Hesitant Fuzzy Linguistic Distance Measures and Its Application in Multiple Attribute Decision Making

doi:10.12005/orms.2023.0046

Abstract

Abstract: A series of new and more reasonable hesitant fuzzy linguistic distance measures are proposed to solve the problems of the existing hesitant fuzzy linguistic distance measures, such as not satisfying the directness, changing the original decision information and ignoring the difference of hesitance degree. Firstly, the limitations of the existing hesitant fuzzy linguistic distance measures are enumerated and analyzed. Secondly, the definition of hesitance degree of hesitant fuzzy linguistic is given, and a series of new distance measures, such as Euclidean distance, Hamming distance, Hamming-Hausdorff distance, Euclidean-Hausdorff distance and their generalized form, weighted form and generalized weighted form, are put forward respectively for hesitant fuzzy linguistic term set, and the related properties and theorems of the new distance measures are proved. On this basis, a multi-attribute decision making method based on the new hesitant fuzzy linguistic distance measures and maximizing deviation is proposed. Finally, the feasibility and effectiveness of the new hesitant fuzzy linguistic distance measures and multi-attribute decision making method are verified by a concrete example and comparative analysis.

Key words: hesitant fuzzy linguistic term set, distance measure, maximizing deviation, multiple attribute decision making

摘要： 针对现有犹豫模糊语言距离测度存在不满足直递性、改变了原始决策信息、忽略了犹豫度差异等方面的问题,提出了一系列更为合理的新型犹豫模糊语言距离测度方法。首先,对现有犹豫模糊语言距离测度的局限性进行了枚举和分析。其次,给出了犹豫模糊语言犹豫度的定义,分别提出了犹豫模糊语言集的Euclidean距离、Hamming距离、Hamming-Hausdorff距离、Euclidean-Hausdorff距离以及它们的广义形式、加权形式和广义加权形式等一系列新型犹豫模糊语言距离测度,并对新型犹豫模糊语言距离测度的相关性质和定理进行了证明。在此基础上,提出了一种基于新型犹豫模糊语言距离测度和离差最大化的多属性决策方法。最后,通过具体算例和对比分析验证了新型犹豫模糊语言距离测度和多属性决策方法的可行性和有效性。

关键词: 犹豫模糊语言集, 距离测度, 离差最大化, 多属性决策

CLC Number:

C934

WU Shuangsheng, LIN Jie, YANG Yushu, HUANG Donghong. Hesitant Fuzzy Linguistic Distance Measures and Its Application in Multiple Attribute Decision Making[J]. Operations Research and Management Science, 2023, 32(2): 61-67.

吴双胜, 林杰, 杨玉舒, 黄冬宏. 犹豫模糊语言距离测度及其在多属性决策中的应用[J]. 运筹与管理, 2023, 32(2): 61-67.

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