Abstract
In this paper we consider the concept of $KM$ -fuzzy metric spaces and we introduce a novel concept of $KM$ -single valued neutrosophic metric graphs based on $KM$ -fuzzy metric spaces. Then we investigate the finite $KM$ -fuzzy metric spaces with respect to $KM$ -fuzzy metrics and we construct the $KM$ -fuzzy metric spaces on any given non-empty sets. We try to extend the concept of $KM$ -fuzzy metric spaces to a larger class of $KM$ -fuzzy metric spaces such as union and product of $KM$ -fuzzy metric spaces and in this regard we investigate the class of products of $KM$ -single valued neutrosophic metric graphs. In the final, we define some operations such as tensor product, Cartesian product, semi-strong product, strong product, union, semi-ring sum, suspension, and complement of $KM$ -single valued neutrosophic metric graphs.
Highlights
Classical theory is a pure concept and without quality or criteria, so it is not attractive to use in our world, that’s why we use the neutrosophic sets theory as one of a generalizations of set theory in order to deal with uncertainties, which is a key action in the contemporary world introduced by Smarandache for the first time in 1998 [22] and in 2005 [23]
The structure of fuzzy metric spaces is equipped with mathematical tools such as triangular norms and fuzzy subsets depending on time parameter and on other variables
We need to construct the KM-single valued neutrosophic metric graphs based on finite or infinite sets, so we develop the concept of KM-fuzzy metric on any nonempty set and prove that for every given set with respect to the concept of C-graphable sets one can construct a KM-metric space
Summary
Classical theory is a pure concept and without quality or criteria, so it is not attractive to use in our world, that’s why we use the neutrosophic sets theory as one of a generalizations of set theory in order to deal with uncertainties, which is a key action in the contemporary world introduced by Smarandache for the first time in 1998 [22] and in 2005 [23] This concept is a new mathematical tool for handling problems involving imprecise, indeterminacy, and inconsistent data. We need to construct the KM-single valued neutrosophic metric graphs based on finite or infinite sets, so we develop the concept of KM-fuzzy metric on any nonempty set and prove that for every given set with respect to the concept of C-graphable sets one can construct a KM-metric space. We have extended some production operations on the KM-fuzzy metric spaces to the KM-single valued neutrosophic metric graphs
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