On invex fuzzy mappings and fuzzy variational-like inequalities

A. Rufián-Lizana; Y. Chalco-Cano; R. Osuna-Gómez; G. Ruiz-Garzón

doi:10.1016/j.fss.2012.02.001

On invex fuzzy mappings and fuzzy variational-like inequalities

A. Rufián-Lizana
, Y. Chalco-Cano
, R. Osuna-Gómez
, G. Ruiz-Garzón

Department of Mathematics

University of Seville
University of Cádiz

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

Abstract

In this paper, we first show the need for introducing invex fuzzy mappings. After that, we show that the concept of invex fuzzy mapping previously given by Wu and Xu are very restrictive and the examples presented there are not correct. Then, we present more general concepts of invex and incave fuzzy mappings involving strongly generalized differentiable fuzzy mapping. Finally, we show that the results obtained by Wu and Xu on the relationship between fuzzy variational-like inequalities and fuzzy optimization problems are still valid using these new concepts.

Original language	English
Pages (from-to)	84-98
Number of pages	15
Journal	Fuzzy Sets and Systems
Volume	200
DOIs	https://doi.org/10.1016/j.fss.2012.02.001
State	Published - 1 Aug 2012

Keywords

Fuzzy optimization
Fuzzy variational-like inequality
Invex fuzzy mappings

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10.1016/j.fss.2012.02.001

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abstract = "In this paper, we first show the need for introducing invex fuzzy mappings. After that, we show that the concept of invex fuzzy mapping previously given by Wu and Xu are very restrictive and the examples presented there are not correct. Then, we present more general concepts of invex and incave fuzzy mappings involving strongly generalized differentiable fuzzy mapping. Finally, we show that the results obtained by Wu and Xu on the relationship between fuzzy variational-like inequalities and fuzzy optimization problems are still valid using these new concepts.",

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AU - Rufián-Lizana, A.

AU - Chalco-Cano, Y.

AU - Osuna-Gómez, R.

AU - Ruiz-Garzón, G.

PY - 2012/8/1

Y1 - 2012/8/1

N2 - In this paper, we first show the need for introducing invex fuzzy mappings. After that, we show that the concept of invex fuzzy mapping previously given by Wu and Xu are very restrictive and the examples presented there are not correct. Then, we present more general concepts of invex and incave fuzzy mappings involving strongly generalized differentiable fuzzy mapping. Finally, we show that the results obtained by Wu and Xu on the relationship between fuzzy variational-like inequalities and fuzzy optimization problems are still valid using these new concepts.

AB - In this paper, we first show the need for introducing invex fuzzy mappings. After that, we show that the concept of invex fuzzy mapping previously given by Wu and Xu are very restrictive and the examples presented there are not correct. Then, we present more general concepts of invex and incave fuzzy mappings involving strongly generalized differentiable fuzzy mapping. Finally, we show that the results obtained by Wu and Xu on the relationship between fuzzy variational-like inequalities and fuzzy optimization problems are still valid using these new concepts.

KW - Fuzzy optimization

KW - Fuzzy variational-like inequality

KW - Invex fuzzy mappings

UR - https://www.scopus.com/pages/publications/84861022620

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DO - 10.1016/j.fss.2012.02.001

M3 - Article

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VL - 200

SP - 84

EP - 98

JO - Fuzzy Sets and Systems

JF - Fuzzy Sets and Systems

ER -

On invex fuzzy mappings and fuzzy variational-like inequalities

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Keywords

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