Standard Operations of Fuzzy Set

Complement set  Ā , union A ∪ B, and intersection A ⋂ B represent the standard operations of fuzzy theory and are arranged as,

We can find out that the above three operations are generalizations of those in crisp set. In the next sections, we’ll see variety of proposed

operators besides these operations. These various operators must satisfy necessary conditions, and they are put into use in diverse application

fields.

Among numerous operators, since complement, Max and Min operators are fundamental and simple, many fuzzy theories are develop based upon

these operators. Table 1.1 includes characteristics of the standard operators. Note that the following two characteristics of crisp set operators

does not hold here.

The reason for this occurrence is that the boundary of complement of A is ambiguous.

Table 1.1. Characteristics of standard fuzzy set operators

Kwang H. Lee, First Course on Fuzzy Theory and Applications, 2005, Springer, pag(27-28)