基于前景理论和属性相关的概率语言SIR多属性群决策方法及应用

doi:10.16381/j.cnki.issn1003-207x.2023.2030

摘要/Abstract

摘要：

在实际多属性群决策中，信息模糊、属性相关以及个体偏好差异普遍存在，如何将这些实际问题提炼为理论问题，并提出最佳备选方案有重要意义。本文基于概率语言提出了一种基于Choquet积分和前景理论的SIR（优劣势排序）多属性群决策方法。首先，利用概率语言Choquet积分算子集结不同决策者的决策信息，以构造群体决策矩阵。其次，考虑决策者风险偏好差异，将前景理论引入经典SIR法的偏好差别函数中，提出了综合前景优劣势度。然后，针对属性相关以及属性权重求解问题，进一步结合Choquet积分和属性综合权重，构造出一种新的能充分刻画方案间差异的综合前景优劣势流。最后，以跨境电商的海外选址问题为例，对比验证所提方法的可行性和有效性。结果表明，本文提出的多属性决策方法能综合考虑决策环境的主客观不确定性，是对经典SIR法在不确定环境中的进一步拓展研究。

关键词: 概率语言术语集, 前景理论, 属性相关, SIR法, Choquet积分

Abstract:

In real life， it’s inevitable that the multi-attribute group decision-making has a series of problems such as fuzzy information， individual preferences and attribute association， which makes it difficult for decision-makers to accurately determine which alternative is the best alternative. How to abstract these practical decision-making problems into theoretical problems， and select the best alternative is the focus of this paper. To solve such a kind of problems， a multi-attribute group decision-making SIR （superiority and inferiority ranking） method based on Choquet integral and prospect theory is proposed. Firstly， a probabilistic linguistic Choquet integral operator is used to aggregate the decision-making information， and construct the group decision-making matrix. After that， considering that the SIR method ignores the risk preferences of experts， the proposed approach introduces prospect theory into the SIR method to construct the comprehensive prospect superiority and inferiority index. Then， to address the problem of attribute association， Choquet integral and attribute comprehensive weights are used to construct a new comprehensive prospect superiority and inferiority flow that can characterize the difference of alternatives. And then， alternatives are sorted according to the sorting rules of the SIR method. Finally， the feasibility and effectiveness of the proposed approach is indicated by an example of overseas location problem for cross-border e-commerce. The conclusion of this article is as follows：（1） Decision makers' risk preferences and linguistic preferences significantly affect the ranking of the alternatives， for example， risk aversion decision makers will tend to choose conservative strategies. （2） Compared with the classic SIR method and prospect theory， the proposed method can more intuitively analyze the differences between alternatives through pairwise comparison. In a word， the proposed approach can comprehensively consider the subjective and objective uncertainties of the decision-making environment， and is a further extension of the classic SIR method.

Key words: probabilistic linguistic term set, prospect theory, attribute association, SIR method, Choquet integral

中图分类号:

F273

杨洁,蔡志坤,郑智文, 等. 基于前景理论和属性相关的概率语言SIR多属性群决策方法及应用[J]. 中国管理科学, 2026, 34(4): 77-88.

Jie Yang,Zhikun Cai,Zhiwen Zheng, et al. A Prospect Theory and Attribute Association Based Probabilistic Linguistic Fuzzy SIR Method for Multi-attribute Group Decision-making and Its Application[J]. Chinese Journal of Management Science, 2026, 34(4): 77-88.

图/表 5

表1

不同偏好差别函数对比"

	偏好差别函数	结果
基于各类一般性准则的偏好差别函数^[9,11]	确定准则： $P j (x i, x t) = 0, d (L t j (p), L i j (p)) ≤ 0 1, d (L t j (p), L i j (p)) > 0$	$S 1 (x 1) = 1,$ $S 1 (x 2) = 2,$ $S 1 (x 3) = 0$
	U型准则： $P j (x i, x t) = 0, d (L t j (p), L i j (p)) ≤ u d (L i j - (p), L i j + (p)) 1, d (L t j (p), L i j (p)) > u d (L i j - (p), L i j + (p))$	$S 1 (x 1) = 0,$ $S 1 (x 2) = 2,$ $S 1 (x 3) = 0$
	线性准则： $P j (x i, x t) = 0, d (L i j (p), L t j (p)) ≤ 0 d (L i j (p), L t j (p)) / θ, 0 < d (L i j (p), L t j (p)) ≤ u d (L i j - (p), L i j + (p)) 1, d (L t j (p), L i j (p)) > u d (L i j - (p), L i j + (p))$	$S 1 (x 1) = 0.6,$ $S 1 (x 2) = 2,$ $S 1 (x 3) = 0$
本文所提偏好差别函数	$P j (x i, x t) = V + (x i, x t), L i j (p) ≻ L t j (p) V - (x i, x t), L i j (p) ≺ L t j (p) 0, 其他$	$S 1 (x 1) = 0 . 3 α κ + (0.3),$ $S 1 (x 2) = (1 . 1 α + 1) κ + (0.3),$ $S 1 (x 3) = 0$

表1

表2

图1

图2

表3

各方法比较"

文献	方法涉及	排序结果
[7]	前景理论、概率语言术语集、属性综合权重	$x 2 ≻ x 4 ≻ x 3 ≻ x 1$
[11]	PROMETHEE、概率语言术语集	$x 4 ≻ x 2 ≻ x 3 ≻ x 1$
[30]	概率语言术语集、TODIM法	$x 4 ≻ x 2 ≻ x 3 ≻ x 1$
本文方法	概率语言术语集、前景理论、属性相关、SIR法	$x 4 ≻ x 2 ≻ x 3 ≻ x 1$

表3

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