基于改进符号距离的犹豫模糊前景理论决策方法

doi:10.3969/j.issn.1001-506X.2019.12.21

系统工程与电子技术 ›› 2019, Vol. 41 ›› Issue (12): 2820-2826.doi: 10.3969/j.issn.1001-506X.2019.12.21

基于改进符号距离的犹豫模糊前景理论决策方法

李贺, 江登英

武汉理工大学理学院, 湖北武汉 430070

出版日期:2019-11-25 发布日期:2019-11-26

Hesitant fuzzy prospect theory decision-making method based on improved signed distance

LI He, JIANG Dengying

College of Science, Wuhan University of Technology, Wuhan 430070, China

Online:2019-11-25 Published:2019-11-26

摘要/Abstract

摘要：

针对犹豫模糊元中人为添加元素影响决策结果的问题,提出一种基于改进符号距离的犹豫模糊前景理论决策方法。首先,根据正负理想点、犹豫模糊元中元素之间的方差以及元素个数定义一种新的符号距离,并证明了改进的符号距离满足符号距离的基本性质。其次,基于改进的符号距离提出犹豫模糊前景价值函数,并通过收益损失函数计算出各方案的收益损失比,确定备选方案的优劣顺序。最后,通过应用算例验证了本文所提出方法的可行性和有效性。该方法既避免了人为添加元素对决策结果的影响,又合理反映了决策者的分歧程度,还考虑了人们面临得失时的心理行为,决策结果更符合实际。

关键词: 多属性决策, 犹豫模糊集, 前景理论, 符号距离, 犹豫度

Abstract:

Aiming at the problem that artificial addition of elements in hesitant fuzzy elements affects decision-making results, a decision-making method based on the improved signed distance for the hesitant fuzzy prospect theory is proposed. Firstly, the signed distance is defined according to the positive and negative ideal points, the variances of hesitant fuzzy elements and the number of elements, and it is proved that the improved signed distance satisfies the basic properties of the signed distance. Furthermore, based on the improved signed distance, the hesitant fuzzy prospect value function is proposed, the hesitant fuzzy decision matrix is transformed into the value matrix, and then the profit-loss ratio of each scheme is calculated through the revenue loss function, and the order of the alternatives is determined accordingly. Finally, the feasibility and validity of the proposed method are verified by a numerical example, which demonstrates that this method not only avoids the influence of artificial adding elements on decision-making results, but also reflects reasonably the degree of divergence of decision-makers. It also considers the psychological behavior of people facing gains and losses,and the decision-making results are more realistic.

Key words: multi-attribute decision-making, hesitant fuzzy sets, prospect theory, signed distance, hesitancy index

李贺, 江登英. 基于改进符号距离的犹豫模糊前景理论决策方法[J]. 系统工程与电子技术, 2019, 41(12): 2820-2826.

LI He, JIANG Dengying. Hesitant fuzzy prospect theory decision-making method based on improved signed distance[J]. Systems Engineering and Electronics, 2019, 41(12): 2820-2826.

基于改进符号距离的犹豫模糊前景理论决策方法

Hesitant fuzzy prospect theory decision-making method based on improved signed distance

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