Volume 2 , Issue 1 , PP: 47-62, 2020 | Cite this article as | XML | Html | PDF | Full Length Article
M.A. Ibrahim, A.A.A. Agboola , E.O. Adeleke, S.A. Akinleye 1 *
The objective of this paper is to introduce and study the notion of neutrosophic subtraction algebras and neutrosophic subtraction semigroups. It also introduces the notion of neutrosophic ideals of neutrosophic subtraction semigroup and presents some of their basic properties. In addition, the notion of neutrosophic homomorphism of neutrosophic subtraction semigroups and neutrosophic quotient subtraction semigroups was also introduced.
Neutrosophy, neutrosophic subtraction algebra,neutrosophic subtraction semigroup, Neutrosophic Ideal
[1] Agboola, A.A.A. and Davvaz, B., Introduction to Neutrosophic BCI/BCK-Algebras, International Journal of Mathematics and Mathematical Sciences. Article ID370267, 2015.
[2] Arshaduzzaman, M.D., A Characterization of a Group with Subtraction as a Binary Operation. International Organization of Scientific Research-Journal of Mathematics , vol. 10(1), pp. 53-55, 2014.
[3] Bakbak, D., Uluc¸ay, V. and S¸ ahin, M., Neutrosophic soft expert multiset and their application to multiple criteria decision making, Mathematics, vol. 7, pp. 50-65, 2019.
[4] Broumi, S., Bakali, A., Talea, M., Smarandache, F.,Singh, P. K., Uluc¸ay, V., and Khan, M., Bipolar complex neutrosophic sets and its application in decision making problem. In Fuzzy Multi criteria Decision-Making Using Neutrosophic Sets. Springer, Cham. pp. 677-710, 2019.
[5] Jun,Y.B, Kim,H.S. and Roh, E.H, Ideal theory of subtraction algebras, Scientiae Mathematicae Japonicae Online, pp. 397-402, 2004.
[6] Jun, Y. B. and Kim, H.S. On ideals in subtraction algebras, Scientiae Mathematicae Japonicae, Online, pp. 1081–1086, 2006.
[7] Jun,Y.B and Kim,K.H., Prime and irreducible ideals in subtraction algebras, International Mathematical Forum, vol.3(10), pp. 457- 462, 2008.
[8] Kyung, H. K, Eun, H. R. and Yong, H. Y., A note on subtraction semigroup. Scientiae Mathematicae Japonicae Online, vol. 10, pp. 393-401, 2004.
[9] Lee, K. J., Jun, Y.B. and Kim, Y.H., Weak forms of subtraction algebras, Bulletin of the Korean Mathematical Society, vol. 45(3), pp. 437-444, 2008.
[10] S¸ ahin, M. and Kargın A., Neutrosophic triplet groups based on set valued neutrosophic quadruple numbers, Neutrosophic Set and Systems, vol. 30, pp. 122 -131, 2019.
[11] S¸ ahin M. and Kargın A., Neutrosophic Triplet v-Generalized Metric Space, Axioms- MDPI, vol.7, pp. 67-73, 2018.
[12] S¸ ahin, M. and Kargın A., Single valued neutrosophic quadruple graphs, Asian Journal of Mathematics and Computer Research, vol. 26(4), pp. 243-250, 2019.
[13] S¸ ahin M., Kargın A. and C¸ oban M. A., Fixed point theorem for neutrosophic triplet partial metric space, Symmetry- MDPI, vol.10(7), pp. 240-246, 2018.
[14] Schein, B.M., Difference semigroups, Communications in Algebra, vol. 20(8), pp. 2153-2169, 1992.
[15] Smarandache, F., A Unifying Field in Logics: Neutrosophic Logic, Neutrosophy, Neutrosophic Set, Neutrosophic Probability, American Research Press, Rehoboth, 2003.
[16] Smarandache, F., Introduction to Neutrosophic Statistics, Sitech and Education Publishing, Romania, 2014.
[17] Smarandache, F., Neutrosophic Probability, Set and Logic, Am Res Press, Rehoboth, USA, 1998.
[18] Ulucay, V., Kılıc¸, A., S¸ ahin, M. and Deniz, H., A New Hybrid Distance-Based Similarity Measure for Refined Neutrosophic sets and its Application in Medical Diagnosis. MATEMATIKA: Malaysian Journal of Industrial and Applied Mathematics, vol. 35(1), pp 83-94, 2019.
[19] Uluc¸ay, V., Kilic¸, A.,Yildiz, I. and Sahin, M., A new approach for multi-attribute decision-making problems in bipolar neutrosophic sets. Neutrosophic Sets and Systems, vol. 23(1), pp.142-159, 2018.
[20] Uluc¸ay, V., Kılıc¸, A., Yıldız, ˙I. and S¸ ahin, M., An Outranking Approach for MCDM-Problems with Neutrosophic Multi-Sets. Neutrosophic Sets and Systems, vol. 30, pp.214-24, 2019.
[21] Uluc¸ay, V., and S¸ ahin, M., Decision-Making Method based on Neutrosophic Soft Expert Graphs. In Neutrosophic Graph Theory and Algorithms. IGI Global, pp. 33-76, 2020.
[22] Ulucay, V., S¸ ahin, M. and Olgun, N. Time-Neutrosophic Soft Expert Sets and Its Decision Making Problem. Matematika, vol. 34(2), pp. 246-260, 2018.
[23] Uluc¸ay, V., S¸ ahin, M., and Hassan, N., Generalized neutrosophic soft expert set for multiple-criteria decision-making. Symmetry, vol.10(10), pp. 437-455, 2018.
[24] Vasantha Kandasamy, W.B and Smarandsche,F., Neutrosophic Ring, Hexis Phoenix, Arizona 2006.
[25] Vansantha Kandasamy, W.B. and Smarandache,F., Some Neutrosophic Algebraic Structures and Neutrosophic N-Algebraic Structures, Hexis, Phoenix, Arizona, 2006.
[26] Yılmaz C. and Mehmet A.O., Some result on subtraction algebra. Hacettepe Journal of Mathematics and Statistics,vol. 38 (3), pp. 299-304, 2009.
[27] Zelinka, B., Subtraction semigroups. Mathematical Bohemica, vol. 120(4), pp. 445-447, 1995.
