T-Superiority and T-Norm-Based Images of Fuzzy Sets

Comparisons of finite fuzzy sets based on the results of conjunctive and disjunctive aggregations of their membership grades are studied. For a given t-norm T, the notion of T-superiority of fuzzy sets is introduced. When a fuzzy set g is T-superior to a fuzzy set f, the description of a vague concept by g is much more desirable than the description by f. For a comparison of a fuzzy set f with the “standard” fuzzy set g (describing the desirable or historically the most common characterization of the vague concept in question) t-norm-based transformations of f with respect to g, called the T-images of f, are suggested. A special type of the T-image of f with respect to g may be considered as a soft evaluation of T-superiority of g to f.