Affiliations: [a]
Department of Informatics and Applied Mathematics – DIMAp, Group of Logic, Language, Information, Theory and Applications – LOLITA, Federal University of Rio Grande do Norte – UFRN, Natal, Rio Grande do Norte, Brazil
| [b]
Center of Exact and Natural Sciences – CCEN, Rural Federal University of SemiArid – UFERSA, Mossoró, Rio Grande do Norte, Brazil
Correspondence:
[*]
Corresponding author. Benjamín Bedregal, Department of Informatics and Applied Mathematics – DIMAp, Group of Logic, Language, Information, Theory and Applications – LOLITA, Federal University of Rio Grande do Norte – UFRN, Natal, Rio Grande do Norte, 59072-970, Brazil. E-mail: [email protected].
Abstract: In this paper, we consider the notions of t-norm, t-conorm, fuzzy negation and De Morgan triples and prove some new results about them. We use the notion of ordinal sums of a family of t-(co)norms and characterize the ordinal sums from a family of the fuzzy negations and automorphisms for proving results involving these concepts in De Morgan triples. In addition, we use the definitions of multiplicative generators of t-norms and t-conorms to prove results involving these concepts and their pseudo inverse. Also, we establish some conditions for obtaining a strict fuzzy negation from the multiplicative generators of a t-norm and a t-conorm in such a way that the triple is a De Morgan triple. Finally, we provide some results on the ordinal sums of the De Morgan triples based on their multiplicative generators.
Keywords: t-norm, t-conorm, fuzzy negation, De Morgan triples, automorphism
