Induced triangular norms and negations on bounded lattices
Metadatos
Afficher la notice complèteAuteur
Lobillo Borrero, Francisco Javier; Navarro Garulo, Gabriel; Merino González, Luis Miguel; Santos Aláez, EvangelinaEditorial
IEEE
Materia
Lattices Fuzzy sets negation triangular norm-conorm
Date
2021-07Referencia bibliográfica
IEEE Transactions on Fuzzy Systems, vol. 29, no. 7, pp. 1802-1814
Résumé
Some relevant notions in fuzzy set theory are those of triangular norm and conorm, and negation, which provide a systematic way of defining set-theoretic operations or, from other point of view, logical connectives. For instance, the majority of fuzzy implications are directly derived from these operators, so they play a prominent role in fuzzy control theory or in approximate reasoning. This incites the search of suitable t-norms, t-conorms and negations for solving each specific problem.
In this paper we propose a procedure, that we call induction, for designing them on spaces of lattice-valued maps. Concretely,
for each family of operators (t-norms, t-conorms or negations) indexed in the domain set, we may induce an operator of the
same kind, so that our method offers a great flexibility in the design task. It may be applied to well-known fuzzy objects as
interval-valued or type-2 fuzzy sets. Nevertheless, the theory is formally developed for arbitrary bounded lattices.