# AG600 Amphibious Aircraft Selection Model Based on Improved Fuzzy Evaluation Algorithm

Authors: Baoku Du; Wei Xiong; Hongwang Du
Journal: Computational Intelligence and Neuroscience
 (2022)

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## Abstract

Aiming at the selection research gap of AG600 amphibious aircraft for salvage of life at sea, the selection index system of AG600 has been established, and an interval intuitionistic fuzzy selection decision model based on fuzzy entropy and score function is constructed. An evaluation index system with 8 indexes was determined based on the rules of the applicability, safety, and accessibility by questionnaire and statistical analysis. Different from the traditional method of determining the fuzzy number of each index solely by experts’ scoring, this paper establishes a 5-grade fuzzy evaluation grade and index membership function, and the interval intuitionistic fuzzy number of the index is determined by combining subjective and objective methods. Fuzzy entropy and score function are used to calculate the weights of each index and AG600 selection score for different accidents, so as to obtain the matching degree of AG600 selection in marine life accidents more scientifically and reasonably. Finally, the effectiveness of the proposed model is demonstrated by a practical case.


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## Body

## 1. Introduction

AG600 is a large-scale amphibious rescue aircraft newly developed in our country. It is a multi-attribute dynamic fuzzy decision-making problem. In the selection decision of AG600, there are completely unknown attribute weights for marine life rescue. Scientific and rational selection of AG600 is the key to ensuring the success rate of rescue missions and is also an important link in the application and exploration of AG600 in maritime rescue. On this basis, a decision-making model is established according to actual engineering needs and appropriate evaluation methods to complete the final evaluation decision. AG600 selection decision must consider indicators such as reliability, applicability, accessibility, and safety. Due to the complexity of evaluation indicators, it has considerable ambiguity and uncertainty. Therefore, AG600 selection and evaluation are difficult to use. The fuzzy comprehensive evaluation method [1–3] provides an effective method for multi-factor fuzzy evaluation, which provides an effective means for multi-factor fuzzy evaluation. Through the principle of fuzzy transformation and the principle of maximum membership, things can be graded or classified and evaluated, which is suitable for the selection and evaluation of AG600. At present, there are few studies based on fuzzy evaluation in the field of marine rescue decision making. Malyszko [1] realized the selection of civil ships in marine rescue missions based on the multi-criteria decision analysis (MCDA) and fuzzy evaluation method. Yang [4] constructed a fuzzy evaluation model of the western inland river search and rescue capability based on the AHP and fuzzy comprehensive evaluation method. Wu and Lan and Wei and Liu [5, 6] optimized and ranked salvage ships based on the analytic hierarchy process and fuzzy evaluation method. Zhang [7] completed the selection and adjustment of marine rescue forces based on the fuzzy analytic hierarchy process and Voronoi diagram. Pan [8] optimized the deployment position of AG600 based on the AHP and fuzzy comprehensive evaluation method. Dai [9] established three mathematical models for dynamic preassessment of marine traffic risk under severe weather, which improved the pertinence and rationality of risk assessment on the basis of fuzzy comprehensive assessment method. Min [10] established a water rescue capability evaluation model based on the analytic hierarchical process (AHP) and fuzzy comprehensive evaluation method. The above studies have considered the fuzziness of indicators and established a corresponding evaluation index system. Atanassov proposed the concept of interval intuitionistic fuzzy set theory (IVIFS) [11]. The hesitation degree is more flexible and practical in dealing with ambiguity and uncertainty, which are more flexible and practical in dealing with ambiguity and uncertainty. The research on IVIFS has been quite mature and has achieved many results [12–17].Based on the interval intuition fuzzy theory and fuzzy comprehensive evaluation method, this paper establishes the AG600 selection decision model based on the improved fuzzy evaluation method. In the process of assigning weights to indicators, the ambiguity and hesitancy of experts’ understanding of evaluation indicators and the limitations of single expert evaluation are considered. On the basis of calculating the index member values, the expert group decision-making method and the fuzzy transformation method are used to establish the interval intuition fuzzy matrix. Then, we use the fuzzy entropy method to assign weights to each index and use the scoring function to calculate the selected score. Finally, according to the evaluation level, the matching degree of AG600 to the current maritime rescue mission is obtained. This provides a new idea for the selection of AG600, making the decision more scientific and reasonable.


