An approach to neutrosophic ideals

Year 2018, Volume: 1 Issue: 2, 132 - 136, 26.06.2018

Vildan Çetkin , Halis Aygün

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

Cited By: 7

https://izlik.org/JA84BK53FP

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.