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Mathematics 2019, 7(1), 95;

Neutrosophic Multigroups and Applications

Department of Mathematics, Gaziantep University, 27310 Gaziantep, Turkey
Author to whom correspondence should be addressed.
Received: 12 December 2018 / Revised: 10 January 2019 / Accepted: 14 January 2019 / Published: 17 January 2019
(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)
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In recent years, fuzzy multisets and neutrosophic sets have become a subject of great interest for researchers and have been widely applied to algebraic structures include groups, rings, fields and lattices. Neutrosophic multiset is a generalization of multisets and neutrosophic sets. In this paper, we proposed a algebraic structure on neutrosophic multisets is called neutrosophic multigroups which allow the truth-membership, indeterminacy-membership and falsity-membership sequence have a set of real values between zero and one. This new notation of group as a bridge among neutrosophic multiset theory, set theory and group theory and also shows the effect of neutrosophic multisets on a group structure. We finally derive the basic properties of neutrosophic multigroups and give its applications to group theory. View Full-Text
Keywords: neutrosophic sets; neutrosophic multisets; neutrosophic multigroups; neutrosophic multisubgroups neutrosophic sets; neutrosophic multisets; neutrosophic multigroups; neutrosophic multisubgroups
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

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Uluçay, V.; Şahin, M. Neutrosophic Multigroups and Applications. Mathematics 2019, 7, 95.

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