Research On New Soft Set Models And Their Applications In Decision Making

We all know that there are full of uncertainty, imprecision and vagueness in information system. Therefore, the modeling and processing of this problem have been a research focus in the field of artificial intelligence. In the existing mathematical tool for dealing with uncertainties, the soft set theory has been successfully applied to many fields especially in decision making, because which is free from the inadequacy of parameter tool. In this paper, the basic aim is to solve the decision making problem in soft set, the notion of soft intuitionistic multiplicative set and interval-valued intuitionistic fuzzy parametrized soft set are introduced and its application to decision making is also investigated. In addition, the notion of incomplete soft discernibility matrix and its application in decision making are researched. The main content of this text are as follow:(1) Due to the problem of soft intuitionistic fuzzy set is partly inconsistent with our intuition, we combine soft set with intuitionistic multiplicative set and defined a new soft set model named soft intuitionistic multiplicative set. Therefore, soft set and intuitionistic multiplicative set are generalized. Then, the basic operations and properties of soft intuitionstic multiplicative set are discussed. Meanwhile, an algorithm based on theory of soft intutitionistic multiplicative sets is proposed. Finally, the application of soft intuitionistic multiplicative set in decision making are researched by example.(2)Based on intuitionstic fuzzy parameterized soft set, we define the concept of interval-valued intuitionistic fuzzy parameterized soft set combine soft set with interval-valued intuitionistc fuzzy set and some basic operations and properties associated with its are researched. At some time, an algorithm based on it is proposed by translated interval-valued intuitionistic fuzzy parameterized soft set into reduced fuzzy set.(3)Finally, this paper based on soft discernibility matrix introduced the notion of incomplete soft discernibility matrix, and some properties associated with incomplete soft discernibility matrix are researched. Then, a novel algorithm based on incomplete soft discernibility matrix is proposed to solve the problems of decision making. It can find not only the optimal choice object and suboptimal object, but also an order relation of all the objects easily by scanning the incomplete soft discernibility matrix at most one time. The correctness and effectiveness of the algorithm are proved in decision making by examples.