An approach to neutrosophic ideals

Year 2018, , 132 - 136, 26.06.2018

Vildan Çetkin , Halis Aygün

https://doi.org/10.32323/ujma.383115

Cited By: 4

Abstract

In this paper, we aim to introduce an approach to single-valued neutorosophic ideals over a given classical ring and over a given neutrosophic subring, respectively, as a continuation of our researches on algebraic structures over single-valued neutrosophic sets. We first propose the two types of neutrosophic ideals and then present their elementary properties.

Keywords

neutrosophic set, single valued neutrosophic set, ring, ideal, homomorphism of rings

References

• [1] I. Arockiarani, I. R. Sumathi, J. Martina Jency, Fuzzy neutrosophic soft topological spaces, International Journalof Mathematical Arhchive 4 (10) (2013) 225-238.
• [2] K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1) (1986) 87-96.
• [3] R. A. Borzooei, H. Farahani, M. Moniri, Neutrosophic deductive lters on BL-algebras, Journal of Intelligent and Fuzzy Systems 26 (6) (2014) 2993-3004.
• [4] V. C etkin, H. Aygun, An approach to neutrosophic subgroup and its fundamental properties, Journal of Intelligent and Fuzzy Systems 29 (2015) 1941-1947.
• [5] V. C etkin, H. Aygun, An approach to neutrosophic subrings, submitted.
• [6] V.N.Dixit, R.Kumar, N.Ajmal, On fuzzy rings, Fuzzy Sets and Systems, 49 (1992) 205-213.
• [7] K. Hur, H. W. Kang, H. K. Song, Intuitionistic fuzzy subgroups and subrings, Honam Math J. 25 (1) (2003) 19-41.
• [8] Vasantha Kandasamy W.B., Florentin Smarandache, Neutrosophic rings, Hexis, Phoenix, Arizona, 2006.
• [9] Vasantha Kandasamy W.B., Florentin Smarandache, Some neutrosophic algebraic structures and neutrosophic N-algebraic structures, Hexis, Phoenix, Arizona, 2006.
• [10] W. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems, 8 (1982) 133-139.
• [11] P. Majumdar, S. K. Samanta, On similarity and entropy of neutrosophic sets, Journal of Intelligent and Fuzzy Systems 26 (3) (2014) 1245-1252.
• [12] L. Martinez, Prime and primary L-fuzzy ideals of L-fuzzy rings, Fuzzy Sets and Systems, 101 (1999) 489-494.
• [13] A. A. Salama, S. A. Al-Blowi, Neutrosophic set and neutrosophic topological spaces, IOSR Journal of Math. 3 (4) (2012) 31-35.
• [14] M. Shabir, M. Ali, M. Naz, F. Smarandache, Soft neutrosophic group, Neutrosophic Sets and Systems 1 (2013) 13-25.
• [15] F. Smarandache, A unifying eld in logics. Neutrosophy: Neutrosophic Probability, Set and Logic, Rehoboth: American Research Press (1999).
• [16] H. Wang et al., Single valued neutrosophic sets, Proc. of 10th Int. Conf. on Fuzzy Theory and Technology, Salt Lake City, Utah, July 21-26 (2005).
• [17] L. Zadeh, Fuzzy sets, Information and Control 8 (1965) 87-96.