Abstract

The notion of Neutrosophic triplet (NT) is a new theory in Neutrosophy. Also, the v-generalized metric is a specific form of the classical metrics. In this study, we introduced the notion of neutrosophic triplet v-generalized metric space (NTVGM), and we obtained properties of NTVGM. Also, we showed that NTVGM is different from the classical metric and neutrosophic triplet metric (NTM). Furthermore, we introduced completeness of NTVGM.

Highlights

  • Neutrosophy is a branch of philosophy and neutrosophy is introduced by Smarandache in 1980.Neutrosophy consists of neutrosophic logic theory, probability theory, and set theory, as in [1]

  • neutrosophic triplet (NT) set is a specific form of the classical set since there exist neutral elements for each element which must be different from other neutral elements

  • We introduce neutrosophic triplet v-generalized metric space (NTVGMS) and we give some properties for neutrosophic triplet v-generalized metric (NTVGM)

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Summary

Introduction

Neutrosophy is a branch of philosophy and neutrosophy is introduced by Smarandache in 1980. A lot of researchers have been dealing with neutrosophic set theory in [4,5,6,7]. The NT group is a specific form of the classical group, since there exist neutral elements for each element in group, which must be different from other neutral elements. A lot of researchers have been dealing with neutrosophic triplet set theory in [11,12,13,14,15,16,17]. Thanks to the general triangular inequality, the v-generalized metric introduced new properties in fixed point theory and topology. We introduce neutrosophic triplet v-generalized metric space (NTVGMS) and we give some properties for neutrosophic triplet v-generalized metric (NTVGM).

Preliminaries
Neutrosophic Triplet v-Generalized Metric Space
Conclusions
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