基于q阶orthopair模糊集和参考理想法的多准则决策方法

doi:10.16381/j.cnki.issn1003-207x.2020.1456

Abstract

Abstract:

Among traditional decision methods， such as TOPSIS and VIKOR， the maximum or minimum value is considered to be the best choice， but the best choice may occur between the maximum and minimum value in the real world， such as the temperature suitable for plant growth. Meanwhile， q-rung orthopair fuzzy set （q-ROFS） can help decision-makers express their opinions freely and comprehensively in the face of complex decision-making problems.To solve the problems of unreasonable determination of ideal solution and rank reversal in existing decision-making methods， a multi-criteria decision-making method based on q-ROFS and reference ideal method （RIM） is proposed. Firstly， the q-rung orthopair fuzzy （q-ROF） possibility degree and q-ROFS cross entropy are defined respectively， and their related properties are discussed； Secondly， the traditional RIM is extended in the q-ROF environment， and a multi-criteria decision-making model based on q-ROFRIM is built， where the q-ROF possibility degree is used to determine the optimal weight of the criteria， and the q-ROF cross entropy， as a measure of the information difference degree of q-ROF， is used to replace the distance measure in the traditional RIM. Finally， an example analysis illustrates the feasibility and effectiveness of the proposed method. In addition， comparison with previous methods shows that the proposed method not only makes the decision process more scientific and reasonable， but also avoids the rank reversal problem.

Key words: q-rung orthopair fuzzy set, q-ROF possibility, q-ROFS cross entropy, q-ROFRIM, multi-criteria decision making

CLC Number:

C934

Hao-lun WANG,Fa-ming ZHANG,WAN-YAN Xiao-pan,Xue HAN. A Multi-Criteria Decision-Making Method Based on q-Rung Orthopair Fuzzy Set and Reference Ideal Method[J]. Chinese Journal of Management Science, 2023, 31(10): 245-253.

Figures/Tables 5

准则	$R ? j$	$I ? j$
C₁	[<0.20,0.98>,<0.98,0.20>]	[<0.87,0.35>,<0.98,0.20>]
C₂	[<0.20,0.98>,<0.98,0.20>]	[<0.87,0.35>,<0.98,0.20>]
C₃	[<0.20,0.98>,<0.98,0.20>]	[<0.70,0.40>,<0.98,0.20>]
C₄	[<0.20,0.98>,<0.98,0.20>]	[<0.87,0.25>,<0.98,0.20>]

方法	A₁	A₂	A₃	A₄	排序
q-ROFWA	sc(A₁)=0.567	sc(A₂)=0.701	sc(A₃)=0.665	sc(A₄)=0.703	$A 4 > A 2 > A 3 > A 1$
q-ROFWG	sc(A₁)=0.512	sc(A₂)=0.656	sc(A₃)=0.645	sc(A₄)=0.647	$A 2 > A 4 > A 3 > A 1$
q-ROFTOPSIS	CI(A₁)=0.102	CI(A₂)=0.555	CI(A₃)=0.476	CI(A₄)=0.598	$A 4 > A 2 > A 3 > A 1$
q-ROFVIKOR	Q(A₁)=1.000	Q(A₂)=0.000	Q(A₃)=0.486	Q(A₄)=0.436	$A 2 > A 4 > A 3 > A 1$
本文方法	RI₁=0.806	RI₂=0.938	RI₃=0.873	RI₄=0.909	$A 2 > A 4 > A 3 > A 1$

方法	A₁	A₂	A₃	A₄	A₅	排序
q-ROFWA	sc(A₁)=0.580	sc(A₂)=0.690	sc(A₃)=0.684	sc(A₄)=0.686	sc(A₅)=0.657	$A 2 > A 4 > A 3 > A 5 > A 1$
q-ROFWG	sc(A₁)=0.533	sc(A₂)=0.637	sc(A₃)=0.659	sc(A₄)=0.627	sc(A₅)=609	$A 3 > A 2 > A 4 > A 5 > A 1$
q-ROFTOPSIS	CI(A₁)=0.195	CI(A₂)=0.548	CI(A₃)=0.558	CI(A₄)=0.599	CI(A₅)=0.467	$A 4 > A 3 > A 2 > A 5 > A 1$
本文方法	RI₁=0.802	RI₂=0.934	RI₃=0.871	RI₄=0.911	RI₅=0.810	$A 2 > A 4 > A 3 > A 5 > A 1$

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方案	I_i⁺	I_i^-	RI_i	排序
A₁	0.103	0.430	0.806	4
A₂	0.032	0.479	0.938	1
A₃	0.064	0.439	0.873	3
A₄	0.047	0.469	0.909	2

A Multi-Criteria Decision-Making Method Based on q-Rung Orthopair Fuzzy Set and Reference Ideal Method

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