Neutrosophic Multigroups and Applications
Abstract
:1. Introduction
2. Preliminary
- 1.
- 2.
- 3.
- 4.
- 1.
- A is said to be Nm-subset of B is denoted by if , , , and .
- 2.
- A is said to be neutrosophic equal of B is denoted by if , , , and .
- 3.
- The union of A and B is denoted by and is defined by
- 4.
- The intersection of A and B is denoted by and is defined by
3. Neutrosophic Multigroups
- Let X be a group with a binary operation and the identity element is e.
- denotes the set of all neutrosophic multisets over the X.
- denotes the set of all neutrosophic multi groups over the group X.
- 1.
- 2.
- 3.
- 1.
- 2.
- 3.
- 1.
- 2.
- 3.
- 1.
- 2.
- 3.
- 1.
- for all .
- 2.
- for all
- 3.
- for all
- 4.
- for all
- : Let Then,
- : Immediate.
- : Let Then,Hence,
4. Applications of Neutrosophic Multi Groups
5. Conclusions
Author Contributions
Funding
Conflicts of Interest
Abbreviations
NMG | Neutrosophic Multigroup |
NMS | Neutrosophic Multiset |
IFMS | Intuitionistic Fuzzy Multiset |
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Uluçay, V.; Şahin, M. Neutrosophic Multigroups and Applications. Mathematics 2019, 7, 95. https://doi.org/10.3390/math7010095
Uluçay V, Şahin M. Neutrosophic Multigroups and Applications. Mathematics. 2019; 7(1):95. https://doi.org/10.3390/math7010095
Chicago/Turabian StyleUluçay, Vakkas, and Memet Şahin. 2019. "Neutrosophic Multigroups and Applications" Mathematics 7, no. 1: 95. https://doi.org/10.3390/math7010095
APA StyleUluçay, V., & Şahin, M. (2019). Neutrosophic Multigroups and Applications. Mathematics, 7(1), 95. https://doi.org/10.3390/math7010095