Mathematical Programming Approach to multiattribute Decision Making under Intuitionistic Fuzzy Environments
Mathematical Programming Approach to multiattribute Decision Making under Intuitionistic Fuzzy Environments
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DOI：
10.1142/s0218488508005418
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发表时间：
2008-08
期刊：
影响因子：
--
通讯作者：
Dengfeng Li;Yongchun Wang
中科院分区：
文献类型：
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作者：
Dengfeng Li;Yongchun Wang
尽管明晰多属性决策和模糊多属性决策都取得了很大的进展，但对直觉模糊环境下多属性决策的研究还很少。在本文中，研究了使用直觉模糊集的多属性决策问题，并进一步扩展了 TOPSIS 以开发一种解决此类问题的新方法。在该方法中，使用 TOPSIS 基于相对紧密系数构建区间分数规划模型。每个备选方案的综合评价可以描述为直观的模糊集或区间数，是使用从本文提出的区间分数规划模型导出的两个辅助数学规划问题来计算的。使用基于区间数排序方法的似然性概念，计算备选方案的最佳隶属度以确定其排序顺序。通过数值例子说明了本文提出的方法的实现过程。
There exists little investigation on multiattribute decision making under intuitionistic fuzzy environments although both crisp and fuzzy multiattribute decision making have achieved a great progress. In this paper, multiattribute decision making problems using intuitionistic fuzzy sets are investigated and the TOPSIS is further extended to develop one new methodology for solving such problems. In this methodology, an interval fractional programming model is constructed on the basis of the relative closeness coefficient using the TOPSIS. Comprehensive evaluation of each alternative, which may be described as an intuitionistic fuzzy set or interval number, is calculated using two auxiliary mathematical programming problems derived from the interval fractional programming model proposed in this paper. Optimal degrees of membership for alternatives are calculated to determine their ranking order using the concept of likelihood based on the ranking method of interval numbers. Implementation process of the method proposed in this paper is illustrated with a numerical example.