基于可能度的语言直觉模糊PROMETHEE多属性群决策

doi:10.12305/j.issn.1001-506X.2022.08.23

摘要/Abstract

摘要：

针对权重信息未知的语言直觉模糊多属性群决策问题, 提出了一种基于改进的可能度和偏好顺序结构评估法(preference ranking organization method for enrichment evaluations, PROMETHEE)的语言直觉模糊多属性群决策方法。首先，基于Atanassov偏序和犹豫度, 改进语言直觉模糊数的可能度, 并证明其具有互补性、传递性等良好性质。其次，基于改进的可能度, 通过最大化决策者在属性上的加权平方可能度, 构造多目标规划模型, 求得每位决策者的属性权重。然后，建立群体共识反馈模型, 提高群体共识度, 结合修正的偏好关系和决策者主观权重, 提出修正系数来确定决策者权重。最后，通过实证分析验证该方法的可行性和有效性。

关键词: 多属性群决策, 语言直觉模糊数, 可能度, 偏好顺序结构评估法

Abstract:

Aiming at the linguistic intuitionistic fuzzy multi-attribute group decision-making with unknown weight information, a new method for linguistic intuitionistic fuzzy multi-attribute group decision-making based on improved possibility degree and preference ranking organization method for enrichment evaluation (PROMETHEE) is established. Firstly, an improved possibility degree of linguistic intuitionistic fuzzy number is proposed based on Atanassov partial order and hesitation degree, which is proved to satisfy complementarity, transitivity and other good properties. Secondly, based on the improved probability, a multi-objective programming model is constructed to obtain the attribute weight of each decision maker by maximizing the weighted square probability of the decision-maker on the attribute. Then, a group consensus feedback model is established to improve the consensus degree of the group. Combined with the modified preference relation and the subjective weight of the decision maker, the adjusted coefficient is defined to determine the weight of decision-makers. Finally, the feasibility and effectiveness of the proposed method are verified by the empirical research.

Key words: multi-attribute group decision-making, linguistic intuitionistic fuzzy number, probability degree, preference ranking organization method for enrichment evaluations (PROMETHEE)

中图分类号:

C934

王雯琦, 江登英. 基于可能度的语言直觉模糊PROMETHEE多属性群决策[J]. 系统工程与电子技术, 2022, 44(8): 2581-2592.

Wenqi WANG, Dengying JIANG. Linguistic intuitionistic fuzzy PROMETHEE multi-attribute group decision-making based on the probability degree[J]. Systems Engineering and Electronics, 2022, 44(8): 2581-2592.

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文献	可能度公式计算结果
文献[5]	p(γ₁>γ₂)=0.33, p(γ₁>γ₃)=0.6, p(γ₁>γ₄)=1, p(γ₂>γ₃)=0.67, p(γ₂>γ₄)=1, p(γ₃>γ₄)=0.5
文献[6]	p(γ₁>γ₂)=0.67, p(γ₁>γ₃)=1, p(γ₁>γ₄)=0, p(γ₂>γ₃)=1, p(γ₂>γ₄)=0, p(γ₃>γ₄)=0
文献[7]	p(γ₁>γ₂)=0, p(γ₁>γ₃)=0.57, p(γ₁>γ₄)=1, p(γ₂>γ₃)=1, p(γ₂>γ₄)=1, p(γ₃>γ₄)=0.5
文献[15]	p(γ₁>γ₂)=0, p(γ₁>γ₃)=0.6, p(γ₁>γ₄)=1, p(γ₂>γ₃)=1, p(γ₂>γ₄)=1, p(γ₃>γ₄)=0.5
文献[23]	p(γ₂>γ₄)=-1, p(γ₃>γ₄)=-0.5
本文	p(γ₁>γ₂)=0, p(γ₁>γ₃)=0.7, p(γ₁>γ₄)=1, p(γ₂>γ₃)=1, p(γ₂>γ₄)=1, p(γ₃>γ₄)=0

	C₁	C₂	C₃	C₄	C₅
A₁	(s₇, s₁)	(s₆, s₂)	(s₄, s₃)	(s₇, s₁)	(s₅, s₂)
A₂	(s₆, s₂)	(s₅, s₂)	(s₆, s₁)	(s₆, s₂)	(s₇, s₁)
A₃	(s₆, s₁)	(s₅, s₃)	(s₇, s₁)	(s₅, s₁)	(s₃, s₄)
A₄	(s₅, s₂)	(s₇, s₁)	(s₄, s₃)	(s₆, s₁)	(s₄, s₄)

	C₁	C₂	C₃	C₄	C₅
A₁	(s₇, s₁)	(s₄, s₄)	(s₆, s₂)	(s₅, s₂)	(s₃, s₅)
A₂	(s₇, s₁)	(s₅, s₁)	(s₆, s₁)	(s₅, s₂)	(s₄, s₃)
A₃	(s₅, s₂)	(s₆, s₁)	(s₇, s₁)	(s₅, s₃)	(s₄, s₄)
A₄	(s₆, s₂)	(s₄, s₃)	(s₅, s₂)	(s₇, s₁)	(s₅, s₃)

	C₁	C₂	C₃	C₄	C₅
A₁	(s₆, s₁)	(s₅, s₂)	(s₃, s₄)	(s₇, s₁)	(s₅, s₂)
A₂	(s₇, s₁)	(s₆, s₂)	(s₇, s₁)	(s₆, s₂)	(s₅, s₁)
A₃	(s₅, s₃)	(s₅, s₂)	(s₆, s₁)	(s₄, s₃)	(s₃, s₁)
A₄	(s₆, s₂)	(s₇, s₁)	(s₅, s₁)	(s₅, s₂)	(s₅, s₃)

	C₁	C₂	C₃	C₄	C₅
A₁	(s₅, s₃)	(s₄, s₄)	(s₇, s₁)	(s₅, s₁)	(s₄, s₂)
A₂	(s₆, s₁)	(s₇, s₁)	(s₆, s₁)	(s₅, s₂)	(s₆, s₁)
A₃	(s₅, s₂)	(s₃, s₄)	(s₆, s₂)	(s₃, s₃)	(s₅, s₂)
A₄	(s₄, s₃)	(s₅, s₁)	(s₄, s₂)	(s₆, s₂)	(s₅, s₂)