Paper Info
Title
Set-valued pseudo-metric families and Ekeland's variational principles in fuzzy metric spaces.
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 , ź ) -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 ź-efficient solutions in the sense of Németh and of Dentcheva and Helbig, respectively. These EVPs improve and generalize the related known results.
Year
DOI
Venue
2016
10.1016/j.fss.2016.02.007
Fuzzy Sets and Systems
Keywords
Field
DocType
Ekeland's variational principle,Locally convex spaces,Partial order,ϵ-efficiency,Fuzzy metric space,Set-valued pseudo-metric family
T-norm,Discrete mathematics,Convex metric space,Fuzzy logic,Metric (mathematics),Product metric,Locally convex topological vector space,Ekeland's variational principle,Injective metric space,Mathematics
Journal
Volume
Issue
ISSN
300
C
0165-0114
Citations 
PageRank 
References 
0
0.34
13
Authors
2
Name
Order
Citations
PageRank
Jing-Hui Qiu1123.19
Fei He23213.85