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

Abstract

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)

CLC Number:

C934

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.

Figures/Tables 12

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References 36

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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)

Linguistic intuitionistic fuzzy PROMETHEE multi-attribute group decision-making based on the probability degree

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决策方法	数值结果	排序
LIFWA算子^[9]	Ls(γ₁)=3.711 2, Ls(γ₂)=4.734 9, Ls(γ₃)=3.137 1, Ls(γ₄)=3.552 2	$ {{A}_{2}}\succ {{A}_{1}}\succ {{A}_{4}}\succ {{A}_{3}}$
可能度^[15]	$ \bar{w}_{1}=0.2917, \bar{w}_{2}=0.375, \bar{w}_{3}=0.125, \bar{w}_{4}=0.2083$	${{A}_{2}}\succ {{A}_{1}}\succ {{A}_{4}}\succ {{A}_{3}} $
LIPFOWA算子^[21]	S(p₁)=s_{6.152 6}, S(p₂)=s_{6.419 4}, S(p₃)=s_{6.007 3}, S(p₄)=s_{6.004 3}	${{A}_{2}}\succ {{A}_{1}}\succ {{A}_{3}}\succ {{A}_{4}} $
证据理论^[24]	Bel(a₁)=0.993 9, Bel(a₂)=0.998 8, Bel(a₃)=0.985 3, Bel(a₄)=0.992 8	$ {{A}_{2}}\succ {{A}_{1}}\succ {{A}_{4}}\succ {{A}_{3}}$
本文方法	Φ(A₁)=－0.125, Φ(A₂)=1.285, Φ(A₃)=－0.996, Φ(A₄)=－0.166	$ {{A}_{2}}\succ {{A}_{1}}\succ {{A}_{4}}\succ {{A}_{3}}$

决策方法	属性权重	决策者权重	集结方法
LIFWA算子^[9]	已知	已知	LIFWA算子
可能度^[15]	已知	已知	GLIFWA算子
LIPFOWA算子^[21]	根据得分函数得到	根据得分函数得到	LIPFOWA算子
证据理论^[24]	比较主观权重和客观权重距离得到	比较主观权重和客观权重距离得到	证据理论
本文方法	根据改进可能度计算	根据偏好关系和修正系数调整	PROMETHEE

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