## 2. Interval Intuitionistic Fuzzy Entropy and Score Function

AG600 selection is a decision-making process full of complexity and uncertainty. Compared with the traditional weight determination method, the fuzzy entropy method that is based on interval intuitionistic fuzzy number is adopted to calculate the weight of the evaluation index, which not only considers the objective fact that the index data cannot be expressed with accurate numbers but also takes into account the fuzziness and hesitation of the experts’ understanding for the index.Definition 1.
(see [11]). Assume int0,1 represents all the closed subsets of the interval number 0,1, X is a given domain, called the interval intuitionistic fuzzy set on the domain XIVIFSsX.(1)A=x,μAx,νAxx∈X.
Among them,(2)μAx:X⟶int0,1,νAx:X⟶int0,1.and meet 0⩽supμAx+supνAx⩽1,∀x∈X. Interval number μAx and νAx respectively represents the membership degree and non-membership degree of the element x in A of X which are denoted as(3)μAx=μALx,μAUx,(4)νAx=νALx,νAUx.
Then, the interval intuitionistic fuzzy setA can be written as(5)A=x,μALx,μAUx,νALx,νAUxx∈X,and πAx=πALx,πAUx is the hesitancy of elements A.(6)πALx=1−μAUx−νAUx,πAUx=1−μALx−νALx.
Especially, whenμALx=μAUx,νALx=νAUx, the interval intuitionistic fuzzy set degenerates into intuitionistic fuzzy set. To simplify things, denote α=a,b,c,d as an interval intuitive fuzzy number, where 0⩽a⩽b⩽1, 0⩽c⩽d⩽1, 0⩽b+d⩽1.Definition 2.
(see [12]). Assume αj=aj,bj,cj,djj=1,2,…,n is a group of interval intuitive fuzzy numbers, and then assume Fwα1,α2,…,αn is an interval intuitionistic fuzzy weighted arithmetic average operator,(7)Fwα1,α2,…,αn=∑j−1nWjαj=1−∏j−1n1−ajWj,1−∏j−1n1−bjWj,∏j−1ncjWj,∏j−1ndjWj.Definition 3.
(see [14–17]). In the interval, intuitionistic fuzzy multi-attribute decision-making problem can be expressed.(8)rij=μijL,μijU,νijL,νijU,i=1,2,…,n;j=1,2,…,m.
Make the interval intuitive fuzzy entropy of the attributejj=1,2,…,m as(9)Ej=1n∑i=1nerij=1n∑i=1n4−μijL−νijL+μijU−νijU2+πijL+πijU28.
The weight of thej attribute can be expressed as(10)wj=1−Ejm−∑j=1mEj.Definition 4.
(see [13]). Make the interval intuitionistic fuzzy number α=a,b,c,d. Its score function is(11)Sα=a+pΔ1−c+1−pΔ21+Δ1+Δ2.
The rule forp is that when the membership degree interval is greater than the non-membership degree interval, p=0.6; when two numbers are equal, p=0.5; when the membership degree interval is smaller than the non-membership degree interval, p=0.4. So, Sα can be written as a piecewise function:(12)Sα=a+0.6Δ1−c−0.4Δ21+Δ1+Δ2,a+b>c+d,a+0.5Δ1−c−0.5Δ21+Δ1+Δ2,a+b=c+d,a+0.4Δ1−c−0.6Δ21+Δ1+Δ2,a+b<c+d.
In formula (4), Δ1=b−a, Δ2=d−c; the larger Sα, the more applicable the AG600 for the current rescue.


## 3. AG600 Selection Model Based on Interval Intuitive Fuzzy Sets

### 3.1. Determining the Selection Index System

The selection decision of AG600 in the rescue of human life at sea requires comprehensive consideration of AG600 design parameters, rescue mode, deployment location, rescue objects, rescue space information, and other factors affecting the implementation of the rescue mission. Taking the South China Sea as the rescue research object, this paper makes a statistical analysis on the natural conditions and construction status of more than 200 islands and reefs, as well as the water depth, channel, and anchorage distribution of accident prone waters through the statistical analysis of wind, wave, and current in each season in the South China sea [18–21]. Combined with the questionnaire survey and score of maritime rescue experts and AG600, the important decision-making indexes affecting AG600 in maritime life rescue are obtained. Index attribute value can be divided into two types from the data type, namely, interval number A and language description V. According to the effect of data, it can be divided into benefit types B and cost types C (see Table 1).Table 1
AG600 maritime rescue selection decision evaluation index.
RuleIndexLabelTypeDescriptionApplicabilityBearing ratiou1A\CThe ratio of the actual rescued number of AG600 passengers to the actual maximum number of AG600 passengersRunwayu2A\BThe area of water runway shall not be less than 10.5km2Water depthu3A\BThe water depth should not be less than 2.5 mReachabilityFlightpathu4A\CThe ratio of theoretical minimum time to actual time from standby point to accident pointDifficulty of rescueu5V\CThe qualitative determination of difficulty from aircraft landing point to target in distressSafetyWindu6A\CThe maximum lateral wind force of aircraft taking off and landing shall not exceed 10.3 m/sWaveu7A\CThe wave height of the landing area shall not exceed 2.5 mVisibilityu8A\BVisibility must not be less than 2 km


