Multi-granularity Fuzzy Soft Rough Set Model And Its Application

In the big data era,uncertain information is everywhere.Fuzzy set theory,soft set theory and rough set theory are also mathematical models that can describe complex,uncertain and ambiguous problem.These theories have been widely used in many fields such as machine learning,decision analysis,knowledge discovery;In order to further describe the complex and uncertain problems by mathematical models,the mathematical research topic which combines the three theories is a question worth exploring issue.In this paper,we construct a multi-granularity fuzzy soft rough set model(MGFSR-set)by fusing the rough set theory,fuzzy soft set theory and multi-granularity ideology of granular computing theory.This model can deal with the uncertainty of the information and can describe fuzzy concept.Which is applied to the attribute reduction problem or decision making problems;And then combined with the knowledge of probability and statistics,the multi-granularity fuzzy soft probability rough set model is further proposed.The specific research contents are listed as follows:Firstly,we study present status of development about the granular computing,rough set theory,soft set,fuzzy soft set and information entropy theory at home and abroad,respectively.In order to put forward the new theory,we accomplish the comprehensive research background analysis.Secondly,this thesis introduce the theoretical basis about granular computing,rough set,soft set,fuzzy soft set,and information entropy including multi-granularity rough set theory,fuzzy soft rough set theory,conditional entropy and extraction and measurement of decision rules.Thirdly,we introduce the concept of multi-granularity fuzzy soft rough set,as well as some related properties and results are given.Then,we construct the multi-granularity fuzzy soft decision system based on multi-granularity fuzzy soft rough set,and on the basis of the positive region with conditional entropy,multi-granularity fuzzy soft relative attribute reduction algorithm based on the information entropy is proposed.The new algorithm is applied to the multiple attribute decision making problems of the supermarket profitability.It proves that multi-granularity fuzzy soft rough set is a wonderful tool to describe the multi-attribute decision making problem.The validity of this algorithmin in practical application is proved by the instance.Finally,based on multi-granularity fuzzy soft rough set model,multi-granularity fuzzy soft probability rough set is put forward and the related properties are expound.Then we apply the proposed model to the analysis of the Bayes decision and give an example.