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Quotient Space Based Problem Solving by Bo Zhang, Ling Zhang

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7.4. The Expansion of Quotient Space Theory

7.4.1. Introduction

The quotient space theory we have discussed so far is based on the following two main assumptions. (1) The domain structure is limited to topology. (2) The domain granulation is based on equivalence relations, i.e., classification without overlap. Now, we will relax the two restrictions. First, we consider the structures formed by closure operations that are broader than topological ones. Second, domain granulation will be extended from equivalence relations to tolerance relations.

7.4.2. Closure Operation-Based Quotient Space Theory

There is a variety of closure operations, so different structures can be defined by the operations. The domain structures described by closure operations ...

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