Fuzzy Multi-granulation Rough Set Model Over Two Universes And Its Applications

Fuzzy set and rough set are two important tools to deal with incomplete and uncertainty information.Based on the need for intelligent decision making,more and more researches have studied fuzzy rough sets and their extended models.By using the weak fuzzy similarity relationship,this thesis gives the reliability of 2-tuples in the approximation set,and puts forward the new fuzzy rough set model over two universes.In addition,with the idea of granular computing,the q-rung dual hesitant fuzzy multi-granularity rough set(q-RDHFMGRS)model over two universes is proposed.In order to reduce the risk of decision making errors in dynamic decision making problems,the variable precision dynamic rough set model over two universes is put forward.The specific research content is as follows:1.By analyzing the shortcomings of the variable precision probabilistic rough set model and the probabilistic S-rough set model over two universes,a variable precision probabilistic S-rough set model over two universes is proposed.Then a numerical example is given to show that the model can significantly reduce the risk of decision failure when dealing with related dynamic problems.2.Based on the weak fuzzy similarity relationship,a new similarity degree is proposed to describe the relationship between 2-tuples in two universes.Since the 2-tuples in each approximation set correspond to different weights,so we give each 2-tuples corresponding reliability and use these reliability to propose a method to calculate the similarity between the 2-tuples and the approximation set.Based on this similarity,the fuzzy rough set model over two universes and its related properties are proposed.Finally,a decision algorithm based on the fuzzy rough set is presented and its practicability and effectiveness are verified by a medical diagnosis example.3.By combining the q-rung dual hesitant fuzzy set(q-RDHFS)with multi-granularity rough set(MGRS)model,a q-RDHFMGRS model is proposed and its basic properties are proved.Based on this model,a multi-attribute decision making algorithm is proposed,and its practicability and effectiveness are verified by a medical diagnosis example.