基于改进得分函数和前景理论的区间值毕达哥拉斯模糊多属性决策

doi:10.12305/j.issn.1001-506X.2022.11.21

Abstract

Abstract:

Decision makers' preference and risk avoidance are normally ignored in the interval-valued Pythagorean fuzzy multi-attribute decision making. The existing score function skips the interval-valued hesitancy, which affects the decision making. To address this problem, an interval-valued Pythagorean fuzzy multi-attribute decision making method is put forward on the basis of improved score function and prospect theory. Firstly, the existing score function for interval-valued Pythagorean fuzzy set (IVPFS) is further analyzed to define an improved score function and prove its theorems and properties. Secondly, the improved score function is applied in the interval-valued Pythagorean fuzzy multi-attribute decision making to obtain the improved score function for each alternative with different attributes. The technique for order preference by similarity to an ideal solution (TOPSIS) is employed to determine the score function sets for the positive and negative ideal alternatives. Thirdly, prospect theory is introduced with prospect value function to describe a decision maker's subjective perception of gains and losses, and determine the comprehensive gains and losses of each alternative. The attribute weight is combined with the comprehensive gain-loss ratio of each alternative to find out the optimal alternative through comparison. Fourthly, the improved method is proved to be correct and accurate in an example, and the results of the comparison analysis with the original score function are demonstrated. This provides a new technical approach to multi-attribute decision making.

Key words: interval-valued Pythagorean fuzzy set, score function, prospect theory, multi-attribute decision making, ideal point method

CLC Number:

N945

Dongliang YIN, Guoheng CUI, Xiaoying HUANG, Huan ZHANG. Interval-valued Pythagorean fuzzy multi-attribute decision-making based on improved score function and prospect theory[J]. Systems Engineering and Electronics, 2022, 44(11): 3463-3469.

Figures/Tables 4

Table 1

Table 2

Table 3

Fig.1

References 25

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备选方案	A₁	A₂	A₃	A₄	A₅
X₁	([0.2, 0.6], [0.3, 0.5])	([0.3, 0.4], [0.5, 0.8])	([0.1, 0.3], [0.3, 0.7])	([0.5, 0.7], [0.6, 0.7])	([0.1, 0.2], [0.7, 0.8])
X₂	([0.7, 0.8], [0, 0.2])	([0.5, 0.7], [0.5, 0.6])	([0.6, 0.8], [0.3, 0.4])	([0.3, 0.4], [0.3, 0.4])	([0.4, 0.5], [0.3, 0.5])
X₃	([0.1, 0.2], [0.7, 0.8])	([0, 0.4], [0.6, 0.9])	([0.2, 0.4], [0.5, 0.6])	([0.1, 0.4], [0.6, 0.8])	([0.2, 0.5], [0.7, 0.8])
X₄	([0.3, 0.5], [0.5, 0.8])	([0.2, 0.4], [0.3, 0.4])	([0.3, 0.6], [0.5, 0.6])	([0.5, 0.7], [0.1, 0.3])	([0.4, 0.5], [0.2, 0.4])

参数	备选项目
参数	X₁	X₂	X₃	X₄
Φ⁺(X_i)	0.723 6	1.999 1	0.107 2	1.433 6
Φ^－(X_i)	3.524 9	0.467 8	4.712 6	2.061 0
τ_i	0.205 3	4.273 7	0.022 8	0.695 6

参数	备选项目
参数	X₁	X₂	X₃	X₄
Φ⁺(X_i)^*	0.484 8	1.092 5	0.255 0	0.890 4
Φ^－(X_i)^*	2.271 7	0.883 6	3.009 0	1.209 1
τ_i^*	0.213 4	1.110 7	0.084 7	0.736 4

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Interval-valued Pythagorean fuzzy multi-attribute decision-making based on improved score function and prospect theory

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