Hesitant Fuzzy Linguistic Regret Theory and ELECTRE Decision Making Method and Its Application

doi:10.3778/j.issn.1002-8331.2006-0038

Abstract

Abstract:

In order to solve the problem of multi-attribute decision making in which the attribute values take the form of hesitant fuzzy linguistic elements and the attribute weights are completely unknown, a multi-attribute decision making method based on regret theory and ELECTRE III is proposed. First of all, the attribute weights are determined by using the grey relational analysis and maximum entropy principle. Secondly, the rejoice and regret functions of the hesitant fuzzy linguistic element are determined. The concordance index and discordance index are determined via the rejoice and regret function. Futher more, the credibility index is obtained for each pair of alternatives. The net credibility degree of alternatives can be got by the credibility index of each pair of alternatives, ranking of alternatives is obtained according to net credibility degree of alternatives. Finally, an example is given to illustrate the feasibility and effectiveness of the proposed method. This method is more practical and reasonable as it considers the decision makers’s psychological behavior and partial compensation among attributes. A sensitivity analysis of regret aversion coefficient[μ]shows the stability of the proposed method, comparisons are made with other two methods to demonstrate the advantage of the proposed method.

Key words: hesitant fuzzy linguistic information;regret theory, ELECTRE III, grey relational analysis

摘要：

针对决策信息为犹豫模糊语言元素形式、属性权重完全未知的多属性决策问题，提出了一种基于后悔理论和ELECTRE III的多属性决策方法。利用灰色关联分析和极大熵原理确定属性权重。确定犹豫模糊语言信息的后悔-欣喜函数，凭借该函数确定方案对的后悔-欣喜和谐指数与不和谐指数，进而确定方案对的可信度指数。通过方案对的可信度指数确定各方案的净可信度，依此对方案进行排序。通过算例说明了所提方法的可行性和有效性。由于该方法同时考虑了决策者的心理行为和属性间的部分可补偿性，因此决策结果更加贴近现实且更为合理。对后悔规避系数[μ]的灵敏度分析表明了所提方法的稳定性，与其他两种方法的对比分析展示了所提方法的优势。

关键词: 犹豫模糊语言信息, 后悔理论, ELECTRE III, 灰关联分析

HUI Hui, WANG Qiuping, LI Miaomiao. Hesitant Fuzzy Linguistic Regret Theory and ELECTRE Decision Making Method and Its Application[J]. Computer Engineering and Applications, 2021, 57(20): 172-179.

惠蕙，王秋萍，李苗苗. 犹豫模糊语言后悔理论和ELECTRE决策方法及应用[J]. 计算机工程与应用, 2021, 57(20): 172-179.

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