面向群体共识的三阶段犹豫模糊型信息融合方法研究

doi:10.12305/j.issn.1001-506X.2021.12.23

Abstract

Abstract:

Individual consistency check, group preference aggregation and group consensus improvement are three key stages of group consensus reaching process (CRP). High degree of consistency and consensus and low consensus cost are important decision-making goals in the three stages of group CRP. By analysing the relation influence of the three stages of group consensus building process on consensus, we construct optimization models for each decision stage. Firstly, considering the evaluation value characteristics of hesitation fuzzy preference relation (HFPR), we design the consistency check and improvement model with local standardization coefficient to provide reliable fuzzy judgment for group information aggregation. Subsequently, the group information aggregation of hesitating fuzzy preference relationship was implemented with proximity degree as induction value, and the consensus threshold is determined by statistical inference, which depicts group consensus level objectively. And then, when the level of group consensus is low, a consensus improvement model containing optimizing aggregation weight and minimum adjustment distance is designed, which effectively reduces the informationloss and iteration. Finally, a comparison with the existing approach is carried out to show the effectiveness and efficiency of the proposed method.

Key words: group consensus, hesitant fuzzy preference relation, consistency, preference adjustment

CLC Number:

C934

Xiwen TAO, Wenqi JIANG. Research on three-stage hesitant fuzzy information fusion method for group consensus[J]. Systems Engineering and Electronics, 2021, 43(12): 3603-3613.

Figures/Tables 16

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References 33

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专家	h^q₁₂	h^q₁₃	h^q₁₄
e₁	{0.3, 0.4}	{0.5, 0.7}	{0.4}
e₂	{0.3, 0.5}	{0.1, 0.2}	{0.5, 0.6, 0.7}
e₃	{0.3, 0.5}	{0.5, 0.7}	{0.7, 0.8}
e₄	{0.4, 0.5, 0.6}	{0.3, 0.4}	{0.5, 0.7}

专家	h^q₂₃	h^q₂₄	h^q₃₄
e₁	{0.7, 0.9}	{0.8, 0.9, 1.0}	{0.6, 0.7}
e₂	{0.7, 0.8}	{0.1, 0.5}	{0.5, 0.7}
e₃	{0.2, 0.4}	{0.5, 0.6}	{0.7, 0.8, 0.9}
e₄	{0.3}	{0.6, 0.7, 0.8}	{0.8, 0.9}

专家	CI₁₂^q	CI₁₃^q	CI₁₄^q	CI₂₃^q	CI₂₄^q	CI₃₄^q
e₁	0.94	0.96	0.90	0.98	0.95	0.95
e₂	0.96	0.89	0.90	0.86	0.87	0.97
e₃	0.90	0.93	0.96	0.94	0.95	0.96
e₄	0.98	0.97	0.96	0.98	0.97	0.98

专家	${\bar h}$^q₁₂	${\bar h}$^q₁₃	${\bar h}$^q₁₄
e₁	{0.3, 0.3, 0.4}	{0.5, 0.5, 0.7}	{0.4, 0.4, 0.4}
e₂	{0.3, 0.38, 0.5}	{0.1, 0.2, 0.2}	{0.5, 0.6, 0.7}
e₃	{0.3, 0.39, 0.5}	{0.5, 0.5, 0.7}	{0.7, 0.7, 0.8}
e₄	{0.4, 0.5, 0.6}	{0.3, 0.33, 0.4}	{0.5, 0.5, 0.7}

专家	${\bar h}$^q₂₃	${\bar h}$^q₂₄	${\bar h}$^q₃₄
e₁	{0.7, 0.7, 0.9}	{0.8, 0.9, 1.0}	{0.6, 0.6, 0.7}
e₂	{0.7, 0.73, 0.8}	{0.1, 0.5, 0.5}	{0.5, 0.7, 0.7}
e₃	{0.2, 0.29, 0.4}	{0.5, 0.6, 0.6}	{0.7, 0.8, 0.9}
e₄	{0.3, 0.3, 0.3}	{0.6, 0.7, 0.8}	{0.8, 0.9, 0.9}

专家	PI₁₂^q	PI₁₃^q	PI₁₄^q	PI₂₃^q	PI₂₄^q	PI₃₄^q
e₁	0.94	0.89	0.85	0.79	0.80	0.90
e₂	0.96	0.84	0.92	0.83	0.82	0.90
e₃	0.96	0.89	0.87	0.82	0.87	0.91
e₄	0.92	0.89	0.92	0.82	0.88	0.89

