On Unconstrained Fuzzy-Valued Optimization Problems

Heidari, Mohammad Mehdi; Zadeh, M R Kebriaei; Fard, Omid Solaymani; Borzabadi, Akbar Hashemi

doi:10.1007/s40815-016-0165-1

Cited by 4 publications

(2 citation statements)

References 15 publications

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“…Proposition 10 (see [24]). One of the first definitions of differentiability for fuzzyvalued functions is the Hukuhara differentiability, which suffers disadvantages in particular to the point that the inverse subtraction does not exist.…”

Section: Definition 9 (Limit Of Fuzzy-valued Function [24]) Letcmentioning

confidence: 98%

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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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Section: Definition 9 (Limit Of Fuzzy-valued Function [24]) Letcmentioning

confidence: 98%

“…is convex (see Example 2.2 [24]). Therefore, the constrained quadratic programming problem (46) is a convex programming problem, by Theorem 20.…”

Section: Numerical Examplesmentioning

confidence: 99%