基于三角直觉模糊数Choquet积分算子的多属性决策方法

中国管理科学 ›› 2014, Vol. 22 ›› Issue (3): 121-129.

基于三角直觉模糊数Choquet积分算子的多属性决策方法

万树平¹, 董九英²

1. 江西财经大学信息管理学院, 江西南昌 330013;
2. 江西财经大学统计学院, 江西南昌 330013

收稿日期:2011-10-30 修回日期:2012-08-30 出版日期:2014-03-20 发布日期:2014-03-19
作者简介:万树平（1974- ），男（汉族），江西乐安人，江西财经大学信息管理学院，教授，博士，研究方向：决策分析、信息融合的研究.
基金资助:
国家自然科学基金资助项目（71061006，61263018）；教育部人文社科项目（09YGC630107）；江西省社会科学"十二五"（2013）规划项目（13GL17）；江西省自然科学基金资助项目（20114BAB201012）；江西财经大学优秀青年学术人才支持计划

Multi-attribute Decision Making based on Triangular Intuitionistic Fuzzy Number Choquet Integral Operator

WAN Shu-ping¹, DONG Jiu-ying²

1. College of Information Technology, Jiangxi University of Finance and Economics, Nanchang 330013, China;
2. College of Statistics, Jiangxi University of Finance and Economics, Nanchang 330013, China

Received:2011-10-30 Revised:2012-08-30 Online:2014-03-20 Published:2014-03-19

摘要/Abstract

摘要： 定义了三角直觉模糊数的Hamming距离，给出了属性独立情形下的三角直觉模糊数算术集成算子，并运用模糊测度和Choquet积分，定义了三角直觉模糊Choquet积分算子，并分析其有关性质。针对方案评价信息为三角直觉模糊数的关联多属性决策问题，利用三角直觉模糊Choquet积分算子集成得到方案的综合属性值，建立多目标优化模型并转化为线性目标规划求解，客观地确定了属性集的模糊测度，进而提出了相应的决策方法。实例分析表明了方法的有效性和合理性。

关键词: 多属性决策, 三角直觉模糊数, Choquet积分, 关联, 集成算子

Abstract: In this paper, the Hamming distance between the triangular intuitionistic fuzzy numbers is defined. The triangular intuitionistic fuzzy arithmetic aggregation operators are developed under the independence of attributes. Combining the fuzzy measure and Choquet integral, the triangular intuitionistic fuzzy Choquet integral aggregation operator is defined. Some desirable properties for this operator are investigated. What's more, for the interactive multiple attribute decision-making problem in which the evaluation information for the alternatives is expressed with the triangular intuitionistic fuzzy numbers, the overall attribute value of alternative is integrated by the triangular intuitionistic fuzzy Choquet integral aggregation operator. The multi-objective programming model is constructed and transformed into linear object programming to solve. The fuzzy measures of the attribute set are objectively derived. The corresponding decision making method is then proposed. The example analysis shows the effectiveness and reasonability of the method.

Key words: multi-attribute decision making, triangular intuitionistic fuzzy number, Choquet integral, interaction, aggregation operator

中图分类号:

C934

万树平, 董九英. 基于三角直觉模糊数Choquet积分算子的多属性决策方法[J]. 中国管理科学, 2014, 22(3): 121-129.

WAN Shu-ping, DONG Jiu-ying. Multi-attribute Decision Making based on Triangular Intuitionistic Fuzzy Number Choquet Integral Operator[J]. Chinese Journal of Management Science, 2014, 22(3): 121-129.

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