Quotient Space Based Problem Solving

Chapter 7

The Expansion of Quotient Space Theory

Abstract

In this chapter, we extend the quotient space theory to general cases. It includes two aspects. First, the falsity- and truth-preserving principles are extended to a general quotient space approximation principle. Second, the quotient space theory based on equivalence relations is extended to that based on tolerant relations and closure operations.

When transforming a solution in the original space to a solution in its quotient space, or vice versa, a precise quotient space should be constructed. This is a problem-dependent work. Therefore, we present a general principle, the quotient space approximation principle. By the principle, a set of quotient spaces is constructed to approximate the ...