基于θ算子的多粒度直觉模糊粗糙集模型

Multi-granularity Intuitive Fuzzy Rough Set Model Based onθOperator

针对在多属性决策中决策者难以在多个属性相互冲突时做出准确判断的问题,文中在直觉模糊近似空间中,首先利用直觉模糊集的隶属度、非隶属度与模糊蕴含算子,提出了基于θ算子和θ*算子的直觉模糊集及其隶属度和非隶属度的概念,并证明了它们的一系列性质。然后,在直觉模糊集与多粒度粗糙集上,定义基于θ算子的多粒度直觉模糊粗糙集的悲观、乐观模型,讨论两种模型的相关性质。最后,给出了基于θ算子的多粒度直觉模糊粗糙集模型的多属性决策算法,将高校引进的人才评价和企业绿色经济供应链的商家评价作为实例进行了分析,同时还与已有方法进行了分析对比,用乐观、悲观模型与已有方法的决策结果的对比证明了所提方法的正确性,并验证了该模型算法的有效性。

In order to solve the problem that it is difficult for decision makers to make accurate judgment when multiple attributes conflict with each other in the multi-attribute decision making.In the intuitive fuzzy approximation space,this paper firstly uses the membership degree,non-membership degree and fuzzy implication operator of intuitive fuzzy set,and proposes the concepts of membership degree and non-membership degree based onθoperator andθ*operator,and proves a series of properties of them.Then,in the intuitive fuzzy set and the multi-granularity rough set,the pessimistic and optimistic models of theintuitive fuzzy rough set based onθoperator are defined,and the related properties of the two models are discussed.Finally,a multi-attribute decision algorithm based on the multi-granularity intuitive fuzzy rough set model based onθoperator is presented.The evaluation of talents introduced by universities and the evaluation of businesses in the green economy supply chain of enterprises are analyzed as examples.The correctness of the proposed method is proved by comparing the results of the optimistic and pessimistic models with those of the existing methods.The effectiveness of the model algorithm is also verified.