Vector-Valued Fuzzy Metric Spaces and Fixed Point Theorems

The purpose of this paper is to generalize the concept of classical fuzzy set to vector-valued fuzzy set which can attend values not only in the real interval [0, 1], but in an ordered interval of a Banach algebra as well. This notion allows us to introduce the concept of vector-valued fuzzy metric...

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Bibliographic Details
Published in:Axioms 2024-04, Vol.13 (4), p.252
Main Authors: Shukla, Satish, Dubey, Nikita, Miñana, Juan-José
Format: Article
Language:English
Subjects:
Algebra
Banach spaces
fixed point
Fixed points (mathematics)
fuzzy contractive mapping
Fuzzy sets
Integral equations
Metric space
strongly minihedral cone
Theorems
vector-valued fuzzy metric space
vector-valued fuzzy set
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Summary:The purpose of this paper is to generalize the concept of classical fuzzy set to vector-valued fuzzy set which can attend values not only in the real interval [0, 1], but in an ordered interval of a Banach algebra as well. This notion allows us to introduce the concept of vector-valued fuzzy metric space which generalizes, extends and unifies the notion of classical fuzzy metric space and complex-valued fuzzy metric space and permits us to consider the fuzzy sets and metrics in a larger domain. Some topological properties of such spaces are discussed and some fixed point results in this new setting are proved. Multifarious examples are presented which clarify and justify our claims and results.
ISSN:2075-1680
2075-1680
DOI:10.3390/axioms13040252