拓展区间Fermatean模糊前景理论综合评价方法

doi:10.16381/j.cnki.issn1003-207x.2022.0663

Abstract

Abstract:

In view of the existing problems of aggregative comprehensive evaluation information， such as single perspective， ignoring the correlation of indicators and abnormal preference information given by the irrational psychology of the evaluator， etc. Therefore， based on the interval-valued Fermatean fuzzy evaluation information， a comprehensive evaluation method of weighted power Heronian average operator and extended prospect theory is established in this paper. First， interval-valued Fermatean fuzzy sets （IVFFS） are used to represent the evaluation information of group experts， and the preference information is included in a larger range. In order to solve the interaction of input indices and the global equilibrium problem， a generalized interval-valued Fermatean fuzzy weighted power Heronian average （GIVFFWPHM） operator is proposed， and the important properties of the operator are discussed. Then， according to the different preferences of each evaluator in the group， the expert prospect weight is established， and the correlation coefficient between two interval-valued Fermatean fuzzy numbers is defined to determine the objective weight of the index. In addition， based on the extended prospect theory， a multi-index comprehensive evaluation process framework considering the bounded rationality of group experts is established. Finally， the feasibility and superiority of the proposed method are verified by robustness test and effective comparative analysis in five regions selected to evaluate the effectiveness of rural revitalization enabling poverty alleviation.

Key words: interval-valued Fermatean fuzzy set, generalized interval-valued Fermatean fuzzy weighted power Heronian mean operator, prospect theory, correlation coefficient, group comprehensive evaluation of rural vitalization

CLC Number:

C934

Shihua Luo, Jun Liu. A Comprehensive Evaluation Method Based on Extended Interval-Valued Fermatean Fuzzy Prospect Theory[J]. Chinese Journal of Management Science, 2025, 33(6): 129-139.

Figures/Tables 12

序号	$p, q$ 参数	综合前景感知价值	综合排序结果
1	$p = 0.5, q = 1$	$ψ 1 = 0.4899, ψ 2 = 0.5417, ψ 3 = 1.7847, ψ 4 = 0.6914, ψ 5 = 1.4665$	$A 3 ≻ A 5 ≻ A 4 ≻ A 2 ≻ A 1$
2	$p = 1 . q = 0.5$	$ψ 1 = 0.4899, ψ 2 = 0.5417, ψ 3 = 1.7847, ψ 4 = 0.6914, ψ 5 = 1.4665$	$A 3 ≻ A 5 ≻ A 4 ≻ A 2 ≻ A 1$
3	$p = 1, q = 2$	$ψ 1 = 0.4689, ψ 2 = 0.5418, ψ 3 = 1.7848, ψ 4 = 0.6911, ψ 5 = 1.4718$	$A 3 ≻ A 5 ≻ A 4 ≻ A 2 ≻ A 1$
4	$p = 2, q = 1$	$ψ 1 = 0.4689, ψ 2 = 0.5418, ψ 3 = 1.7848, ψ 4 = 0.6911, ψ 5 = 1.4718$	$A 3 ≻ A 5 ≻ A 4 ≻ A 2 ≻ A 1$
5	$p = 2, q = 5$	$ψ 1 = 0.4600, ψ 2 = 0.5415, ψ 3 = 1.7859, ψ 4 = 0.6910, ψ 5 = 1.4748$	$A 3 ≻ A 5 ≻ A 4 ≻ A 2 ≻ A 1$
6	$p = 5, q = 2$	$ψ 1 = 0.4600, ψ 2 = 0.5415, ψ 3 = 1.7859, ψ 4 = 0.6910, ψ 5 = 1.4748$	$A 3 ≻ A 5 ≻ A 4 ≻ A 2 ≻ A 1$
7	$p = 5, q = 10$	$ψ 1 = 0.4615, ψ 2 = 0.5412, ψ 3 = 1.7868, ψ 4 = 0.6912, ψ 5 = 1.4745$	$A 3 ≻ A 5 ≻ A 4 ≻ A 2 ≻ A 1$
8	$p = 10, q = 5$	$ψ 1 = 0.4615, ψ 2 = 0.5412, ψ 3 = 1.7868, ψ 4 = 0.6912, ψ 5 = 1.4745$	$A 3 ≻ A 5 ≻ A 4 ≻ A 2 ≻ A 1$

