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 $f$.
@article{438,
title = {T-superiority and t-norm-based images of fuzzy sets},
journal = {Tatra Mountains Mathematical Publications},
volume = {65},
year = {2016},
doi = {10.2478/tatra.v66i0.438},
language = {EN},
url = {http://dml.mathdoc.fr/item/438}
}
Bodjanova, Slavka; Kalina, Martin. T-superiority and t-norm-based images of fuzzy sets. Tatra Mountains Mathematical Publications, Tome 65 (2016) . doi : 10.2478/tatra.v66i0.438. http://gdmltest.u-ga.fr/item/438/