Soft-fuzzy Rough Decision Model Based On Variable Precision

Recently, as a new tool to deal with uncertain and incomplete knowledge, the soft set theory has brought the attention by many scholars in various fields. Especially, the researches of the theory for combining the soft set theory with other mathematical theory of theoretical results have been developed by many scholars. Researchers provided a framework to combining fuzzy set with rough set and soft set. Based on fuzzy set, rough set and soft set and a large number of research results, a new concept of variable precision soft-fuzzy rough sets was proposed and the concept of binary quasi fuzzy relationship (or quasi fuzzy soft sets) was defined through combining fuzzy rough sets based on inclusion degree with quasi fuzzy soft sets. At the same time, the soft fuzzy rough approximation was given under some deformation. In addition, some basic properties of approximation operators also were discussed. Then through analysing the limitations and advantages of existing rough set model, soft fuzzy rough set model is proposed and applied to practical application. Moreover, the algorithm of the model is given. The main work of this paper are as follows:(I) Based on soft rough sets, new soft set and fuzzy soft sets are defined and named them as quasi soft sets and quasi fuzzy soft sets by exchanging the role of universe U and the parameter set E. In fact, from the definition of quasi fuzzy soft set, a fuzzy subset of a parameter set E is defined for any object of U. So quasi fuzzy soft sets can be regarded as a binary fuzzy relation between parameter set E and universe U. Based on a large number of research results, we studied a power inclusion degree on fuzzy sets and established the soft fuzzy rough set model based on it with the foundation of pseudo fuzzy partition soft set. Some important properties of this model are approached, and then soft fuzzy set approximate method for calculating precision and roughness accuracy coefficient are given.(Ⅱ) By means of introducing the quasi fuzzy soft set, we reconstructed the soft-fuzzy rough sets, degree soft rough set and soft-fuzzy rough set structure and then discussed the related properties. Combing the idea of uncertainty decision-making, we present the decision rules and the algorithm of the model is given, so as to multiple attribute decision making providing new ideas and new methods.(Ⅲ) At last, the validity of the decision method is verified by an applica-tion example.