基于Vague集相似度量的多准则模糊决策方法

邓维斌, 许昌林, 樊自甫

系统工程理论与实践 ›› 2014, Vol. 34 ›› Issue (4) : 981-990.

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系统工程理论与实践 ›› 2014, Vol. 34 ›› Issue (4) : 981-990. DOI: 10.12011/1000-6788(2014)4-981
论文

基于Vague集相似度量的多准则模糊决策方法

    邓维斌1,2, 许昌林2, 樊自甫1
作者信息 +

Multi-criteria fuzzy decision making method based on similarity measures between vague sets

    DENG Wei-bin1,2, XU Chang-lin2, FAN Zi-fu1
Author information +
文章历史 +

摘要

在分析已有关于Vague值（集）相似度量方法存在不足的基础上，综合考虑Vague值区间端点间的距离、核距离以及未知部分对支持度和反对度的影响等主要因素，提出了一种新的Vague值（集）相似度量方法，并对其性质进行讨论. 通过与现有方法的比较，表明该方法具有很强的相似度区分能力. 最后将所提出的Vague值（集）相似度量用于多准则模糊决策中，通过最优化方法选取每个准则的最优权重，根据候选方案与理想方案在相应准则下相似度加权和的大小得出最佳方案. 通过实例分析，表明了这种方法的有效性和可行性.

Abstract

The inadequacies of existed similarity measures between vague values (sets) are analyzed. A new similarity measure between vague values (sets), which considers the distance of vague value interval endpoints, core distance and influence of unknown part on truth-membership function and false-membership function respectively, is proposed and the properties are discussed. The new method is illustrated by comparison with the present measure methods that it has stronger discrimination of similarity measures. Finally, the similarity measures between vague values (sets) are applied to multi-criteria fuzzy decision making. The linear programming method is constructed to generate optimal weights for every criteria and the best alternative is obtained by the weighted sum of similarity measures between each alternative and the idea alternative with respect to a set of criteria. Feasibility and effectiveness of the proposed method are illustrated using a numerical example.

关键词

多准则模糊决策 / Vague集 / 相似度量 / 线性规划

Key words

multi-criteria fuzzy decision making / vague sets / similarity measures / linear programming

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邓维斌 , 许昌林 , 樊自甫. 基于Vague集相似度量的多准则模糊决策方法. 系统工程理论与实践, 2014, 34(4): 981-990 https://doi.org/10.12011/1000-6788(2014)4-981
DENG Wei-bin , XU Chang-lin , FAN Zi-fu. Multi-criteria fuzzy decision making method based on similarity measures between vague sets. Systems Engineering - Theory & Practice, 2014, 34(4): 981-990 https://doi.org/10.12011/1000-6788(2014)4-981
中图分类号： C934   

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基金

国家自然科学基金（61309014）；国家社会科学基金（12XGL015，12BGL017）；教育部人文社科规划基金（11YJA63 0016）
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