On the migrativity of uninorms and nullnorms over overlap and grouping functions

Qiao, Junsheng; Hu, Bao Qing

doi:10.1016/j.fss.2017.11.012

Cited by 52 publications

(13 citation statements)

References 55 publications

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“…In especial, a uninorm is a t-norm if e is one while it is a t-conorm if e is zero. Because this kind of aggregation operations is a unification of t-norms and t-conorms, it is important both from a theoretical point of view (De Baets 1999;De Baets et al 2009;Drewniak and Drygaś 2002;Drygaś, Ruiz-Aguilera, and Torrens 2016;Drygaś 2010;Drygaś, Qin, and Rak 2017;Fodor, Yager, and Rybalov 1997;Qiao and Hu 2018;Su, Liu, and Pedrycz 2017) and for their practical applications, such as decision making (Yager 2002), neural networks (Pedrycz and Hirota 2007), fuzzy system modeling (Yager 1994(Yager , 2001, fuzzy mathematical morphology and image processing, and also fuzzy logic, in general (Metcalfe and Montagna 2007). In particular, uninorms are important in bipolar decision making, e.g.…”

Section: A Brief Review On Uninormsmentioning

confidence: 99%

New construction approaches of uninorms on bounded lattices

Çaylı

2021

International Journal of General Systems

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This article continuous to investigate the construction approaches for uninorms on bounded lattices. We introduce some new methods to obtain uninorms with an identity e ∈ L\{0, 1} by using closure (interior) operators on a bounded lattice L. As a by-product of these methods, we present two families of idempotent uninorms on bounded lattices. Furthermore, we provide some corresponding examples to illustrate that our methods can differ for different closure (interior) operators.

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Section: A Brief Review On Uninormsmentioning

confidence: 99%

New construction approaches of uninorms on bounded lattices

Çaylı

2021

International Journal of General Systems

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“…For further properties and related concepts on overlap functions, see [8,12,17,18,21,22,30,44,45,46,47,48,49].…”

Section: From Aggregation Functions To General Overlap Functionsmentioning

confidence: 99%

Fuzzy implication functions constructed from general overlap functions and fuzzy negations

Pinheiro¹,

Bedregal²,

Santiago³

et al. 2021

Preprint

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Fuzzy implication functions have been widely investigated, both in theoretical and practical fields. The aim of this work is to continue previous works related to fuzzy implications constructed by means of non necessarily associative aggregation functions. In order to obtain a more general and flexible context, we extend the class of implications derived by fuzzy negations and t-norms, replacing the latter by general overlap functions. We also investigate their properties, characterization and intersections with other classes of fuzzy implication functions.

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“…For all properties and related concepts on overlap functions and grouping functions, see [2,5,7,9,10,21,[23][24][25].…”

Section: Definition 4 [4] a Binary Functionmentioning

confidence: 99%

General Grouping Functions

Santos

Dimuro

Asmus

et al. 2020

Communications in Computer and Information Science

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Some aggregation functions that are not necessarily associative, namely overlap and grouping functions, have called the attention of many researchers in the recent past. This is probably due to the fact that they are a richer class of operators whenever one compares with other classes of aggregation functions, such as t-norms and t-conorms, respectively. In the present work we introduce a more general proposal for disjunctive n-ary aggregation functions entitled general grouping functions, in order to be used in problems that admit n dimensional inputs in a more flexible manner, allowing their application in different contexts. We present some new interesting results, like the characterization of that operator and also provide different construction methods.

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On the migrativity of uninorms and nullnorms over overlap and grouping functions

Cited by 52 publications

References 55 publications

New construction approaches of uninorms on bounded lattices

New construction approaches of uninorms on bounded lattices

Fuzzy implication functions constructed from general overlap functions and fuzzy negations

General Grouping Functions

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