基于直觉模糊信息的多属性排序问题的软集决策方法

A Soft Set Based Decision-making Method to Multi-attribute Ranking Problem with Intuitionistic Fuzzy Information

针对属性信息具有模糊性的一类多属性方案排序问题,提出一种基于直觉模糊软集的决策方法。直觉模糊软集结合软集和直觉模糊集的优势,对对象近似描述时没有任何限制,并且能够更客观地表达事物的模糊性本质。首先定义直觉模糊软集的综合精确度、综合犹豫度和综合得分值,以及直觉模糊软集水平集的选择值和接受水平。在此基础上,提出关于多属性方案排序的选择值准则、精确度准则、犹豫度准则以及得分值准则。然后,提出一种组合使用各排序准则的多属性方案排序方法。最后,通过数值算例及讨论证实该方法的可行性和有效性。这种方法充分考虑决策者的直觉信息及主观偏好,能够有效完成多属性方案的优选和排序决策。

The paper aims to propose a method to solve ranking alternatives problem with multiple attribute based on intuitionistic fuzzy soft set, in which the attributes information are fuzzy. Intuitionistic fuzzy soft set combines with the advantages of intuitionistic fuzzy set and the soft set. They are approximating description of the object without any constraints and expressing the fuzzy nature of things more objectively. Firstly, three concepts are given which are named synthetic degree-hesitation, synthetic score and synthetic accuracy of intuitionistic fuzzy soft set. It also comes the concept both the value-choice and the level-acceptance of decision-maker regarding level intuitionistic fuzzy soft set. Furthermore, four decision principles are presented, namely, value-choice principle, degree- hesitation principle, accuracy principle and score principle. Then, a concrete algorithm is presented on the basis of combining these four principles. Finally, an example and some discussions have been verified to test the feasibility and effectiveness. The method presented in this paper can not only solve the ranking problem, but also get the only one optimal-selection considering the intuitive information and subjective preference of the decision maker.