A parametric approach to evaluate fuzzy quantities

Anzilli, Luca; Facchinetti, Gisella; Mastroleo, Giovanni

doi:10.1016/j.fss.2014.02.018

Cited by 14 publications

(14 citation statements)

References 23 publications

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“…In some works such as [1,3,13,15,16], the authors have tried to solve an optimization problem to obtain a trapezoidal fuzzy number as a nearest approximation. Recently, some works have been done on approximation of a fuzzy number [4,[6][7][8][9]11] by defining distance functions.…”

Section: Introductionmentioning

confidence: 99%

Fuzzy semi-numbers and a distance on them with a case study in medicine

2018

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In this paper, we present the novel concept of fuzzy semi-numbers. Then, a method for assigning distance between every pair of fuzzy semi-numbers is given. Moreover, it is shown that this distance is a metric on the set of all trapezoidal fuzzy semi-numbers with the same height and is a pseudo-metric on the set of all fuzzy semi-numbers. Also, by utilizing this distance, we propose an approximation of a fuzzy semi-number with given height and apply this approximation method in a medical case study.

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Section: Introductionmentioning

confidence: 99%

Fuzzy semi-numbers and a distance on them with a case study in medicine

2018

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“…The Ralescu proposal is for normal sets that may be not convex, but may be easily rewritten in the non-normal case. We prove that proposal [17], although very general, does not contain as particular case the Ralescu idea.…”

Section: Interval Approximation Of a Fuzzy Quantity: Previous Proposalsmentioning

confidence: 83%

“…This idea offers two opportunities: one point of the interval like the middle point or a convex combination of its extremes may be the evaluation of the fuzzy set, the width of the interval may be considered as its ambiguity. Even in this case several results are present in literature for fuzzy numbers [1,5,14,15,13], while few information are present for general fuzzy sets [16,17]. Our work goes in this direction not only to produce a new way to associate to a general fuzzy set an interval and therefore an evaluation, but also to offer a general method that, depending from two parameters, may be red as a generalization of the previous methods existing in literature.…”

Section: Introductionmentioning

confidence: 95%

“…The first is due to Ralescu [16] and the second has been proposed by Anzilli and Facchinetti in [17]. The Ralescu proposal is for normal sets that may be not convex, but may be easily rewritten in the non-normal case.…”

Section: Interval Approximation Of a Fuzzy Quantity: Previous Proposalsmentioning

confidence: 99%

“…In [17] Anzilli and Facchinetti proposed a procedure to approximate a fuzzy quantity A with the interval…”

Section: Anzilli and Facchinetti Proposal [17]mentioning

confidence: 99%

See 2 more Smart Citations

A general fuzzy set representation for decision making

Anzilli¹,

Facchinetti²

2015

Proceedings of the 2015 Conference of the International Fuzzy Systems Association and the European Society for Fuzzy Logic and

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In this paper we propose a general procedure to represent a fuzzy set that may be non-normal and/or non-convex. This representation will be offered by an interval and a crisp value. This idea is useful either in optimization and decision making problems or in defuzzification step of a fuzzy inference system. This proposal, depending on some parameters, either offers new methods or contains previous ones present in literature.

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A Fuzzy Quantity Mean-Variance View and Its Application to a Client Financial Risk Tolerance Model

Anzilli

Facchinetti

2016

Int. J. Intell. Syst.

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In this paper, we associate a probability distribution to a fuzzy variable represented by a continuous fuzzy quantity, where a fuzzy quantity is a fuzzy set that may be nonnormal and/or nonconvex. Our proposal is quite general and contains as particular cases other transformations presented in the literature. Furthermore, we define the variance of a fuzzy quantity as the variance of the probability distribution associated with it. The proposed variance agrees in the case of fuzzy numbers with the possibilistic one introduced by Irina Georgescu. We also apply our transformation to the evaluation of fuzzy quantities. The expected value of such probability distribution agrees with those introduced for fuzzy numbers by other authors; moreover, it matches the defuzzification value of a fuzzy quantity proposed by the same authors in other papers. To capture more information contained in a fuzzy quantity, or for ranking problems, we suggest to evaluate it by means of the pair mean variance, using the probability distribution associated with it. To illustrate how our method works, we apply it to evaluate the financial risk tolerance of a bank client using a fuzzy inference system.

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A parametric approach to evaluate fuzzy quantities

Cited by 14 publications

References 23 publications

Fuzzy semi-numbers and a distance on them with a case study in medicine

Fuzzy semi-numbers and a distance on them with a case study in medicine

A general fuzzy set representation for decision making

A Fuzzy Quantity Mean-Variance View and Its Application to a Client Financial Risk Tolerance Model

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