On the relationship between fuzzy subgroups and indistinguishability operators

Boixader, Dionís; Recasens, J.

doi:10.1016/j.fss.2018.09.002

Cited by 10 publications

(3 citation statements)

References 10 publications

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“…For example, isotone functions which are ( * -)supmultiplicative are called ( * -)closed, see Definition 7.1 in [16]. Moreover, if F is * -supmultiplicative and F (1) = 1 then it is called an * -fuzzy monoid [7].…”

Section: Functions Preserving Properties Of Fuzzy Binary Relationsmentioning

confidence: 99%

Aggregation of fuzzy quasi-metrics

Pedraza

Rodrı́guez-López

Valero

2021

Information Sciences

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Section: Functions Preserving Properties Of Fuzzy Binary Relationsmentioning

confidence: 99%

Aggregation of fuzzy quasi-metrics

Pedraza

Rodrı́guez-López

Valero

2021

Information Sciences

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“…Min-subgroups can be identified as indistinguishability operators that are invariant by translations (see [8]). This type of indistinguishability operator plays a fundamental role in some applications, notably in mathematical morphology (see [8][9][10][11]).…”

Section: Introductionmentioning

confidence: 99%

On Self-Aggregations of Min-Subgroups

Bejines

Ardanza-Trevijano

Elorza

2021

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Preservation of structures under aggregation functions is an active area of research with applications in many fields. Among such structures, min-subgroups play an important role, for instance, in mathematical morphology, where they can be used to model translation invariance. Aggregation of min-subgroups has only been studied for binary aggregation functions . However, results concerning preservation of the min-subgroup structure under binary aggregations do not generalize to aggregation functions with arbitrary input size since they are not associative. In this article, we prove that arbitrary self-aggregation functions preserve the min-subgroup structure. Moreover, we show that whenever the aggregation function is strictly increasing on its diagonal, a min-subgroup and its self-aggregation have the same level sets.

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“…Since indistinguishability fuzzy relations were introduced by Trillas, many authors have explored their properties, methods for generating them, and their applications (see, for instance, [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]).…”

Section: Introductionmentioning

confidence: 99%

Aggregation of Indistinguishability Fuzzy Relations Revisited

2021

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Indistinguishability fuzzy relations were introduced with the aim of providing a fuzzy notion of equivalence relation. Many works have explored their relation to metrics, since they can be interpreted as a kind of measure of similarity and this is, in fact, a dual notion to dissimilarity. Moreover, the problem of how to construct new indistinguishability fuzzy relations by means of aggregation has been explored in the literature. In this paper, we provide new characterizations of those functions that allow us to merge a collection of indistinguishability fuzzy relations into a new one in terms of triangular triplets and, in addition, we explore the relationship between such functions and those that aggregate extended pseudo-metrics, which are the natural distances associated to indistinguishability fuzzy relations. Our new results extend some already known characterizations which involve only bounded pseudo-metrics. In addition, we provide a completely new description of those indistinguishability fuzzy relations that separate points, and we show that both differ a lot.

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On the relationship between fuzzy subgroups and indistinguishability operators

Cited by 10 publications

References 10 publications

Aggregation of fuzzy quasi-metrics

Aggregation of fuzzy quasi-metrics

On Self-Aggregations of Min-Subgroups

Aggregation of Indistinguishability Fuzzy Relations Revisited

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