评价方法	计算结果	综合排序结果
PWA	$s c 1 = 0.1014, s c 2 = 0.0701, s c 3 = 0.2519, s c 4 = 0.0136, s c 5 = 0.0860$	$A 3 ≻ A 1 ≻ A 5 ≻ A 2 ≻ A 4$
PWG	$s c 1 = 0.1081, s c 2 = 0.0768, s c 3 = 0.2537, s c 4 = 0.0148, s c 5 = 0.0973$	$A 3 ≻ A 1 ≻ A 5 ≻ A 2 ≻ A 4$
TOPSIS	$C I 1 = 0.4035, C I 2 = 0.4235, C I 3 = 0.5981, C I 4 = 0.4744, C I 5 = 0.5746$	$A 3 ≻ A 5 ≻ A 4 ≻ A 2 ≻ A 1$
VIKOR	$Q 1 = 1.0000, Q 2 = 0.4204, Q 3 = 0.0000, Q 4 = 0.5865, Q 5 = 0.7006$	$A 3 ≻ A 2 ≻ A 4 ≻ A 5 ≻ A 1$
PT	$V 1 = 0.2611, V 2 = 0.5010, V 3 = 0.7303, V 4 = 0.3852, V 5 = 0.5126$	$A 3 ≻ A 5 ≻ A 2 ≻ A 4 ≻ A 1$
IVFFS-PT	$ψ 1 = 0.4794, ψ 2 = 0.5418, ψ 3 = 1.7846, ψ 4 = 0.6912, ψ 5 = 1.4690$	$A 3 ≻ A 5 ≻ A 4 ≻ A 2 ≻ A 1$

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区域	C₁	C₂	C₃	C₄	C₅
A₁	{[0.51,0.60],[0.38,0.70]}	{[0.37,0.50],[0.62,0.69]}	{[0.24,0.53],[0.51,0.62]}	{[0.17,0.36],[0.57,0.72]}	{[0.11,0.25],[0.80,0.92]}
A₂	{[0.52,0.74],[0.22,0.35]}	{[0.77,0.92],[0.31,0.43]}	{[0.47,0.61],[0.60,0.85]}	{[0.36,0.42],[0.64,0.82]}	{[0.18,0.32],[0.33,0.65]}
A₃	{[0.63,0.82],[0.50,0.62]}	{[0.54,0.64],[0.65,0.73]}	{[0.53,0.66],[0.11,0.25]}	{[0.63,0.87],[0.42,0.56]}	{[0.47,0.76],[0.34,0.54]}
A₄	{[0.33,0.57],[0.64,0.81]}	{[0.47,0.62],[0.54,0.69]}	{[0.42,0.70],[0.60,0.65]}	{[0.65,0.80],[0.55,0.78]}	{[0.22,0.55],[0.55,0.90]}
A₅	{[0.15,0.25],[0.60,0.85]}	{[0.30,0.54],[0.53,0.60]}	{[0.47,0.63],[0.50,0.65]}	{[0.50,0.65],[0.40,0.60]}	{[0.20,0.45],[0.35,0.66]}

