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Intuitionistic Fuzzy Approximations and

Intuitionistic Fuzzy σ-Algebras

Wei-Zhi Wu1

Lei Zhou2

1School of Mathematics, Physics and Information Science,

Zhejiang Ocean University, China

2Institute for Information and System Sciences, Faculty of Science,

Xi’an Jiaotong University, China

Wei-Zhi Wu, Lei Zhou

Intuitionistic Fuzzy Approximations and Intuitionistic Fuzzy σ

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Speaker: Wei-Zhi Wu

Wei-Zhi Wu, Lei Zhou

Intuitionistic Fuzzy Approximations and Intuitionistic Fuzzy σ

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Contents

Introduction

Motivation

Basic notions

Our results

Summary

Wei-Zhi Wu, Lei Zhou

Intuitionistic Fuzzy Approximations and Intuitionistic Fuzzy σ

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Introduction

Approximation spaces in rough set theory and measurable spaces

in measure theory are two important structures to represent knowl-

edge. An approximation space in Pawlak’s rough set theory con-

sists of a universe of discourse and an equivalence relation im-

posed on it. Based on the approximation space, the notions

of lower and upper approximation operators can be induced. A

rough set algebra including a set algebra with two approximation

operators is then generated. A measurable space in measure

theory contains a universe of discourse and a family of measur-

able sets called a σ−algebra. Based on the measurable space,

uncertainty of knowledge can be analyzed.

Wei-Zhi Wu, Lei Zhou

Intuitionistic Fuzzy Approximations and Intuitionistic Fuzzy σ

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An equivalence relation in Pawlak’s original rough set model

is a very restrictive condition which may affect the application

of rough set theory. The generalization of Pawlak’s rough set

model is thus one of the main directions for the study of rough

set theory. Many authors have developed Pawlak’s rough set

model by using nonequivalence relations in crisp and/or fuzzy

environments. Other researchers have also defined rough ap-

proximations of intuitionistic fuzzy sets (see e.g. literature listed

in this paper).

Wei-Zhi Wu, Lei Zhou

Intuitionistic Fuzzy Approximations and Intuitionistic Fuzzy σ