Research On Four Extended Models Of Rough Sets

Rough set theory,as a powerful and efficient tool for handling uncertainty prob-lem,is successfully applied to many fields,such as data mining,decision making,intelligent control,pattern recognition,etc.Compared with other mathematical tools of uncertainty problem,rough sets can obtain relevance of data and acquire extracting rules without any prior information.However,evidence theory and fuzzy sets demand probabilistic evaluation and membership degree,respectively.Hence,rough sets is a more objective tool.Meanwhile,there is no mechanism to deal with imprecise or un-certain original data in rough sets,which means there exists strong complementarity between rough sets and probability theory,fuzzy mathematics,evidence theory.Thus,the combination of rough sets and other algebraic structure or mathematical tools can be applied to solve more application problems.So far,there axe two main approaches in the research of rough sets,i.e.constructive approach and axiomatic approach.Con-structive approach aims to handle practical problems,and axiomatic approach focuses on investigating the essential properties of rough sets.This paper can be divided into 3 parts.In the first part,we explored the single axiom characterization of L-fuzzy rough sets based on residuated lattices.In the sec-ond part,we investigated multi-scale decision theoretic rough sets from constructive as well as axiomatic perspectives.In the third part,neutrosophic sets was introduced into rough sets and single valued neutrosophic rough approximation operators were defined based on single valued neutrosophic logical operators.Subsequently,we estab-lished generalized interval neutrosophic rough set frame based on interval neutrosophic relation.Moreover,the application of generalized interval neutrosophic rough sets in multi-attribute decision making was discussed.This paper consists of 5 chapters.Chapter 1 briefly reviewed some basic concept and properties of rough set theory,residuated lattice,multi-scale information table and neutrosophic sets.In chapter 2,we were devoted to searching axiomatic characterization of L-fuzzy rough approximation operators based on residuated lattices.First,We demonstrated that the lower(upper)L-fuzzy rough approximation operators generated by a gen-eralized L-fuzzy relation can be characterized by only one axiom.Furthermore,by analysing the connection of L-fuzzy approximation operators and special L-fuzzy rela-tions,we also explored single axiomatic characterization of L-fuzzy rough approxima-tion operators produced by L-fuzzy serial,reflexive,symmetric and transitive relations as well as any of their compositions.Due to the tight relation between rough set the-ory and modal logic,axiomatic characterization can provide more convenient method for constructing and studying various fuzzy modal logic,which can contribute solid theoretical foundation for the development of artificial intelligent.Chapter 3 focused on investigating multi-scale decision-theoretic rough sets based on muti-scale information.Multi-scale information table plays significant role in deci-sion making problems,since decision makers sometimes need consider one object with respect to different levels of an attribute.At the same time,decision-theoretic rough sets provides unique perspective for handling decision making problems.By com-bining multi-scale information table and decision-theoretic rough sets,from overall viewpoints,we proposed arithmetic mean decision-theoretic rough sets and weighted mean decision-theoretic rough sets.Then,from local point of view,we put forward the thought of conservative and aggressive models of multi-scale decision-theoretic rough sets.Specifically,conservative acceptance and conservative rejection model,conserva-tive acceptance and aggressive rejection model,aggressive acceptance and conservative rejection model,aggressive acceptance and aggressive rejection model were systemati-cally investigated.Simultaneously,we also explored some essential properties of these multi-scale decision-theoretic rough,set models in detail.Finally,a numerical example was given to illustrate the feasibility and effectiveness of the proposed models.In chapter 4,(I,N)-single valued neutrosophic rough sets was studied from con-structive and axiomatic perspectives.In the constructive approach,a pair of single valued neutrosophic rough approximation operators were first proposed based on single valued neutrosophic implicator I and single valued neutrosophic norm N.Moreover,some basic properties of(I,N)-single valued neutrosophic rough approximation op-erators were explored.In addition,connections between single valued neutrosophic relations and(I,N)-single valued neutrosophic rough approximation operators were systematically discussed.In the axiomatic approach,axiomatic characterization of(I,N)-single valued neutrosophic approximation operators was investigated.Specifi-cally,different axiom sets characterizing the intrinsic properties of(I,N)-single valued neutrosophic rough approximation operators associated with diverse single valued neu-trosophic relations were discussed in detail.In chapter 5,we elaborated the generalized hybrid model of interval neutrosophic sets and rough sets from constructive as well as axiomatic approaches.On one hand,generalized interval neutrosophic approximation operators were defined based on inter-val neutrosophic relations.Furthermore,we established the connection between special interval neutrosophic relations and generalized interval neutrosophic rough approxi-mation operators.On the other hand,we explored the axiomatic characterization of approximation operators and showed that different axiom sets correspond to different types of approximation operators.In order to apply the generalized interval neutro-sophic rough sets to resolve more practical problems,we extended the hybrid model to two universes and further proposed an algorithm of multi-attribute decision making.Moreover,an example was given to demonstrate the validity of the generalized interval neutrosophic rough set model.