPA extenics correlation focuses on the internal attributes of matter-element features, that is, identifies the position of each fuzzy index in the fuzzy interval, and then evaluates how much its uncertain internal attributes affect corporate HRMPA.Therefore, the values of fuzzy extenics factorsα and β can be determined according to the ratio of internal uncertainty to external uncertainty of HRMPA matter-element features. Let G, H, and F be the number of externally uncertain indices, the number of internally uncertain indices, and other indices in all the matter-element features, respectively. Then, the values of α and β can be, respectively, approximated by(24)α=G+F/2G+H+F,β=H+F/2G+H+F.The values ofα and β are generally selected based on the fuzzy features of the object, including both external and internal features. If neither type of feature is clear, the two types of features can be fully considered by setting α = β = 0.5, without sacrificing the consistency and applicability of the analysis results.


### 6.4. Model Implementation

According to the integrated correlationθjkP between HRMPA matter-element Rk(P) and HRMPA classic domain matter-element Rj, the performance level of Rk(P) can be determined by(25)θl=maxθ1kP,…,θjkP,…,θmkP.This means that theRk(P) on the performance level of l corresponds to the HRMPA classic domain matter-element Rl.To sum up, the extenics theory-based corporate HRMA can be realized in the steps of Figure3.Figure 3
Framework of corporate HRMPA based on extenics theory.


## 6.1. AHP-Based Weighting of Matter-Element Features

The AHP is a simple, flexible, and practical method for multicriteria decision-making, offering a desirable tool to reliably quantify qualitative problems. Through the AHP, the weights of matter elements can be determined quickly and accurately [27–30].Several experts were invited to make pairwise comparisons of HRMPA matter-element features and rate the relative importance of each feature to the other in the pair against a 9-point scale. Letaij be the importance of matter-element feature ci relative to cj, and aij = 1/aji be the importance of matter-element feature cj relative to ci. The possible values of aij and the corresponding meanings are listed in Table 1.Table 1
The 9-point scale for pairwise comparison.
aijMeaning1ci and cj are equally important3ci is slightly more important than cj5ci is moderately more important than cj7ci is strongly more important than cj9ci is extremely more important than cj2, 4, 6, 8Intermediate states between adjacent levelsReciprocalsImportance ofcj relative to ciTable1 lists a total of 9 states. Among them, state 1 means equal importance; state 3 means slight importance; state 5 means relative importance; state 7 means strong importance; state 9 means extremely strong importance; states 2, 4, 6, and 8 are between states 1 and 3, 3 and 5, 5 and 7, and 7 and 9, respectively.Based on the pairwise comparison, the judgement matrixA of matter-element features can be obtained as follows:(17)A=a11⋯a1j⋯a1n⋮⋮⋮⋮⋮ai1⋯aij⋯ain⋮⋮⋮⋮⋮an1⋯anj⋯ann.According to the judgement matrixA, the maximum eigenvalue λmaxA and the corresponding eigenvector WA were obtained. The AHP is a decision-making method that quantifies and qualifies the elements related to the decision-making process, after breaking down them into the layers of goals, criteria, and alternatives. The process of AHP involves constructing the judgement matrix and solving its maximum eigenvalue. However, it is difficult to construct a consistent matrix, when the order of the matrix is being judged. Besides, the judgement matrix should not deviate from the consistent condition too much. Therefore, it is necessary to test whether the judgement matrix is sufficiently consistent. Then, the consistency index CI(A) of the judgement matrix A can be obtained as follows:(18)CIA=λmaxA−nn−1.Then, the table of average random consistency indicesRI was looked up based on the number n of HRMPA matter-element features. The specific results are shown in Table 2.Table 2
Correspondence betweenRI and n.
n12345RI000.580.901.12n678910RI1.241.321.411.451.49Based on theRI value, the consistency ratio CR(A) corresponding to the judgement matrix A can be obtained as follows:(19)CRA=CIARIA.Then, the judgement matrixA was subjected to a consistency test. If CR(A) < 0.1, then the judgement matrix A meets the consistency requirement. Thus, the weight wi of matter-element feature ci can be obtained as follows:(20)wi=∑j=1naij∑i=1n∑j=1naij.


## 6.2. Construction of the Integrated Model

Considering the effects of the weights of different matter-element features, the integrated weighted fuzzy closenessκjk∗P between HRMPA matter-element Rk(P) and HRMPA classic domain matter-element Rj on the matter-element features of the same level can be established as follows:(21)κjk∗P=∑i=1nwi∗κijkP=∑i=1nwi∗1−dijkP.Similarly, the integrated weighted extenics correlation coefficientτjk∗P between HRMPA matter-element Rk(P) and HRMPA classic domain matter-element Rj on the matter-element features of the same level can be established as follows:(22)τjkP=∑i=1nwi∗KijkP.The uncertainty of HRMPA matter-element features may affect the corporate HRMPA results. On this basis, the authors set up the integrated performance analysis model between HRMPA matter-elementRk(P) and HRMPA classic domain matter-element Rj. In other words, the integrated correlation θjkP between Rk(P) and Rj can be expressed as follows:(23)θjkP=α∗κjk∗P+β∗τjk∗P,where α and β (α = 1−β) are fuzzy extenics factors.


