THE OPERATION OF FUZZY SET -Standard Operations of Fuzzy Set
المؤلف:
Kwang H. Lee
المصدر:
First Course on Fuzzy Theory and Applications
الجزء والصفحة:
27-28
5-7-2016
1140
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)
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