Inequality relation between fuzzy numbers and its use in fuzzy optimization

Ramík, Jaroslav; ímánek, Josef

doi:10.1016/s0165-0114(85)80013-0

Cited by 311 publications

(82 citation statements)

References 4 publications

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“…We define orders on F(R) based on orderings of level sets of fuzzy sets. 5,8,10,12]). Let a, b ∈ F (R).…”

Section: Preliminariesmentioning

confidence: 99%

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Fuzzy Distance and Fuzzy Norm

Kon

2017

JORSJ

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We consider fuzzy sets on a metric, vector, or normed space. It is not assumed that the fuzzy sets have compact supports. In the present paper, a fuzzy distance and a fuzzy norm are proposed in order to measure the difference between two fuzzy sets, and their fundamental properties are investigated. Their definitions are based on Zadeh's extension principle. Although they are different from the classical ones based on the Hausdorff metric, they are suitable for data containing uncertainty or vagueness. The obtained results can be expected to be useful for analyzing such data when the data are represented as fuzzy sets.

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“…We define orders on F(R) based on orderings of level sets of fuzzy sets. 5,8,10,12]). Let a, b ∈ F (R).…”

Section: Preliminariesmentioning

confidence: 99%

“…The fuzzy max order for fuzzy numbers has been primarily defined in [12], and many researches have dealt with it. Then, the fuzzy max order for fuzzy numbers has been extended for fuzzy vectors in [10], for fuzzy sets which are closed, convex, normal, and support bounded in [8], and for general fuzzy sets in [5].…”

Section: Definition 22 ([mentioning

confidence: 99%

Fuzzy Distance and Fuzzy Norm

Kon

2017

JORSJ

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“…In fact, there are many ways to define the fuzzy order among the set of all fuzzy numbers [19][20][21][22]. For example, Ramík andímánek [22] proposed a partial order relation called the fuzzy-max order; Molinari [20] considered a new criterion of choice between generalized triangular fuzzy numbers and so on. In this paper, two specific partial ordering relations on fuzzy numbers using parametric representation are introduced.…”

Section: Fuzzy Numbers and Their Arithmeticmentioning

confidence: 99%

On Fuzzy Portfolio Selection Problems: A Parametric Representation Approach

Fard

Ramezanzadeh

2017

Complexity

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Fuzzy portfolio selection problem is a major issue in the financial field and a special case of constrained fuzzy-valued optimization problems (CFOPs). In this respect, the present paper aims to investigate the CFOP with regard to the features of the parametric representation of fuzzy numbers named as convex constraint function (CCF) which is proposed by Chalco-Cano et al. in 2014. Furthermore, relying on this parametric representation, some proper conditions are provided for the existence of solutions to a CFOP. To this end, by the increasing representation of CCF, the main problem is converted to a parametric multiobjective programming problem and some solution concepts from a similar framework in the multiobjective programming are proposed for the CFOP. Eventually to illustrate the proposed results, the fuzzy portfolio selection problem is discussed.

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“…First however, we need to convert the imprecise constraints into crisp ones using the fuzzy ranking concept. All constraints with imprecise coefficients can be replaced by three auxiliary constraints [64] A α l x ≤ b α l , (C Once α is known, we again have crisp constraints with a fuzzy objective.…”

Section: C3 Fuzzy Objective Constraint and Limit Coefficientsmentioning

confidence: 99%