General L-fuzzy aggregation functions based on complete residuated lattices

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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“…Similarly, strictly decreasing maps are defined. Recent studies have focused on n-ary maps on bounded lattices [23,41,42]. Definition 1 ([41]).…”

Section: Aggregation Functions On Bounded Latticesmentioning

confidence: 99%

General Pseudo Quasi-Overlap Functions on Lattices

Paiva

Bedregal

2022

Axioms

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show abstract

“…Similarly, strictly decreasing mappings are defined. Recent studies have focused on n-ary mappings on bounded lattices called aggregation functions [5,11,14].…”

Section: Aggregation Functions On Bounded Latticesmentioning

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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“…There exists a large collection of construction methods as well as different important classes of aggregation operators. In particular, aggregation functions classes in the fuzzy context pL " r0, 1sq have been widely studied (BORKOTOKEY et al, 2017;DAN;HU;QIAO, 2020) and many of algebraic properties and classes of aggregations have been explored in (KOMORNÍKOVÁ; MESIAR, 2011; CALVO; MAYOR; MESIAR, 2012). The strategy followed here is to study the operations that naturally arise from the topological ordered structures studied in the last sections.…”

Section: Aggregations and I-set Descriptors On Archimedean O-ringsmentioning

confidence: 99%

Toward deep neural networks with generalized morphological components

Contreras¹

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General L-fuzzy aggregation functions based on complete residuated lattices

Cited by 4 publications

References 60 publications

General Pseudo Quasi-Overlap Functions on Lattices

General Pseudo Quasi-Overlap Functions on Lattices

General quasi-overlap functions on lattices

Toward deep neural networks with generalized morphological components

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