### 3.2. Grading of Evaluation

This paper refers to the International Aviation and Maritime Search and Rescue Manual, Civil Aviation Law of the People’s Republic of China, Emergency Response Law of the People’s Republic of China, and other documents; combined with fuzzy classification standards, the evaluation level of language description was divided into 5 grades; in order to facilitate fuzzy operation and make fuzzy evaluation more precise and intuitive, fuzzy number interval is used to quantify each grade (see Table2 for the fuzzy evaluation grades obtained).Table 2
Fuzzy evaluation level of AG600.
LevelFuzzy numberDescription10～0.45Poor, not applicable at allRescue efficiency and success rate approach 020.45～0.60Not qualified, not applicableRescue efficiency and success rate are low30.60～0.75Qualified, applicableRescue efficiency and success rate are high40.75～0.90Good, very applicableRescue efficiency and success rate are very high50.90～1Excellent, very applicableRescue efficiency and success rate approach 1


### 3.3. Constructing the Membership Function

The Delphi method and questionnaire are usually used to determine the interval intuitionistic fuzzy number, and the results are too subjective. According to the characteristics of AG600 selection, this paper proposes to construct membership function for each index that affects AG600 selection (see Table3). Firstly, the membership degree and non-membership degree of the index are calculated according to the objective data of the accident. On this basis, the interval intuitionistic fuzzy number of the index is determined by combining expert analysis. Due to space limitation, the construction process of index membership function is not discussed in this paper.Table 3
AG600 decision index membership function.
IndexMembership functionu1U1x=1,0≤x≤0.81−x/0.2,0.8<x<10,x≥1u2U2x=0,0<x<0.51,x≥0.5u3U6x=0,x−2/0.5,0<x≤22<x<2.51,x≥2.5u4U4x=1,0≤x≤11.5−x/0.5,1<x<1.50,x≥1.5u5U5x=1,0<x≤25−x/3,2<x<50,x≥5u6U6x=1,0≤x≤810.5−x/2.5,8<x<10.50,x≥10.5u7U7x=1,0≤x≤22.5−x/0.5,2<x<2.50,x≥2.5u8U8x=0,0≤x≤2x−2/8,2<x<101,x≥10To sum up, the specific steps of applying AG600’s fuzzy selection model to actual rescue decision making are as follows:Step 1: construct AG600 selection decision matrix, namely, case matching degree matrixR. Identify cases of life at sea. Ai,i=1,2,…,m. Selected indicators Uj,j=1,2,…,n. According to the actual accident data and the index membership function, calculate the index membership degree. On this basis, determine the interval intuitionistic fuzzy number of indicators objectively by combining expert experience, rij=μijL,μijU,νijL,νijU, and the interval intuitionistic fuzzy matrix is obtained R=rijm×n.Step 2: according to the decision matrix, the objective weight of each attribute can be obtained by formulas (2) and (3), wj,j=1,2,…,m.Step 3: formula (1) is used to calculate the comprehensive matching attribute value αi of case Ai.Step 4: the comprehensive matching scoreSαi of Ai is calculated by formula (4). That is, for the rescue of human life on the water, the degree of suitability of AG600 is selected.


## 3.1. Determining the Selection Index System

The selection decision of AG600 in the rescue of human life at sea requires comprehensive consideration of AG600 design parameters, rescue mode, deployment location, rescue objects, rescue space information, and other factors affecting the implementation of the rescue mission. Taking the South China Sea as the rescue research object, this paper makes a statistical analysis on the natural conditions and construction status of more than 200 islands and reefs, as well as the water depth, channel, and anchorage distribution of accident prone waters through the statistical analysis of wind, wave, and current in each season in the South China sea [18–21]. Combined with the questionnaire survey and score of maritime rescue experts and AG600, the important decision-making indexes affecting AG600 in maritime life rescue are obtained. Index attribute value can be divided into two types from the data type, namely, interval number A and language description V. According to the effect of data, it can be divided into benefit types B and cost types C (see Table 1).Table 1
AG600 maritime rescue selection decision evaluation index.
RuleIndexLabelTypeDescriptionApplicabilityBearing ratiou1A\CThe ratio of the actual rescued number of AG600 passengers to the actual maximum number of AG600 passengersRunwayu2A\BThe area of water runway shall not be less than 10.5km2Water depthu3A\BThe water depth should not be less than 2.5 mReachabilityFlightpathu4A\CThe ratio of theoretical minimum time to actual time from standby point to accident pointDifficulty of rescueu5V\CThe qualitative determination of difficulty from aircraft landing point to target in distressSafetyWindu6A\CThe maximum lateral wind force of aircraft taking off and landing shall not exceed 10.3 m/sWaveu7A\CThe wave height of the landing area shall not exceed 2.5 mVisibilityu8A\BVisibility must not be less than 2 km


