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Quotient Space Based Problem Solving by Bo Zhang, Ling Zhang

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2.5. The Applications of Quotient Space Theory

2.5.1. Introduction

In this section, we will present a new constructional definition of fuzzy sets by using fuzzy equivalence relations, and discuss its properties. We will also discuss the isomorphism and similarity principles of fuzzy sets, the necessary and sufficient condition of the isomorphism and ε-similarity of two fuzzy equivalence relations. These principles and results can overcome the subjectivity of the concept of fuzzy sets defined by membership functions to a certain extent, and deepen the understanding of fuzzy set theory so that a more objectively fuzzy set theory can be established probably. More details can be seen in (Zhang and Zhang, 2003b, 2003d, 2005b, 2005c).
Zadeh (1965) presented ...

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