毕达哥拉斯犹豫模糊集多属性决策研究

doi:10.12305/j.issn.1001-506X.2024.03.24

Abstract

Abstract:

In view of the multi-attribute decision-making problem in which the attributes are interrelated and the evaluation information is Pythagorean hesitation fuzzy information, first of all, by studying the influence of hesitation on the decision-making results, a new Pythagorean hesitation fuzzy set score function is proposed to solve the shortcomings of the existing score functions. Secondly, a least common multiple standardization principle is proposed to solve the defect that the existing methods are easy to introduce errors. Finally, for the multi-attribute decision-making problem of attribute association, based on λ-fuzzy measure and Choquet integral, an extended interative multi-criteria decision-making (TODIM) method is put forward, which not only solves the problem of criteria interaction, but also reflects the psychological behavior characteristics of decision makers through prospect theory. The correctness and effectiveness of the proposed algorithm are verified through case analysis and sensitivity analysis.

Key words: Pythagorean hesitation fuzzy set, score function, least common multiple normalization principle, attribute association, interative multi-criteria decision-making (TODIM) method

CLC Number:

C934

Xin GUAN, Ying LIU. Research on multi-attribute decision-making for Pythagorean hesitation fuzzy sets[J]. Systems Engineering and Electronics, 2024, 46(3): 982-991.

Figures/Tables 9

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References 29

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物流公司	C₁	C₂	C₃	C₄
A₁	〈{0.3, 0.8}, {0.4}〉	〈{0.6, 0.8}, {0.4, 0.5}〉	〈{0.7, 0.8}, {0.4, 0.5}〉	〈{0.5, 0.7, 0.8}, {0.4}〉
A₂	〈{0.7, 0.8}, {0.3, 0.4}〉	〈{0.3, 0.4, 0.5}, {0.7}〉	〈{0.3, 0.4}, {0.7, 0.8}〉	〈{0.6, 0.7}, {0.3, 0.4}〉
A₃	〈{0.4, 0.5}, {0.6}〉	〈{0.4, 0.5, 0.6}, {0.5}〉	〈{0.7, 0.8}, {0.4, 0.5}〉	〈{0.8, 0.9}, {0.3}〉
A₄	〈{0.5, 0.6}, {0.2, 0.3}〉	〈{0.7}, {0.4, 0.5}〉	〈{0.5, 0.6, 0.7}, {0.6}〉	〈{0.7, 0.8}, {0.2, 0.3}〉

属性组合	重要度	属性组合	重要度
ϕ	0	{C₂, C₃}	0.808 5
{C₁}	0.700 0	{C₂, C₄}	0.850 3
{C₂}	0.600 0	{C₃, C₄}	0.808 5
{C₃}	0.500 0	{C₁, C₂, C₃}	0.958 7
{C₄}	0.600 0	{C₁, C₂, C₄}	0.972 0
{C₁, C₂}	0.892 0	{C₁, C₃, C₄}	0.958 7
{C₁, C₃}	0.860 0	{C₂, C₃, C₄}	0.937 2
{C₁, C₄}	0.892 0	{C₁, C₂, C₃, C₄}	1

方法		全局比较值/贴近度	排序结果
传统TODIM法		ξ(x₁)=1, ξ(x₂)=0, ξ(x₃)=0.601 6, ξ(x₄)=0.743 7	A₁＞A₄＞A₃＞A₂
TOPSIS方法	D_PHFWA	δ(x₁)=0.549, δ(x₂)=0.281, δ(x₃)=0.654, δ(x₄)=0.592	A₃＞A₄＞A₁＞A₂
	D_PHFOWA	δ(x₁)=0.671, δ(x₂)=0.208, δ(x₃)=0.619, δ(x₄)=0.622	A₁＞A₄＞A₃＞A₂
	D_GPHFHWA	δ(x₁)=0.703, δ(x₂)=0.047, δ(x₃)=0.679, δ(x₄)=0.603	A₁＞A₃＞A₄＞A₂
本文算法		ξ(x₁)=1, ξ(x₂)=0, ξ(x₃)=0.801 6, ξ(x₄)=0.772 5	A₁＞A₃＞A₄＞A₂

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Research on multi-attribute decision-making for Pythagorean hesitation fuzzy sets

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