Multi-Attribute Decision Making Method Based on Possibility variance coefficient of triangular Intuitionistic Fuzzy numbers
Multi-Attribute Decision Making Method Based on Possibility variance coefficient of triangular Intuitionistic Fuzzy numbers
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DOI：
10.1142/s0218488513500128
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发表时间：
2013-04
期刊：
影响因子：
--
通讯作者：
S. Wan
中科院分区：
文献类型：
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作者：
S. Wan
三角直觉模糊数（TIFNs）是直觉模糊集的一个特例。针对属性值为TIFNs形式且权重偏好信息不完全的多属性决策问题，提出了一种基于可能性方差系数的决策方法.引入了TIFN的可能性均值、方差和标准差以及可能性方差系数。在此基础上，给出了一种基于可能性方差系数的TIFNs排序方法。建立了以方案总体属性值的隶属函数和非隶属函数的可能性方差系数最小为目标的双目标数学规划模型。利用极大极小法，通过Charnes变换和库珀变换，将两个非线性分式规划模型转化为线性规划模型。因此，双目标数学规划的Pareto最优解可以通过求解单目标规划模型得到。根据最小可能性方差系数确定方案的排序。最后通过一个人员选拔实例验证了该方法的可行性和有效性。并与其它方法进行了比较分析。
Triangular intuitionistic fuzzy numbers (TIFNs) are a special case of intuitionistic fuzzy sets. The purpose of this paper is to develop a new decision making method based on possibility variance coefficient to solve the multi-attribute decision making (MADM) problems, in which the attribute values are in the form of TIFNs and the weight preference information is incomplete. The possibility mean, variance and standard deviation for a TIFN are introduced as well as the possibility variance coefficient. Hereby, a new method to rank TIFNs is given on the basis of the possibility variance coefficients. The bi-objective mathematical programming, which minimizes the possibility variance coefficients of membership and non-membership functions for alternative's overall attribute values, is constructed. Using the max-min method, two non-linear fractional programming models are transformed into the linear programming models through the Charnes and Cooper transformation. Thus, the Pareto optimal solution to the bi-objective mathematical programming can be derived by solving the single-objective programming model. The ranking order of alternatives is obtained according to the minimum possibility variance coefficients. A personal selection example is given to verify the developed method and to demonstrate its feasibility and effectiveness. The analysis of comparison with other method is also conducted.