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

摘要/Abstract

摘要：

针对专家决策带有犹豫性和偏好性的多属性决策问题,提出一种基于概率犹豫-直觉模糊熵和证据推理的决策方法。在概率犹豫模糊集和犹豫直觉模糊集的基础上,考虑专家偏好,提出一种新的概率犹豫-直觉模糊集,对混合型属性的决策信息进行统一描述;基于犹豫熵和直觉模糊熵,提出概率犹豫-直觉模糊熵对决策信息的犹豫性和不确定性进行测度,并确定属性权重;采用证据推理算法进行属性信息的集结,并基于效用理论对方案进行排序。通过算例对比分析验证了所提方法得到的决策结果更为科学、准确。

关键词: 多属性决策, 概率犹豫-直觉模糊集, 概率犹豫-直觉模糊熵, 证据推理

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

中图分类号:

TP181

李岩, 陈云翔, 罗承昆, 蔡忠义. 基于概率犹豫-直觉模糊熵和证据推理的多属性决策方法[J]. 系统工程与电子技术, 2020, 42(5): 1116-1123.

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.

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参考文献 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