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Quotient Space Based Problem Solving by Bo Zhang, Ling Zhang

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4.7. Fuzzy Reasoning Based on Quotient Space Structures

In this section, we present a framework of fuzzy reasoning based on quotient space structures. They are: (1) introduce quotient structure into fuzzy set theory, i.e., establish fuzzy set representations and their relations in multi-granular spaces, (2) introduce the concept of fuzzy set into quotient space theory, i.e., fuzzy equivalence relation and its reasoning, (3) the transformation of three different granular computing methods, (4) the methods for transforming statistical reasoning models into quotient space structures. The combination of the two (fuzzy set and quotient space) methodologies is intended to embody the language-processing capacity of fuzzy set method and multi-granular ...

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