Multi-granulation Intuitionistic Fuzzy Rough Set Over Two Universes And Its Matrix Representation

The theories of rough sets and intuitionistic fuzzy sets,proposed by Pawlak and Atanassov respectively,are mathematic tools for dealing with the problems of uncertainty and ambiguity.And multi-granulation rough sets are proposed by professor Yuhua Qian in2010,which provides convenience for the processing of approximate concepts in multiple relationships.In the case of the two universes,this thesis proposes multi-granulation intuitionistic fuzzy rough set models over two universes by combining multi-granulation rough set theory and intuitionistic fuzzy set theory,and investigates the problem about uncertainty measures of the approximation space by using the concept of entropy.In addition,another problem is about calculating the upper and lower approximates of rough set in approximation space.Because a relation can be represented by a matrix and matrix operations are simple and intuitive,the calculation of the upper and lower approximates in rough set based on relation matrix and matrix operations are proposed.The main ideas in this thesis are listed in the following.(1)From the perspective of two universes,multi-granulation intuitionistic fuzzy rough set models over two universes are proposed.Then some important properties of the models are studied,and the application of the models in real life is given by a practical example.(2)The uncertainty measures of the generalized approximation space,the generalized fuzzy approximation space and the generalized intuitionistic fuzzy approximation space are studied.The concepts of information entropy and information granulation are proposed.It is shown the necessity to study the uncertainty of the approximation space itself.(3)The thesis introduces the calculation of the upper and lower approximates of rough set in the three kinds of approximation spaces in matrix method,which is considered under the single granulation condition.Then the compositions of the three kinds of approximation spaces and related properties in approximation spaces are described by matrix.