Quotient Space Based Problem Solving

4.5. Operations and Quotient Structures

There is a variety of operations defined on a domain. In fact, an operation implicitly defines an interrelationship among elements of the domain. Under different grain-size worlds, the following issues should be answered. The induction of a corresponding operation on a quotient space from an operation defined on its original space, and the synthesis of two operations defined on different grain-size spaces becomes a new operation on their synthetic space, i.e. a finer space.

Let us consider two simple examples.

Example 4.10

is a set of non-negative integers, is a quotient set of X denoted by , where .

Let ‘+’ ...