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

摘要/Abstract

摘要：

在区间值毕达哥拉斯模糊环境下的多属性决策中, 针对决策过程一般未考虑决策人偏好习惯和风险规避的问题, 同时为解决现有得分函数忽略区间犹豫度对决策影响的情况, 提出了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方法。首先, 对区间值毕达哥拉斯模糊集(interval-valued Pythagorean fuzzy set, IVPFS)现有得分函数深入分析, 定义一种改进后的新得分函数, 并证明其相关定理和性质。其次, 将新得分函数应用于区间值毕达哥拉斯模糊多属性决策问题中, 得出各备选方案在各属性下的新得分函数, 基于熵权逼近理想解排序法(technique for order preference by similarity to ideal soution, TOPSIS)确定正、负理想方案的得分函数集。然后, 引入前景理论利用前景价值函数对决策人由于损益表现出的主观感受进行描述, 得出备选方案的综合损益值, 结合各属性权重融合不同方案的综合损益比, 通过对比综合损益比大小得出最优方案。最后，利用算例验证了该改进方法的正确性和有效性, 展示了与原得分函数的对比分析结果, 为多属性决策问题提供了新的技术途径。

关键词: 区间值毕达哥拉斯模糊集, 得分函数, 前景理论, 多属性决策, 理想点法

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

中图分类号:

N945

尹东亮, 崔国恒, 黄晓颖, 张欢. 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[J]. 系统工程与电子技术, 2022, 44(11): 3463-3469.

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.

图/表 4

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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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