Aggregation of fuzzy quasi-metrics

Pedraza, Tatiana; Rodrı́guez-López, Jesús; Valero, Óscar

doi:10.1016/j.ins.2020.08.045

Cited by 23 publications

(28 citation statements)

References 35 publications

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“…This question for metrics has been also considered recently by Mayor and Valero [4]. Therefore, we have two different but related problems, which gave rise to two different families of functions that we next define using the terminology of [9,17,20].…”

Section: Aggregation Of Metrics and Normsmentioning

confidence: 95%

“…The reason for having chosen the definition of weak fuzzy (quasi-)norm as considered in 3 instead of other definition of fuzzy norm is that every weak fuzzy (quasi-)norm (N, * ) on a vector space V induces a fuzzy (quasi-)metric (M N , * ) on V (in the sense of the paper [26]) given as M N (x, y, t) = N(y − x, t) for all x, y ∈ V and all t ≥ 0 (see [18]). Since (quasi-)metric aggregation functions have been already characterized in [17] and we plan to characterize here the functions that aggregate fuzzy (quasi-)norms, it is natural to select a concept of fuzzy (quasi-)norm that allows constructing a fuzzy (quasi-)metric.…”

Section: Remarkmentioning

confidence: 99%

“…In Section 2 we have summarized the known results about the aggregation of (quasi-)metrics and asymmetric norms on products and on sets. On the other hand, in [17], the functions that aggregate fuzzy (quasi-)metrics on products and on sets were completely characterized. Nevertheless, to the best of our knowledge, the problem for fuzzy (quasi-)norms has not been already solved.…”

Section: Aggregation Of Weak Fuzzy (Quasi-)normsmentioning

confidence: 99%

“…Recently, Valero, Pedraza and Rodríguez-López [17] have studied the functions that permit the generation of a unique fuzzy (quasi-)metric from a collection of fuzzy (quasi-)metrics. They proved that, compared to the classical case, the functions aggregating fuzzy metrics are exactly the same than compared to the functions that aggregate fuzzy quasimetrics.…”

Section: Introductionmentioning

confidence: 99%

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Aggregation of Weak Fuzzy Norms

2021

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Aggregation is a mathematical process consisting in the fusion of a set of values into a unique one and representing them in some sense. Aggregation functions have demonstrated to be very important in many problems related to the fusion of information. This has resulted in the extended use of these functions not only to combine a family of numbers but also a family of certain mathematical structures such as metrics or norms, in the classical context, or indistinguishability operators or fuzzy metrics in the fuzzy context. In this paper, we study and characterize the functions through which we can obtain a single weak fuzzy (quasi-)norm from an arbitrary family of weak fuzzy (quasi-)norms in two different senses: when each weak fuzzy (quasi-)norm is defined on a possibly different vector space or when all of them are defined on the same vector space. We will show that, contrary to the crisp case, weak fuzzy (quasi-)norm aggregation functions are equivalent to fuzzy (quasi-)metric aggregation functions.

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Section: Aggregation Of Metrics and Normsmentioning

confidence: 95%

Section: Remarkmentioning

confidence: 99%

Section: Aggregation Of Weak Fuzzy (Quasi-)normsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Aggregation of Weak Fuzzy Norms

2021

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“…In other words, the problem is determining conditions guarantee that the output has the same structure. Preservation of structures under aggregation has been widely studied in recent decades (see [12][13][14][15][16][17][18][19][20][21]).…”

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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