## 3.2. Grading of Evaluation

This paper refers to the International Aviation and Maritime Search and Rescue Manual, Civil Aviation Law of the People’s Republic of China, Emergency Response Law of the People’s Republic of China, and other documents; combined with fuzzy classification standards, the evaluation level of language description was divided into 5 grades; in order to facilitate fuzzy operation and make fuzzy evaluation more precise and intuitive, fuzzy number interval is used to quantify each grade (see Table2 for the fuzzy evaluation grades obtained).Table 2
Fuzzy evaluation level of AG600.
LevelFuzzy numberDescription10～0.45Poor, not applicable at allRescue efficiency and success rate approach 020.45～0.60Not qualified, not applicableRescue efficiency and success rate are low30.60～0.75Qualified, applicableRescue efficiency and success rate are high40.75～0.90Good, very applicableRescue efficiency and success rate are very high50.90～1Excellent, very applicableRescue efficiency and success rate approach 1


## 3.3. Constructing the Membership Function

The Delphi method and questionnaire are usually used to determine the interval intuitionistic fuzzy number, and the results are too subjective. According to the characteristics of AG600 selection, this paper proposes to construct membership function for each index that affects AG600 selection (see Table3). Firstly, the membership degree and non-membership degree of the index are calculated according to the objective data of the accident. On this basis, the interval intuitionistic fuzzy number of the index is determined by combining expert analysis. Due to space limitation, the construction process of index membership function is not discussed in this paper.Table 3
AG600 decision index membership function.
IndexMembership functionu1U1x=1,0≤x≤0.81−x/0.2,0.8<x<10,x≥1u2U2x=0,0<x<0.51,x≥0.5u3U6x=0,x−2/0.5,0<x≤22<x<2.51,x≥2.5u4U4x=1,0≤x≤11.5−x/0.5,1<x<1.50,x≥1.5u5U5x=1,0<x≤25−x/3,2<x<50,x≥5u6U6x=1,0≤x≤810.5−x/2.5,8<x<10.50,x≥10.5u7U7x=1,0≤x≤22.5−x/0.5,2<x<2.50,x≥2.5u8U8x=0,0≤x≤2x−2/8,2<x<101,x≥10To sum up, the specific steps of applying AG600’s fuzzy selection model to actual rescue decision making are as follows:Step 1: construct AG600 selection decision matrix, namely, case matching degree matrixR. Identify cases of life at sea. Ai,i=1,2,…,m. Selected indicators Uj,j=1,2,…,n. According to the actual accident data and the index membership function, calculate the index membership degree. On this basis, determine the interval intuitionistic fuzzy number of indicators objectively by combining expert experience, rij=μijL,μijU,νijL,νijU, and the interval intuitionistic fuzzy matrix is obtained R=rijm×n.Step 2: according to the decision matrix, the objective weight of each attribute can be obtained by formulas (2) and (3), wj,j=1,2,…,m.Step 3: formula (1) is used to calculate the comprehensive matching attribute value αi of case Ai.Step 4: the comprehensive matching scoreSαi of Ai is calculated by formula (4). That is, for the rescue of human life on the water, the degree of suitability of AG600 is selected.


