Abstract
J.A. Goguen introduced the L-fuzzy sets (that are extension of Zadeh’s fuzzy sets), in which the image set of the membership function is an ordered set \((L, \le _L)\) (base set of the L-fuzzy set). Since then, a lot of papers studying different classes of those sets have been published. One of the main topics in this field has been the involutions in each set L, but these involutions are not totally independent. So the present paper is devoted to relate the involutions on the base sets L of some L-fuzzy sets, being L a certain bounded lattice. In particular, we consider L being the bounded lattices defined by [0, 1] and \([0,1]^2\), as well as by the base sets of the Atanassov’s and interval-valued fuzzy sets.
This research has been partially supported by the Government of Spain (grant PCG2018-096509-B-100), Comunidad de Madrid (Convenio Plurianual con la Universidad Politécnica de Madrid en la línea de actuación Programa de Excelencia para el Profesorado Universitario), Universidad Politécnica de Madrid (Spain) and Universidad Autónoma de Chile.
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Cubillo, S., Torres-Blanc, C., Magdalena, L., Hernández-Varela, P. (2022). Involutions on Different Goguen L-fuzzy Sets. In: Ciucci, D., et al. Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2022. Communications in Computer and Information Science, vol 1601. Springer, Cham. https://doi.org/10.1007/978-3-031-08971-8_57
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