基于QUALIFLEX和LINMAP的简化中性犹豫模糊多属性决策方法

在处理多属性决策问题中,QUALIFLEX是一种非常有用的排序算法。针对属性取值为简化中性犹豫模糊集的多属性决策问题,提出了SNHFS-QUALIFLEX算法。另外考虑到属性权重不确定的情况,将LINMAP扩展到简化中性犹豫模糊集中,定义了符号距离,建立了最优数学规划模型来确定属性权重。最后将SNHFS-QUALIFLEX方法应用到多属性决策实例中,并验证了其可行性和有效性。     

Extension of the LINMAP for multiattribute decision making under Atanassov’s intuitionistic fuzzy environment

The aim of this article is further extending the linear programming techniques for multidimensional analysis of preference (LINMAP) to develop a new methodology for solving multiattribute decision making (MADM) problems under Atanassov’s intuitionistic fuzzy (IF) environments. The LINMAP only can deal with MADM problems in crisp environments. However, fuzziness is inherent in decision data and decision making processes. In this methodology, Atanassov’s IF sets are used to describe fuzziness in decision information and decision making processes by means of an Atanassov’s IF decision matrix. A Euclidean distance is proposed to measure the difference between Atanassov’s IF sets. Consistency and inconsistency indices are defined on the basis of preferences between alternatives given by the decision maker. Each alternative is assessed on the basis of its distance to an Atanassov’s IF positive ideal solution (IFPIS) which is unknown a prior. The Atanassov’s IFPIS and the weights of attributes are then estimated using a new linear programming model based upon the consistency and inconsistency indices defined. Finally, the distance of each alternative to the Atanassov’s IFPIS can be calculated to determine the ranking order of all alternatives. A numerical example is examined to demonstrate the implementation process of this methodology. Also it has been proved that the methodology proposed in this article can deal with MADM problems under not only Atanassov’s IF environments but also both fuzzy and crisp environments.