## 6.3. Determination of Fuzzy Extenics Factors

According to fuzzy system theory, in the physical sense, the calculation model of HRMPA fuzzy closeness focuses on the external attributes of matter-element features, that is, evaluates how much the uncertain external attributes of each fuzzy index affect corporate HRMPA, while the internal attributes are clear.According to extenics theory, in the physical sense, the calculation model of HRMPA extenics correlation focuses on the internal attributes of matter-element features, that is, identifies the position of each fuzzy index in the fuzzy interval, and then evaluates how much its uncertain internal attributes affect corporate HRMPA.Therefore, the values of fuzzy extenics factorsα and β can be determined according to the ratio of internal uncertainty to external uncertainty of HRMPA matter-element features. Let G, H, and F be the number of externally uncertain indices, the number of internally uncertain indices, and other indices in all the matter-element features, respectively. Then, the values of α and β can be, respectively, approximated by(24)α=G+F/2G+H+F,β=H+F/2G+H+F.The values ofα and β are generally selected based on the fuzzy features of the object, including both external and internal features. If neither type of feature is clear, the two types of features can be fully considered by setting α = β = 0.5, without sacrificing the consistency and applicability of the analysis results.


## 6.4. Model Implementation

According to the integrated correlationθjkP between HRMPA matter-element Rk(P) and HRMPA classic domain matter-element Rj, the performance level of Rk(P) can be determined by(25)θl=maxθ1kP,…,θjkP,…,θmkP.This means that theRk(P) on the performance level of l corresponds to the HRMPA classic domain matter-element Rl.To sum up, the extenics theory-based corporate HRMA can be realized in the steps of Figure3.Figure 3
Framework of corporate HRMPA based on extenics theory.


