An improved ranking method for generalized fuzzy numbers based on Euclidian distance concept

Eslamipoor, Reza; Hosseini-Nasab, Hasan; Sepehriar, Abbas

doi:10.1007/s13370-014-0285-4

Cited by 6 publications

(3 citation statements)

References 17 publications

(33 reference statements)

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“…In addition, some methods for ranking fuzzy numbers using distances have been developed [39,40], but none of those trapezoidal approximations is useful to us because, although they preserve certain properties, they do not impose preservation of inclusivity and so they are not valid for semantic interpretations.…”

Section: Corollary 2 Under the Above Conditions Of Theoremmentioning

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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Section: Corollary 2 Under the Above Conditions Of Theoremmentioning

confidence: 99%

A Generalization of Trapezoidal Fuzzy Numbers Based on Modal Interval Theory

Jorba

Adillon

2017

Symmetry

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“…Ban, Coroianu and Khastan [4] developed a general method to study the LâȂŞR approximations of fuzzy numbers preserving ambiguity, value and width. Recently some methods for ranking fuzzy numbers using distances have been developed [12], [6].…”

Section: Fuzzy Modal Extensions and Semanticsmentioning

confidence: 99%

“…Let us consider the trapezoidal fuzzy equation (2, 5, 7, 9) + X = (6,7,8,9). There is no traditional fuzzy number X which is a solution of the equation.…”

Section: Applications and Numerical Examplesmentioning

confidence: 99%

Quantified trapezoidal fuzzy numbers

Adillon

Jorba

2017

IFS

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The aim of this work is to construct quantified trapezoidal fuzzy numbers as an extension of trapezoidal fuzzy numbers, by using modal intervals and accepting the possibility that the α-cuts of a trapezoidal fuzzy number may also be improper intervals. In addition, this paper addresses the inclusion relationship which is deduced from the inclusion of modal intervals and is related to the classical setinclusion relationship between trapezoidal fuzzy numbers as well as the extensions of real continuous functions over the set of quantified trapezoidal fuzzy numbers.Using the semantic interpretation of the calculations over modal intervals will enable us to interpret the meaning of the calculus accurately over quantified trapezoidal fuzzy numbers.With quantified trapezoidal fuzzy numbers, we will be able to overcome some operational limitations that are usually faced when working with trapezoidal fuzzy numbers from a classical point of view. In order to show the applicability of quantified trapezoidal fuzzy numbers, we propose fuzzy equations which have no solution in the set of proper fuzzy numbers yet do have solutions that are improper fuzzy numbers. We also propose two applications of quantified trapezoidal fuzzy numbers, one of them about financial calculations and the other one in an optical problem.

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