Construction of admissible linear orders for pairs of intervals

Miguel, Laura De; Bustince, Humberto; Induráin, Esteban; Kolesárová, Anna; Mesiar, Radko; Baets, Bernard De

doi:10.2991/ifsa-eusflat-15.2015.164

Cited by 3 publications

(4 citation statements)

References 16 publications

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“…The notion of admissible order was first introduced in [16] for interval-valued fuzzy sets and later on in [28] for interval-valued Atanassov's intuitionistic fuzzy sets. In this section, we first generalize the notion of admissible order to the setting of n-dimensional fuzzy sets showing some particular examples.…”

Section: Admissible Orders and Owa Operators On Fuzzy Multisetsmentioning

confidence: 99%

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An algorithm for group decision making using n-dimensional fuzzy sets, admissible orders and OWA operators

et al. 2017

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In this paper we propose an algorithm to solve group decision making problems using n-dimensional fuzzy sets, namely, sets in which the membership degree of each element to the set is given by an increasing tuple of n elements. The use of these sets has naturally led us to define admissible orders for n-dimensional fuzzy sets, to present a construction method for those orders and to study OWA operators for aggregating the tuples used to represent the membership degrees of the elements. In these conditions, we present an algorithm and apply it to a case study, in which we show that the exploitation phase which appears in many decision making methods can be omitted by just considering linear orders between tuples.

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Section: Admissible Orders and Owa Operators On Fuzzy Multisetsmentioning

confidence: 99%

“…Step 2) arbitrarily. In some others studies, such as in [19,28], a comparison between the different solutions using some different orders is made. However, since our sole intention is to show the validity of our proposal, we have only shown the results corresponding to one order.…”

Section: Illustrative Examplementioning

confidence: 99%

An algorithm for group decision making using n-dimensional fuzzy sets, admissible orders and OWA operators

et al. 2017

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“…orders which refines the natural order for intervals, starts with the work of Bustince et al [2]. Latelly, this notion was adapted for other domains in [3,4,5,6].…”

Section: Introductionmentioning

confidence: 99%

Admissible orders on fuzzy numbers

Zumelzu¹,

Bedregal²,

Mansilla³

et al. 2020

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From the more than two hundred partial orders for fuzzy numbers proposes in the literature, only a few are totals. In this paper, we introduce the notion of admissible orders for fuzzy numbers equipped with a partial order, i.e. a total order which refines the partial order. In particular, is given special attention when thr partial order is the 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 strictly increasing upper dense sequence, proving that this order is admissible for a given partial order.

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“…Uma vantagem das ordens admissíveis é que incluem a maioria dos exemplos usuais de ordens lineares que aparecem na literatura, entre eles, as ordens lineares lexicográficas 1 e 2, e Xu e Yager [37]. As aplicações das ordens admissíveis baseadas em funções de agregação são encontradas em tomada de decisões [36,38,39] e processamento de imagens [20].…”

Section: Introductionunclassified

Detecção de bordas de imagens digitais baseada em morfologia matemática L-fuzzy e h-Ordens

Corbacho Carazas

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AgradecimentosO presente trabalho foi realizado com apoio da Coordenação de Aperfeiçoamento de Pessoal de Nível Superior -Brasil (CAPES) -Código de Financiamento 001, e com apoio do Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq), número de processo 142461/2018-0.Minha imensa gratidão ao meu orientador, professor Dr. Peter Sussner, por toda a dedicação, orientação, pelas discussões acadêmicas e pelos desafios colocados, os quais foram fundamentais para a concretização desta tese e o meu crescimento profissional.

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Construction of admissible linear orders for pairs of intervals

Abstract: In this work we construct linear orders between pairs of intervals by using aggregation functions. We apply these orders in a decision-making problem where the experts provide their opinions by means of interval-valued fuzzy sets.

Cited by 3 publications

References 16 publications

An algorithm for group decision making using n-dimensional fuzzy sets, admissible orders and OWA operators

An algorithm for group decision making using n-dimensional fuzzy sets, admissible orders and OWA operators

Admissible orders on fuzzy numbers

Detecção de bordas de imagens digitais baseada em morfologia matemática L-fuzzy e h-Ordens

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