概率q阶犹豫模糊TODIM方法及其应用

doi:10.6040/j.issn.1671-9352.0.2022.260

Abstract

Abstract:

To measure differences in probabilistic q-rung hesitant fuzzy information, a novel measure of the probabilistic q-rung hesitant fuzzy distance is proposed based on the score function and overall hesitancy. The properties of this measure are discussed. A probabilistic q-rung hesitant fuzzy TODIM method is proposed based on the new distance measure. Finally, a practical example is presented to illustrate the reasonableness and effectiveness of the proposed method, and a sensitivity analysis is performed.

Key words: probabilistic q-rung hesitant fuzzy set, distance measure, TODIM, multi-attribute decision-making

CLC Number:

O159

Yu ZHOU,Ligang ZHOU,Zhichao LIN,Xin XU. Probabilistic q-rung hesitant fuzzy TODIM method and its application[J].JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(6): 9-17.

Figures/Tables 4

Table 1

Table 2

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References 24

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	C₁	C₂	C₃	C₄
X₁	{〈0.5, 0.2〉(0.6), 〈0.6, 0.3〉(0.4)}	{〈0.4, 0.3〉(1)}	{〈0.2, 0.5〉(0.3), 〈0.3, 0.6〉(0.7)}	{〈0.6, 0.1〉(0.5), 〈0.7, 0.2〉(0.5)}
X₂	{〈0.3, 0.3〉(0.3), 〈0.5, 0.3〉(0.4), 〈0.5, 0.4〉(0.3)}	{〈0.5, 0.1〉(0.3), 〈0.6, 0.2〉(0.5), 〈0.7, 0.1〉(0.2)}	{〈0.4, 0.2〉(0.5), 〈0.5, 0.2〉(0.3), 〈0.6, 0.3〉(0.2)}	{〈0.5, 0.2〉(0.6) 〈0.7, 0.2〉(0.4)}
X₃	{〈0.3, 0.2〉(0.4), 〈0.7, 0.2〉(0.6)}	{〈0.6, 0.2〉(0.5), 〈0.7, 0.2〉(0.5)}	{〈0.1, 0.3〉(0.2), 〈0.2, 0.5〉(0.2), 〈0.3, 0.6〉(0.6)}	{〈0.2, 0.4〉(0.6), 〈0.3, 0.6〉(0.4)}
X₄	{〈0.3, 0.2〉(0.4), 〈0.4, 0.3〉(0.3), 〈0.5, 0.3〉(0.3)}	{〈0.4, 0.1〉(0.6), 〈0.6, 0.3〉(0.4)}	{〈0.3, 0.3〉(0.4), 〈0.4, 0.4〉(0.6)}	{〈0.5, 0.1〉(0.6), 〈0.6, 0.2〉(0.4)}
X₅	{〈0.3, 0.1〉(0.7), 〈0.5, 0.2〉(0.3)}	{〈0.4, 0.1〉(0.6), 〈0.6, 0.3〉(0.4)}	{〈0.3, 0.5〉(0.4), 〈0.4, 0.2〉(0.2), 〈0.5, 0.2〉(0.4)}	{〈0.5, 0.2〉(1)}

	C₁	C₂	C₃	C₄
X₁	{〈0.5, 0.2〉(0.6), 〈0.5, 0.2〉(0), 〈0.6, 0.3〉(0.4)}	{〈0.4, 0.3〉(0), 〈0.4, 0.3〉(0), 〈0.4, 0.3〉(1)}	{〈0.3, 0.6〉(0.7), 〈0.2, 0.5〉(0), 〈0.2, 0.5〉(0.3)}	{〈0.6, 0.1〉(0.5), 〈0.6, 0.1〉(0), 〈0.7, 0.2〉(0.5)}
X₂	{〈0.3, 0.3〉(0.3), 〈0.5, 0.4〉(0.3), 〈0.5, 0.3〉(0.4)}	{〈0.5, 0.1〉(0.3), 〈0.6, 0.2〉(0.5), 〈0.7, 0.1〉(0.2)}	{〈0.4, 0.2〉(0.5), 〈0.5, 0.2〉(0.3), 〈0.6, 0.3〉(0.2)}	{〈0.5, 0.2〉(0.6) 〈0.5, 0.2〉(0), 〈0.7, 0.2〉(0.4)}
X₃	{〈0.3, 0.2〉(0.4), 〈0.3, 0.2〉(0), 〈0.7, 0.2〉(0.6)}	{〈0.6, 0.2〉(0.5), 〈0.6, 0.2〉(0), 〈0.7, 0.2〉(0.5)}	{〈0.3, 0.6〉(0.6), 〈0.2, 0.5〉(0.2), 〈0.1, 0.3〉(0.2)}	{〈0.3, 0.6〉(0.4), 〈0.2, 0.4〉(0), 〈0.2, 0.4〉(0.6)}
X₄	{〈0.3, 0.2〉(0.4), 〈0.4, 0.3〉(0.3), 〈0.5, 0.3〉(0.3)}	{〈0.4, 0.1〉(0.6), 〈0.4, 0.1〉(0), 〈0.6, 0.3〉(0.4)}	{〈0.3, 0.3〉(0.4), 〈0.3, 0.3〉(0), 〈0.4, 0.4〉(0.6)}	{〈0.5, 0.1〉(0.6), 〈0.5, 0.1〉(0), 〈0.6, 0.2〉(0.4)}
X₅	{〈0.3, 0.1〉(0.7), 〈0.3, 0.1〉(0), 〈0.5, 0.2〉(0.3)}	{〈0.4, 0.1〉(0.6), 〈0.4, 0.1〉(0), 〈0.6, 0.3〉(0.4)}	{〈0.3, 0.5〉(0.4), 〈0.4, 0.2〉(0.2), 〈0.5, 0.2〉(0.4)}	{〈0.5, 0.2〉(0), 〈0.5, 0.2〉(0), 〈0.5, 0.2〉(1)}

Probabilistic q-rung hesitant fuzzy TODIM method and its application

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