基于模糊测度与累积前景理论的区间二型模糊多准则决策方法

doi:10.12005/orms.2020.0229

运筹与管理 ›› 2020, Vol. 29 ›› Issue (9): 70-81.DOI: 10.12005/orms.2020.0229

基于模糊测度与累积前景理论的区间二型模糊多准则决策方法

刘超^1,2, 汤国林^1,2, 刘培德³

1. 北京工业大学经济与管理学院, 北京 100124;
2. 北京现代制造业发展基地, 北京 100124;
3. 山东财经大学管理科学与工程学院, 山东济南 250014

收稿日期:2019-03-17 出版日期:2020-09-25
作者简介:刘超(1969-), 男, 山东枣庄人, 教授, 博士生导师, 研究方向:社会经济系统分析与优化;汤国林(1989-), 男, 山东临沂人, 博士研究生, 研究方向:决策理论与方法;刘培德(1966-), 男, 山东临朐人, 教授, 博士生导师, 研究方向:决策理论与方法。
基金资助:
国家自然科学基金项目(61773029, 61273230, 61703014, 71471172);北京市属高校高水平教师队伍建设支持计划长城学者培养计划项目(CIT&TCD20170304);山东省高等学校科技计划项目(J16LN25);北京市社科基金研究基地项目(16JDGLC005);泰山学者工程专项经费(ts201511045)

Interval Type-2 Fuzzy Muti-criteria Decision Making Method Based on Fuzzy Measures and Cumulative Prospect Theory

LIU Chao^{1, 2}, TANG Guo-lin^{1, 2}, LIU Pei-de³

1. College of Economics and Management, Beijing University of Technology, Beijing 100124, China;
2. Research Base of Beijing Modern Manufacturing Development, Beijing 100124, China;
3. School of Management Science and Engineering, Shandong University of Finance and Economics, Shandong 250014, China

Received:2019-03-17 Online:2020-09-25

摘要/Abstract

摘要： 针对准则值为区间二型模糊数且准则间存在关联关系的风险型多准则决策问题, 本文提出一种基于模糊测度理论与累积前景理论的区间二型模糊多准则决策方法。首先, 为全面反映准则间的关联关系, 本文提出Shapley区间二型模糊Choquet积分算子, 并证明该算子的一些性质。其次, 为反映专家行为偏好, 本文定义区间二型模糊前景效应与前景价值函数, 并提出累积前景Shapley区间二型模糊Choquet积分算子。然后, 为确定准则集的模糊测度, 本文建立基于区间二型模糊双向投影与Shapley函数的权重优化模型。在此基础上, 本文给出一种用于解决准则值为区间二型模糊数, 准则间存在关联关系, 专家存在风险偏好以及准则权重部分未知的多准则决策方法。最后, 通过风险投资实例佐证所提出的方法的适用性与科学性。

关键词: 累积前景理论, 模糊测度理论, 区间二型模糊集, 双向投影, 多准则决策

Abstract: For risk muti-criteria decision making problems with interactive condition and interval type-2 fuzzyinformation, an interval type-2 fuzzy decision making method is proposed based on fuzzy measures theory and cumulative prospect theory. Firstly, in order to globally consider the interactions among the criteria, this paper proposes the Shapley interval type-2 fuzzy Choquet operator. Meanwhile, some desirable properties of this operator are studied. Then, to capture the diversities of risk attitudes and sensitivities among experts with limited relational behaviors, this paper defines the prospect effect and the prospect value function of interval type-2 fuzzy number, and proposes the cumulative prospect Shapley interval type-2 fuzzy Choquet operator. In addition, based on the defined bidirectional projection measures of interval type-2 fuzzy sets and the Shapley function, the models for the optimal fuzzy measures on a criteria set are established. After that, an approach to muti-criteria decision making with interaction condition, experts’ risk preference and incomplete weight information under interval type-2 fuzzy environment is developed. Finally, a practical example regarding risk investment is provided to demonstrate the applicability and validity of the developed approach.

Key words: cumulative prospect theory, fuzzy measures theory, interval type-2 fuzzy set, bidirectional projection, muti-criteria decision making

中图分类号:

C934

刘超, 汤国林, 刘培德. 基于模糊测度与累积前景理论的区间二型模糊多准则决策方法[J]. 运筹与管理, 2020, 29(9): 70-81.

LIU Chao, TANG Guo-lin, LIU Pei-de. Interval Type-2 Fuzzy Muti-criteria Decision Making Method Based on Fuzzy Measures and Cumulative Prospect Theory[J]. Operations Research and Management Science, 2020, 29(9): 70-81.

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基于模糊测度与累积前景理论的区间二型模糊多准则决策方法

Interval Type-2 Fuzzy Muti-criteria Decision Making Method Based on Fuzzy Measures and Cumulative Prospect Theory

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