<abstract xmlns="http://www.w3.org/1999/xhtml"><p> 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.</p></abstract>

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.

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

Texas A&M University-Kingsville Department of Mathematics, MSC 172 Kingsville TX 78363,

Slovak University of Technology in Bratislava Faculty of Civil Engineering Dept. of Mathematics Radlinského 11 SK–810-05 Bratislava,

Tatra Mountains Mathematical Publications

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

{"article-title":"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,...

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

Published Online: Jan 20, 2017

Page range: 25 - 37

Received: Jul 15, 2016

DOI: https://doi.org/10.1515/tmmp-2016-0017

Keywords
coarser images of fuzzy sets, comparison of fuzzy sets, t-norm

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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

Published Online: Jan 20, 2017

Page range: 25 - 37

Received: Jul 15, 2016

DOI: https://doi.org/10.1515/tmmp-2016-0017

Keywordscoarser images of fuzzy sets, comparison of fuzzy sets, t-norm

© 2017

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Keywords
coarser images of fuzzy sets, comparison of fuzzy sets, t-norm