专家	ω^q₁₂	ω^q₁₃	ω^q₁₄	ω^q₂₃	ω^q₂₄	ω^q₃₄
e₁	0.18	0.44	0.15	0.15	0.15	0.22
e₂	0.44	0.15	0.44	0.44	0.17	0.18
e₃	0.23	0.23	0.18	0.18	0.23	0.44
e₄	0.15	0.18	0.23	0.23	0.45	0.16

Research on three-stage hesitant fuzzy information fusion method for group consensus

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专家	ω′^q₁₂	ω′^q₁₃	ω′^q₁₄	ω′^q₂₃	ω′^q₂₄	ω′^q₃₄
e₁	0.10	0.67	0.08	0.08	0.08	0.15
e₂	0.67	0.08	0.67	0.67	0.10	0.10
e₃	0.15	0.15	0.10	0.10	0.15	0.67
e₄	0.08	0.10	0.15	0.15	0.67	0.08

算例	对比方法	e₁	e₂	e₃	e₄
算例1	文献[2, 33]	0.886 5	0.847 3	0.894 2	0.950 3
算例1	本文方法	0.901 0	0.857 9	0.903 3	0.955 5
算例2	文献[2, 33]	0.959 8	0.953 2	0.938 6	0.936 9
算例2	本文方法	0.965 4	0.963 2	0.943 7	0.943 2
算例3	文献[2, 33]	0.946 7	0.935 6	0.936 7	0.938 5
算例3	本文方法	0.951 7	0.943 2	0.945 7	0.941 7

算法	对比算法	满足阈值	调整距离
本文算法	算例1	×	0.125 6
	算例2	√	0
	算例3	√	0
文献[13]	算例1	×	0.823 4(θ=0.6)
	算例2	×	0.321 5(θ=0.8)
	算例3	×	0.298 7(θ=0.8)

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[3]	Xiwen TAO, Wenqi JIANG. Three-stage consensus improvement model under interval-valued intuitionistic multi-criteria group decision-making environment based on adjustment cost [J]. Systems Engineering and Electronics, 2020, 42(11): 2570-2580.
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专家	h^q₁₂	h^q₁₃	h^q₁₄
e₁	{0.52, 0.60}	{0.30, 0.60}	{0.27, 0.30, 0.80}
e₂	{0.42, 0.70}	{0.31, 0.45, 0.50}	{0.27, 0.55}
e₃	{0.26, 0.40, 0.55}	{0.60, 0.70}	{0.20, 0.55}
e₄	{0.22, 0.58}	{0.25, 0.50}	{0.45, 0.60, 0.70}

专家	${\bar h}$^q₂₃	${\bar h}$^q₂₄	${\bar h}$^q₃₄
e₁	{0.22, 0.53, 0.73}	{0.30, 0.60}	{0.30, 0.78}
e₂	{0.35, 0.55}	{0.36, 0.57}	{0.63, 0.80}
e₃	{0.30, 0.45}	{0.25, 0.30, 0.45}	{0.48, 0.55, 0.61}
e₄	{0.52, 0.63, 0.78}	{0.26, 0.56}	{0.25, 0.45, 0.66}

专家	h^q₁₂	h^q₁₃	h^q₁₄
e₁	{0.25, 0.40}	{0.25, 0.35}	{0.30, 0.46, 0.50}
e₂	{0.15, 0.30}	{0.15, 0.15, 0.15}	{0.25, 0.45}
e₃	{0.35, 0.45, 0.55}	{0.60, 0.80}	{0.52, 0.63}
e₄	{0.61, 0.84}	{0.15, 0.50}	{0.20, 0.40, 0.55}

专家	${\bar h}$^q₂₃	${\bar h}$^q₂₄	${\bar h}$^q₃₄
e₁	{0.37, 0.43, 0.50}	{0.28, 0.38}	{0.25, 0.30}
e₂	{0.10, 0.25}	{0.65, 0.78}	{0.46, 0.53}
e₃	{0.53, 0.76}	{0.12, 0.33, 0.65}	{0.12, 0.23, 0.30}
e₄	{0.35, 0.35, 0.35}	{0.46, 0.72}	{0.43, 0.50}