Three Types Of Fuzzy Rough Set Models Derived From Overlap And Grouping Functions

Rough set is a mathematical model for dealing with inaccuracies and uncertain-ties in data analysis.The main idea of rough set is to derive decision or classification rules by knowledge reduction on the premise of keeping the classification ability un-changed.Since rough set was put forward,it has been widely concerned and studied by many scholars at home and abroad.At present,it has been successfully applied to solve problems involving decision-making,conflict analysis and medical diagno-sis.On the other hand,overlap and grouping functions,as two novel aggregation functions and mathematical model to handle the problems involving in informa-tion fusion,have been successfully applied to solve problems involving classification,decision-making and image processing.Recently,the research on the combination of overlap and grouping functions with rough sets has become a hot topic.This thesis will continue to focus on this research topic,and mainly gives three types of fuzzy rough set models based on overlap and grouping functions.To be specific,this thesis contains the following contents.(1)On the basis of overlap and grouping functions,we propose a new fuzzy rough set model named(G_o,O)-fuzzy rough sets.Meanwhile,we discuss some basic properties of(G_o,O)-fuzzy rough sets,especially for the topological properties ofO-lower fuzzy rough approximation operators.We also focus on the characteriza-tions betweenO-lower fuzzy rough approximation operators in(G_o,O)-fuzzy rough sets and some special fuzzy relations,such as serial fuzzy relations,reflexive fuzzy relations,symmetric fuzzy relations,O-transitive fuzzy relations and O-Euclidean fuzzy relations.(2)We utilize the conditional probability constructed from overlap functions to define fuzzy probabilistic rough set model based on overlap functions and give a practical example to illustrate the feasibility and effectiveness of the proposed models.In the meantime,we study several elementary properties of the upper and lower approximation operators in fuzzy probabilistic rough set model based on overlap functions.We also show a short comparison of the proposed models with existing fuzzy probabilistic rough set models.(3)We introduce a multigranulation fuzzy probabilistic rough set model de-rived from overlap functions and give a practical example to illustrate the feasibility and effectiveness of it.Meanwhile,we discuss some elementary properties of upper and lower approximation operators in multigranulation fuzzy probabilistic rough set model.The theoretical results are applied to decision-making problem,and the experimental results show that the advantages of the model proposed via overlap functions have better classification performance than fuzzy probabilistic rough sets obtained via t-norms.