基于概率犹豫-直觉模糊熵和证据推理的多属性决策方法

doi:10.3969/j.issn.1001-506X.2020.05.19

Abstract

Abstract:

For the multi-attribute decision making problems with hesitation and preference in expert decision-making, a decision making method based on probabilistic hesitant-intuitionistic fuzzy entropy and evidential reasoning is proposed. Based on the probabilistic hesitant fuzzy set and the hesitant intuitionistic fuzzy set, a new probabilistic hesitant-intuitionistic fuzzy set is proposed by considering the preference of experts and is used to describe uniformly the decision making information of the mixed attribute. Based on the hesitant entropy and the intuitionistic fuzzy entropy, the probabilistic hesitance-intuitionistic fuzzy entropy is proposed to measure the hesitance and uncertainty of decision making information, and it is used to determine the weight of each attribute. The evidential reasoning algorithm is used to aggregate the attribute information, and the schemes are arranged based on the utility theory. The comparison results of the numerical example analysis verify that the decision making results obtained by the proposed method are more scientific and accurate.

Key words: multi-attribute decision making, probabilistic hesitant-intuitionistic fuzzy set, probabilistic hesitant-intuitionistic fuzzy entropy, evidential reasoning

CLC Number:

TP181

Yan LI, Yunxiang CHEN, Chengkun LUO, Zhongyi CAI. Multi-attribute decision making method based on probabilistic hesitant-intuitionistic fuzzy entropy and evidential reasoning[J]. Systems Engineering and Electronics, 2020, 42(5): 1116-1123.

Figures/Tables 8

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References 30

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候选者	属性o₁
a₁	{0.55\|0.15, 0.65\|0.25, 0.76\|0.1, 0.8\|0.5}
a₂	{0.4\|0.25, 0.58\|0.25, 0.69\|0.25, 0.95\|0.25}
a₃	{0.3\|0.1, 0.5\|0.35, 0.6\|0.3, 0.68\|0.25}
a₄	{0.15\|0.1, 0.37\|0.15, 0.4\|0.25, 0.6\|0.25, 0.73\|0.25}

候选者	属性o₂
a₁	{0.2\|0.05, 0.3\|0.325, 0.4\|0.125, 0.65\|0.25, 0.75\|0.25}
a₂	{0.35\|0.25, 0.6\|0.075, 0.65\|0.25, 0.7\|0.35, 0.8\|0.075}
a₃	{0.45\|0.25, 0.55\|0.125, 0.56\|0.25, 0.66\|0.125, 0.85\|0.25}
a₄	{0.48\|0.4, 0.55\|0.25, 0.62\|0.1, 0.66\|0.25}

候选者	属性o₃
a₁	{0.55\|0.5, 0.75\|0.25, 0.8\|0.15, 0.94\|0.1}
a₂	{0.25\|0.25, 0.45\|0.375, 0.65\|0.375}
a₃	{0.45\|0.25, 0.55\|0.25, 0.68\|0.25, 0.75\|0.25}
a₄	{0.38\|0.25, 0.5\|0.125, 0.7\|0.125, 0.75\|0.25, 0.85\|0.25}

熵值	属性o₁	属性o₂	属性o₃
${\bar E}$_Hp1(o_j)	0.818 1	0.875 9	0.838 4
${\bar E}$_Hp2(o_j)	0.784 4	0.898 7	0.922 5
${\bar E}$_Hp3(o_j)	0.953 6	0.885 8	0.922 6
${\bar E}$_Hp4(o_j)	0.896 4	0.973 6	0.826 0
${\bar E}$_Hp(o_j)	0.863 1	0.908 5	0.877 4
${\bar E}$_Fp(o_j)	0.567 1	0.589 6	0.577 7

候选者	取值
候选者	$\hat{\beta}$₁	$\hat{\beta}$₂	$\hat{\beta}$_Θ	${\bar D}$(a_i)
a₁	0.712 2	0.178 8	0.109 0	0.533 4
a₂	0.631 3	0.223 2	0.145 5	0.408 1
a₃	0.632 4	0.270 8	0.096 8	0.361 6
a₄	0.609 8	0.269 8	0.120 4	0.340 0

Multi-attribute decision making method based on probabilistic hesitant-intuitionistic fuzzy entropy and evidential reasoning

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方法	排序结果
HPFO^aWA	a₁＞a₂＞a₃＞a₄
HPFOWA	a₂＞a₁＞a₃＞a₄
HPFOⁱWA	a₁＞a₃＞a₂＞a₄
QUALIFLEX	a₃＞a₄＞a₁＞a₂
PROMETHEE Ⅱ	a₃＞a₁＞a₄＞a₂
本文方法(θ≤0.73)	a₁＞a₂＞a₃＞a₄
本文方法(θ＞0.73)	a₁＞a₃＞a₂＞a₄

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