## 7. Case Analysis

To verify its effectiveness and operability, the proposed HRMPA index system and HRMPA model were applied to the HRMPA of a medium private enterprise. Under the corporate HRMPA index system, the initial evaluation data were obtained from the enterprise and normalized by the proposed normalization method (Table3). On this basis, an HRMPA model was established for the enterprise.Table 3
Original and normalized values of HRMPA indices.
Original valuesNormalized valuesRPZ1=NPZ1c1195c1285c1375−78c1485c1572c1682−85RPZ1=NPZ1c110.95c120.85c130.75,0.78c140.85c150.72c160.82,0.85RPZ2=NPZ2c2193c2266−68c2381c2485c2558RPZ2=NPZ2c210.93c220.66,0.68c230.81c240.85c250.58RPZ3=NPZ3c3185c3228%c3375−79c3486−88RPZ3=NPZ3c310.85c320.80c330.75,0.79c340.86,0.88RPZ4=NPZ4c4185−88c4275−78c4365c4485c4585RPZ4=NPZ4c410.85,0.88c420.75,0.78c430.65c440.85c450.85RPZ5=NPZ5c514.5%c5283c5392c5495c5585c5685−88RPZ5=NPZ5c510.775c520.83c530.92c540.95c550.85c560.85,0.88RPZ6=NPZ6c6115.6%c6276−88c6326.6%c6422.4%c6598.5%c6695c6798RPZ6=NPZ6c610.78c620.76,0.88c630.887c640.896c650.985c660.95c670.98RPZ7=NPZ7c7193%c7276%c7382%c7465c7585RPZ7=NPZ7c710.93c720.76c730.82c740.65c750.85Then, the AHP was introduced to weigh the criteria. Experts were invited to rate the criteria through pairwise comparison, producing the judgement matrixAZ for the criteria layer.(26)AZ=1111112112131312121121112131313111313121323113312333131223213131.The judgement matrixAZ was analyzed by the relevant formulas in our research. In this way, the weight ranking of the criteria was obtained as WAZ = {0.144, 0.088, 0.077, 0.103, 0.196, 0.268, 0.124}. Similarly, the weights of HRMPA matter-element features under each criterion were obtained (Table 4).Table 4
Weights of matter-element features.
FeatureWeightFeatureWeightFeatureWeightFeatureWeightC110.261C250.171C510.141C650.128C120.158C310.157C520.376C660.122C130.100C320.272C530.152C670.113C140.243C330.483C540.210C710.123C150.169C340.088C550.052C720.219C160.069C410.068C560.069C730.044C210.096C420.378C610.149C740.268C220.407C430.262C620.124C750.346C230.054C440.109C630.212C240.272C450.183C640.152After normalization, the HRMPA matter-element features were divided into four levels: excellent, good, medium, and poor. The division points between the four levels correspond to the classic domain nodes of 0.9, 0.8, and 0.6, respectively. According to the proposed corporate HRMPA model, the fuzzy closeness and extenics correlation results were obtained (Tables5 and 6).Table 5
Results on fuzzy closeness.
FeatureR1R2R3R4FeatureR1R2R3R4C110.3500.7500.9001.000C450.4500.8501.0000.900C120.4500.8501.0000.900C510.5250.9250.9250.825C130.5350.9350.9150.815C520.4700.8700.9800.880C140.4500.8501.0000.900C530.3800.7800.9300.970C150.5800.9800.8700.770C540.3500.7500.9001.000C160.4650.8630.9850.885C550.4500.8501.0000.900C210.3700.7700.9200.980C560.4450.8450.9950.905C220.6300.9000.7500.690C610.5200.9200.9300.830C230.4900.8900.9600.860C620.5400.9400.9100.810C240.4500.8501.0000.900C630.4130.8130.9630.937C250.7000.8100.7300.630C640.4040.8040.9540.946C310.4500.8501.0000.900C650.3150.7150.8650.965C320.5000.9000.9500.900C660.3500.7500.9001.000C330.5300.9300.9200.820C670.3200.7200.8700.970C340.4300.8300.9800.920C710.3700.7700.9200.980C410.4500.8501.0000.900C720.5400.9400.9100.810C420.5400.9400.9100.810C730.4800.8800.9700.870C430.6500.9500.8000.700C740.6500.9500.8000.700C440.4500.8501.0000.900C750.4500.8501.0000.900Table 6
Results on extenics correlation.
FeatureR1R2R3R4FeatureR1R2R3R4C11−0.875−0.75−0.500.50C45−0.625−0.250.50−0.25C12−0.625−0.250.50−0.25C51−0.4380.125−0.10−0.357C13−0.4130.175−0.130−0.365C52−0.575−0.150.30−0.292C14−0.625−0.250.50−0.25C53−0.80−0.60−0.200.20C15−0.300.40−0.222−0.391C54−0.875−0.75−0.500.50C16−0.588−0.1750.35−0.283C55−0.625−0.250.50−0.25C21−0.825−0.65−0.300.30C56−0.638−0.2750.25−0.237C22−0.1750.35−0.283−0.411C61−0.450.10−0.083−0.353C23−0.525−0.0500.10−0.321C62−0.400.20−0.143−0.368C24−0.625−0.250.50−0.25C63−0.718−0.4350.13−0.103C250.033−0.045−0.344−0.432C64−0.74−0.480.04−0.037C31−0.625−0.250.50−0.25C65−0.963−0.925-0.850.15C32−0.5000−0.333C66−0.875−0.75−0.500.50C33−0.4250.15−0.115−0.361C67−0.95−0.90−0.800.20C34−0.675−0.350.30−0.188C71−0.825−0.65−0.300.30C41−0.625−0.250.20−0.25C72−0.400.20−0.143−0.368C42−0.400.20−0.143−0.368C73−0.55−0.100.20−0.308C43−0.1250.25−0.30−0.417C74−0.1250.25−0.30−0.417C44−0.625−0.250.50−0.25C75−0.625−0.250.50−0.25Considering the weights of matter-element features, the fuzzy extenics factors were both set to 0.5. After normalizing the results on fuzzy closeness and extenics correlation, the integrated correlation of HRMPA was derived asθ = {−0.055, 0.320, 0.433, 0.365}, indicating that the enterprise has good HRM performance.To further improve the performance, the HRMPA results should be analyzed to identify the weaknesses in HRM. Then, targeted measures should be adopted to solve the weaknesses and promote the HRM level and capacity, giving stronger support to corporate development. The HRMPA level of the current enterprise can be determined from the analysis results. Then, the evaluation results can be analyzed reversely from the subordinate indices to the superior indices in the proposed evaluation index system. If the fuzzy proximity and extensible correlation are both lower than the final evaluation level, then the evaluation results are negatively affected, calling for pertinent revisions.


## 8. Conclusions

Our fuzzy analysis model for corporate HRM performance can analyze the HRM performance of enterprises completely and holistically. On this basis, it is possible to determine the level of HRM performance of each enterprise and identify the weaknesses in corporate HRM. The example analysis demonstrates the implementation process of the model and verifies the effectiveness of our model and algorithm.The findings of our research concentrate on the following aspects:(1)
This paper sets up a novel corporate HRMPA index system and clarifies the index selection criteria, hierarchical structure, and index contents, making the index system complete and consistent.(2)
The fuzzy corporate HRMPA model and the extenics corporate HRMPA model were established based on fuzzy theory and extenics theory, respectively. Then, the fuzzy extenics factors were introduced to construct an improved, integrated, and fuzzy corporate HRMPA model, which analyzes corporate HRM in a comprehensive and complete manner.(3)
The proposed index system and model were explained and verified through case analysis. The results demonstrate that our model is highly effective. The proposed index system and model are good at solving decision-making problems in complex systems, providing a good reference for other complex systems with similar features. The research results enjoy great applicable value in engineering.



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*Source: 5108338-2022-02-21.xml*