区域	C₁	C₂	C₃	C₄	C₅
A₁	{[0.30,0.65],[0.25,0.50]}	{[0.30,0.70],[0.65,0.84]}	{[0.20,0.63],[0.50,0.75]}	{[0.15,0.28],[0.55,0.80]}	{[0.17,0.32],[0.70,0.90]}
A₂	{[0.45,0.75],[0.20,0.35]}	{[0.70,0.83],[0.50,0.75]}	{[0.35,0.65],[0.30,0.85]}	{[0.41,0.62],[0.80,0.91]}	{[0.10,0.35],[0.30,0.75]}
A₃	{[0.33,0.62],[0.50,0.65]}	{[0.35,0.76],[0.55,0.80]}	{[0.50,0.86],[0.20,0.30]}	{[0.55,0.83],[0.42,0.74]}	{[0.40,0.75],[0.30,0.55]}
A₄	{[0.50,0.65],[0.34,0.53]}	{[0.30,0.75],[0.55,0.80]}	{[0.22,0.45],[0.70,0.82]}	{[0.55,0.70],[0.65,0.85]}	{[0.32,0.65],[0.72,0.83]}
A₅	{[0.15,0.45],[0.55,0.83]}	{[0.32,0.65],[0.43,0.70]}	{[0.75,0.84],[0.44,0.65]}	{[0.60,0.75],[0.32,0.40]}	{[0.20,0.41],[0.30,0.65]}

区域	C₁	C₂	C₃	C₄	C₅
A₁	{[0.50,0.75],[0.22,0.55]}	{[0.37,0.68],[0.55,0.80]}	{[0.24,0.65],[0.44,0.77]}	{[0.16,0.35],[0.55,0.84]}	{[0.15,0.41],[0.65,0.82]}
A₂	{[0.32,0.74],[0.21,0.36]}	{[0.48,0.72],[0.40,0.76]}	{[0.23,0.66],[0.33,0.85]}	{[0.27,0.61],[0.72,0.87]}	{[0.13,0.42],[0.30,0.55]}
A₃	{[0.30,0.65],[0.43,0.69]}	{[0.48,0.71],[0.50,0.78]}	{[0.52,0.89],[0.25,0.45]}	{[0.42,0.73],[0.50,0.84]}	{[0.42,0.85],[0.34,0.65]}
A₄	{[0.35,0.58],[0.43,0.65]}	{[0.32,0.47],[0.59,0.93]}	{[0.20,0.45],[0.67,0.82]}	{[0.45,0.76],[0.60,0.82]}	{[0.52,0.75],[0.63,0.81]}
A₅	{[0.12,0.55],[0.56,0.85]}	{[0.30,0.75],[0.40,0.70]}	{[0.57,0.75],[0.53,0.67]}	{[0.65,0.87],[0.30,0.50]}	{[0.23,0.45],[0.35,0.75]}

区域	C₁	C₂	C₃	C₄	C₅
A₁	0.1986	0.2087	0.1982	0.2107	0.2151
A₂	0.1911	0.1758	0.2141	0.2092	0.2003
A₃	0.1933	0.2024	0.1877	0.1823	0.1805
A₄	0.2063	0.2039	0.2017	0.1961	0.2065
A₅	0.2107	0.2092	0.1983	0.2017	0.1976

区域	C₁	C₂	C₃	C₄	C₅
A₁	0.1976	0.2032	0.2031	0.2039	0.2114
A₂	0.1903	0.1891	0.2072	0.2123	0.2004
A₃	0.2017	0.2003	0.1921	0.1950	0.1817
A₄	0.1963	0.2012	0.2082	0.2033	0.2072
A₅	0.2141	0.2062	0.1894	0.1855	0.1993

A Comprehensive Evaluation Method Based on Extended Interval-Valued Fermatean Fuzzy Prospect Theory

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区域	C₁	C₂	C₃	C₄	C₅
A₁	0.1936	0.1999	0.2029	0.2095	0.2055
A₂	0.1921	0.1949	0.2065	0.2084	0.2067
A₃	0.2010	0.1975	0.1834	0.2022	0.1860
A₄	0.2000	0.2128	0.2110	0.2009	0.1991
A₅	0.2133	0.1949	0.1962	0.1790	0.2027

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