Fuzzy Set-Theoretic Operators

In this chapter, we will concentrate on some fuzzy set-theoretic operations and their distinctive properties. First, we will review the standard fuzzy complements—along with different triangular norms and conforms with their properties: increasing and decreasing generators and their pseudo-inverse elaborately. Then fuzzy intersection, union operators, Archimedean t-norm and t-conorm, and the averaging operator are explained by citing suitable examples. Some general aggregation operations and their classifications, such as arithmetic mean aggregation, geometric and harmonic mean aggregation operations, etc., are also described. Some other functions like generalized means, ordered weighted averaging, norm, associative averaging, parameterized class of norm, symmetric sums, and symmetric difference equivalence operations are also incorporated with illustrative examples.