## 4. Instance Analysis

Table4 shows the cited cases of drowning rescue in the South China Sea in the past three years for statistical analysis [18]. Yongxing Island, as a rescue base, found four typical cases in the same sea area where life-threatening accidents often occur. Taking Yongxing Island as the rescue base, four typical cases A=A1,A2,A3,A4 were identified in the same sea area where life accidents often occur; because the article is limited in length, details of the case will not be described in this paper. According to the index system U=u1,u2,u3,u4,u5,u6,u7,u8 of AG600 selection, interval intuitionistic fuzzy matrix R=rijm×n, rij=μijL,μijU,νijL,νijU, is established by index membership function and expert group decision (see Table 4).Table 4
Decision matrixR.
u1u2u3u4A1([0.85, 0.95], [0.1, 0.2])([0.85, 0.95], [0.1, 0.2])([0.8, 0.9], [0.1, 0.2])([0.9, 0.95], [0.05, 0.15])A2([0.85, 0.95], [0.1, 0.2])([0.8, 0.9], [0.05, 0.15])([0.8, 0.9], [0.1, 0.3])([0.7, 0.9], [0.1, 0.2])A3([0.1, 0.2], [0.8, 0.95])([0.1, 0.2], [0.85, 0.95])([0.8, 0.9], [0.1, 0.2])([0.7, 0.9], [0.1, 0.2])A4([0.85, 0.95], [0.1, 0.2])([0.8, 0.9], [0.05, 0.15])([0.8, 0.9], [0.1, 0.2])([0.05, 0.15], [0.9, 0.95])u5u6u7u8A1([0.4, 0.45], [0.5, 0.65])([0.85, 0.95], [0.1, 0.25])([0.9, 0.95], [0.1, 0.2])([0.8, 0.9], [0.1, 0.2])A2([0.1, 0.2], [0.8, 0.95])([0.15, 0.3], [0.8, 0.9])([0.3, 0.45], [0.8, 0.9])([0.25, 0.4], [0.6, 0.8])A3([0.15, 0.2], [0.85, 0.95])([0.05, 0.15], [0.85, 0.95])([0.1, 0.2], [0.9, 0.95])([0.1, 0.2], [0.85, 0.9])A4([0.15, 0.2], [0.85, 0.95])([0.05, 0.15], [0.9, 0.0.95])([0.1, 0.2], [0.9, 0.95])([0.9, 0.95], [0.05, 0.15])Table5 is the decision matrix on the basis of equations (2) and (3), the weight wj,j=1,2,…,m of each attribute uj.Table 5
Index weightwj.
Indexw1w2w3w4w5w6w7w8Weight0.12510.12450.12640.12390.12260.12600.12590.1256In order to focus on the contribution of all attributes to selection decision, formula (1) is used to calculate the comprehensive attribute value αi of case Ai.(13)α1=0.81,0.91,0.15,0.27,α2=0.60,0.77,0.27,0.44,α3=0.45,0.61,0.41,0.55,α4=0.64,0.67,0.36,0.51.Table6 shows the AG600 scheduling score of Sαi; each case is calculated according to the formula, as shown in Table 6.Table 6
AG600 match score for casesSαi.
CaseSα1Sα2Sα3Sα4Score0.81800.50620.16530.5501Table7 shows the combination of all tables. In these four cases, the results of the AG600 selection were obtained by replacing the scores Sαi into the assessment scale (see Table 7).Table 7
AG600 selection decision result.
CaseGrade of selection evaluationEvaluation result12345A100010ApplicableA201000Not applicableA310000Not applicable at allA401000Not applicableIn order to obtain the sea rescue option of ag600 amphibious aircraft, the AG600 amphibious aircraft marine rescue selection index system was established, and an interval intuition fuzzy selection decision-making model based on fuzzy entropy and scoring function was established. Through questionnaire survey and statistical analysis, according to the principles of applicability, safety, and accessibility, an evaluation index system including 8 indicators was determined. Different from the traditional method of determining the fuzzy number of each index by only relying on expert scoring, this paper establishes a 5-level fuzzy evaluation level and index membership function and determines the interval intuition fuzzy number of the index by combining subjective and objective methods. We use fuzzy entropy and scoring function to calculate the weight of each index and the AG600 selection score of different accidents, so as to obtain the matching degree of AG600 selection in marine biological accidents more scientifically and reasonably. Finally, the effectiveness of the model is verified by an example.


## 5. Conclusion

In this paper, the AG600 selection decision in marine life rescue with completely unknown attribute weight is taken as the research background, and the AG600 selection model based on improved fuzzy algorithm is constructed. The selection index system of AG600 in marine life accidents was proposed and determined for the first time; based on the interval intuitionistic fuzzy theory, the method of determining subjective and objective interval intuitionistic fuzzy number combining index membership function and expert experience is innovatively proposed. We constructed the interval intuitionistic fuzzy matrix and calculated objectively the weight of each index and the selection score of AG600 based on the interval intuitionistic fuzzy entropy method and score function. Finally, the application degree of AG600 in marine life accident is determined through the evaluation grade; to conclude whether AG600 is suitable for selection in the current case, the model is verified by a practical case, and the results meet the actual needs of marine life rescue. In this paper, AG600 amphibious aircraft is first brought into the maritime rescue system, and the selection decision problem is put forward. According to the importance of considering both objective facts and expert experience in the decision-making process, the AG600 selection model is constructed. It provides scientific basis and guarantee for AG600 deployment and application in the future.



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