Article ID Journal Published Year Pages File Type
389067 Fuzzy Sets and Systems 2016 23 Pages PDF
Abstract

In this paper, we introduce a set-valued pseudo-metric family on a fuzzy metric space and the notion of compatibility between the set-valued pseudo-metric family and the original fuzzy metric. By means of this notion, we prove a general set-valued EVP, where the perturbation involves a set-valued pseudo-metric family compatible with the original fuzzy metric. From the general EVP, we deduce several particular EVPs, which extend the EVPs in Qiu (2013) [36] and in Gutiérrez et al. (2008) [20] to fuzzy metric spaces. By using set-valued pseudo-metric families and using the unified approach for approximate solutions introduced by Gutiérrez, Jiménez and Novo, we deduce a general version of set-valued EVP based on (C,ϵ)(C,ϵ)-efficient solutions in fuzzy metric spaces, where C is a coradiant set contained in the order cone. By choosing two specific versions of the coradiant set C in the general version of EVP, we obtain several particular set-valued EVPs for ϵ-efficient solutions in the sense of Németh and of Dentcheva and Helbig, respectively. These EVPs improve and generalize the related known results.

Related Topics
Physical Sciences and Engineering Computer Science Artificial Intelligence
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