@misc{10481/93952,
year = {2021},
month = {7},
url = {https://hdl.handle.net/10481/93952},
abstract = {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.},
publisher = {IEEE},
keywords = {Lattices},
keywords = {Fuzzy sets},
keywords = {negation},
keywords = {triangular norm-conorm},
title = {Induced triangular norms and negations on bounded lattices},
doi = {10.1109/TFUZZ.2020.2985337},
author = {Lobillo Borrero, Francisco Javier and Navarro Garulo, Gabriel and Merino González, Luis Miguel and Santos Aláez, Evangelina},
}