Residuated implications derived from quasi-overlap functions on lattices

Paiva, Rui; Bedregal, Benjamín R. C.; Santiago, Regivan H. N.; Vieira, Thiago Kistenmacher

doi:10.1016/j.ijar.2021.04.008

Cited by 21 publications

(2 citation statements)

References 40 publications

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“…In [20] the authors used a special class of binary general overlap functions to expand the notion of BL-algebras (which are the algebraic counterpart of a type of fuzzy logic modeled by Peter Hájek). This class of functions offers a promising field of research [7,[21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

General Pseudo Quasi-Overlap Functions on Lattices

Paiva

Bedregal

2022

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The notion of general quasi-overlaps on bounded lattices was introduced as a special class of symmetric n-dimensional aggregation functions on bounded lattices satisfying some bound conditions and which do not need to be continuous. In this paper, we continue developing this topic, this time focusing on another generalization, called general pseudo-overlap functions on lattices, which in a given classification system measures the degree of overlapping of several classes and for any given object where symmetry is an unnecessarily restrictive condition. Moreover, we also provide some methods of constructing these functions, as well as a characterization theorem for them. Also, the notions of pseudo-t-norms and pseudo-t-conorms are used to generalize the concepts of additive and multiplicative generators for the context of general pseudo-quasi-overlap functions on lattices and we explore some related properties.

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Section: Introductionmentioning

confidence: 99%

General Pseudo Quasi-Overlap Functions on Lattices

Paiva

Bedregal

2022

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“…As one kind of binary general overlap functions, in [13] the authors extended the notion of BL-algebras, which are the algebraic counterpart of the a type of fuzzy logic modeled by Peter Hájek. This class of functions offers a promising field of research [2,4,8,14,15]. In [14], Paiva et al introduced the concept of quasioverlap functions on bounded lattices and investigated some vital properties of them.…”

Section: Introductionmentioning

confidence: 99%

General quasi-overlap functions on lattices

Paiva¹,

Bedregal²

2021

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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One recent work, Paiva et al. introduced the concept of quasi-overlap functions on bounded lattices and investigated some vital properties of them. In this paper, we continue consider this research topic and focus on a generalization, called general quasi-overlap functions, which measure the degree of overlapping of several classes in a given classification system and for any given object. We also provide a characterization, as well as some methods of constructing these functions.

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