2022
DOI: 10.1109/tfuzz.2022.3160326
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Admissible Orders on Fuzzy Numbers

Abstract: From the more than two hundred partial orders for fuzzy numbers proposed in the literature, only a few are total. In this paper, we introduce the notion of admissible order for fuzzy numbers equipped with a partial order, i.e. a total order which refines the partial order. In particular, it is given special attention to the partial order proposed by Klir and Yuan in 1995. Moreover, we propose a method to construct admissible orders on fuzzy numbers in terms of linear orders defined for intervals considering a … Show more

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Cited by 19 publications
(6 citation statements)
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“…We denote the set R L to be the set of all fuzzy numbers; R L can be equipped with a partial order in the following manner: x ≤ y if and only if x αl ≤ y αl and x αr ≤ y αr for all α ∈ L 0 . Additionally, in [24], the authors investigated linear orders on fuzzy numbers which refine this partial order. In this scenario, Gahler et al showed that the concepts of semi-algebras can be utilized to extend the concept of fuzzy numbers, according to the following proposition:…”
Section: Fuzzy Set Theory and Semi-algebrasmentioning
confidence: 99%
“…We denote the set R L to be the set of all fuzzy numbers; R L can be equipped with a partial order in the following manner: x ≤ y if and only if x αl ≤ y αl and x αr ≤ y αr for all α ∈ L 0 . Additionally, in [24], the authors investigated linear orders on fuzzy numbers which refine this partial order. In this scenario, Gahler et al showed that the concepts of semi-algebras can be utilized to extend the concept of fuzzy numbers, according to the following proposition:…”
Section: Fuzzy Set Theory and Semi-algebrasmentioning
confidence: 99%
“…It is worth noting that this relation is the restriction to the TFN's of the Klir and Yuan partial order on the fuzzy numbers. In the following, we adapt the definition of admissible orders on fuzzy numbers introduced in [9] to the context of TFN's.…”
Section: Note That (−1)amentioning
confidence: 99%
“…Additionally, there are several proposal of partial orders (totals and non totals) for fuzzy numbers or a subclass of the fuzzy numbers as for example in [5,6,7,8]. More recently, Zumelzu et al in [9], in the light of the notion of admissible orders in the context of extensions of fuzzy set theory as in [10,11,12,13], proposed the notion of admissible orders for fuzzy numbers as total orders which refines the order of Klir and Yuan in [4].…”
Section: Introductionmentioning
confidence: 99%
“…For simplicity, if (𝑥, 𝑦) ∈ , we denote it by 𝑥 ⪯ 𝑦, and we will say that ⪯ is the binary relation on 𝑋. A binary relation ⪯ is total (or linear) if 𝑥 ⪯ 𝑦 or 𝑦 ⪯ 𝑥 whatever 𝑥, 𝑦 ∈ 𝑋 (see [37]). Each total binary relation is reflexive (that is, 𝑥 ⪯ 𝑥 for each 𝑥 ∈ R).…”
Section: Preliminariesmentioning
confidence: 99%