Real vector space of LR-fuzzy intervals with respect to the shape-preserving t-norm-based addition

Makó, Zoltán

doi:10.1016/j.fss.2012.02.014

Cited by 9 publications

(4 citation statements)

References 26 publications

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“…Nesse contexto, a teoria dos conjuntos fuzzy tem se mostrado bastanteútil na busca por solução de problemas com características imprecisas, incompletas e inconsistentes [4]. 1 espalmeira@uesc.br 2 vrufino@ymail.com 3 gildsonj@gmail.com 2 Proposta por Zadeh [6] em 1965, essa teoria traz para a teoria usual de conjuntos uma extensão definindo infinitos possíveis graus de pertinência para um determinado elemento em conjuntos com características imprecisas.…”

Section: Palavras-chave Problema Dos Mínimos Quadrados Otimização Funclassified

Uma Abordagem Fuzzy do Problema dos Mínimos Quadrados

Palmeira¹,

Rufino²,

Jesus³

2017

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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Resumo. O Problema dos Mínimos Quadrados (PMQ)é um dos mais antigos e utilizados métodos de estimação de variáveis. Desde sua origem, diversas versões e propostas já foram estudadas e desenvolvidas com uma grande variação de métodos e aplicações. Em sua versão clássica determinística, o problema parte da estimação de uma variável em um sistema de equações inconsistente. Este trabalho propõe uma versão fuzzy para este problema onde, a partir das características intrínsecas da variável fuzzy próprias para modelagem de inconsistências e utilizando sua relação com a matemática intervalar, pretende-se formular uma versão mais completa para o PMQ.

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Section: Palavras-chave Problema Dos Mínimos Quadrados Otimização Funclassified

Uma Abordagem Fuzzy do Problema dos Mínimos Quadrados

Palmeira¹,

Rufino²,

Jesus³

2017

Proceeding Series of the Brazilian Society of Computational and Applied Mathematics

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“…For the sake of preserving the shapes of fuzzy intervals during the practical computation, some shape-preserving operations on fuzzy intervals with sigmoid and bell-shaped membership functions (Dombi and Gyorbiro 2006;Hong 2007;Hong et al 2007) were investigated. With the same aim, Mak (2012) constructed the real vector space of LR-FIs, and then presented the algebraic forms and the associated application. Based upon the definition of unrestricted LR-FI (Kaur and Kumar 2012), Kaur and Kumar (2013) presented the product of unconstrained LR-FI, thereby formulating a Mehar's method to deal with the fully linear programming problems.…”

Section: Introductionmentioning

confidence: 99%

An Extensive Operational Law for Monotone Functions of LR Fuzzy Intervals with Applications to Fuzzy Optimization

Zhao

Han

Zhou

2021

Preprint

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The operational law put forward by Zhou et al. on strictly monotone functions with regard to regular LR fuzzy numbers makes a valuable push to the development of fuzzy set theory. However, its applicable conditions are confined to strictly monotone functions and regular LR fuzzy numbers, which restricts its application in practice to a certain degree. In this paper, we propose an extensive operational law that generalizes the one proposed by Zhou et al. to apply to monotone (but not necessarily strictly monotone) functions with regard to regular LR fuzzy intervals (LR-FIs), of which regular fuzzy numbers can be regarded as particular cases. By means of the extensive operational law, the inverse credibility distributions (ICDs) of monotone functions regarding regular LR-FIs can be calculated efficiently and effectively. Moreover, the extensive operational law has a wider range of applications, which can deal with the situations hard to be handled by the original operational law. Subsequently, based on the extensive operational law, the computational formulae for expected values (EVs) of LR-FIs and monotone functions with regard to regular LR-FIs are presented. Furthermore, the proposed operational law is also applied to dispose fuzzy optimization problems with regular LR-FIs, for which a solution strategy is provided, where the fuzzy programming is converted to a deterministic equivalent first and then a newly-devised solution algorithm is utilized. Finally, the proposed solution strategy is applied to a purchasing planning problem, whose performances are evaluated by comparing with the traditional fuzzy simulation-based genetic algorithm. Experimental results indicate that our method is much more efficient, yielding high-quality solutions within a short time.

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“…Modal intervals have been used combined with fuzzy sets [10,11]. The study that we present is based on the set of trapezoidal fuzzy numbers, expanding this set using modal intervals.…”

Section: Introductionmentioning

confidence: 99%

A Generalization of Trapezoidal Fuzzy Numbers Based on Modal Interval Theory

Jorba

Adillon

2017

Symmetry

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Abstract:We propose a generalization of trapezoidal fuzzy numbers based on modal interval theory, which we name "modal interval trapezoidal fuzzy numbers". In this generalization, we accept that the alpha cuts associated with a trapezoidal fuzzy number can be modal intervals, also allowing that two interval modalities can be associated with a trapezoidal fuzzy number. In this context, it is difficult to maintain the traditional graphic representation of trapezoidal fuzzy numbers and we must use the interval plane in order to represent our modal interval trapezoidal fuzzy numbers graphically. Using this representation, we can correctly reflect the modality of the alpha cuts. We define some concepts from modal interval analysis and we study some of the related properties and structures, proving, among other things, that the inclusion relation provides a lattice structure on this set. We will also provide a semantic interpretation deduced from the modal interval extensions of real continuous functions and the semantic modal interval theorem. The application of modal intervals in the field of fuzzy numbers also provides a new perspective on and new applications of fuzzy numbers.

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Real vector space of LR-fuzzy intervals with respect to the shape-preserving t-norm-based addition

Cited by 9 publications

References 26 publications

Uma Abordagem Fuzzy do Problema dos Mínimos Quadrados

Uma Abordagem Fuzzy do Problema dos Mínimos Quadrados

An Extensive Operational Law for Monotone Functions of LR Fuzzy Intervals with Applications to Fuzzy Optimization

A Generalization of Trapezoidal Fuzzy Numbers Based on Modal Interval Theory

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