Abstract
In this paper, we introduce the notion of fuzzy interior ideal, fuzzy bi-ideal, intuitionistic fuzzy interior ideal and intuitionistic fuzzy bi-ideal of a subtraction semigroup. We characterize a non-empty subset of a subtraction semigroup X through intuitionistic fuzzy ideal, intuitionistic fuzzy bi-ideal and intuitionistic fuzzy interior ideal. We give some equivalent conditions related to these notions.
Keywords
Subtraction semigroups fuzzy interior ideal fuzzy bi-ideal intuitionistic fuzzy interior ideal intuitionistic fuzzy bi-ideal
References
- Atanassov K.T., 1986. Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20, 87-96.
- Atanassov K.T., 1994. New operations defined over the intuitionistic fuzzy sets,
- Fuzzy Sets and Systems 61, 137-142. Abbott J.C., 1969. Sets, Lattices and Boolean Algebras, Allyn and Bacon, Boston.
- Dheena P., Satheesh Kumar G., 2007. On strongly regular near-subtraction semigroups, Commun. Korean Math. Soc. 22, No.3, 323-330.
- Dheena P., Mohanraj G., 2012. Fuzzy weakly prime ideals of near-subtraction semigroups, Annals of Fuzzy Mathematics and Informatics, Vol.4, No.2, 235-242.
- Jun Y.B., Kim H.S., Roh E.H., 2004. Ideal theory of subtraction algebras, Sci. Math. Jpn. Online e-2004, 397-402.
- Jun Y.B., Kim H.S., 2006. On ideals in subtraction algebras, Sci. Math. Jpn. Online e-2006, 1081-1086.
- Kim H.S., Jun Y.B., 2002. Intuitionistic fuzzy ideals of semigroups, Indian J. Pure Appl. Math., 33(4), 443-449.
- Lee K.J., Park C.H., 2007. Some questions on fuzzifications of ideals in subtraction algebras, Commun. Korean Math. Soc. 22, No.3, 359-363.
- Öztürk M.A., Çeven Y., Jun Y.B., 2007. Intuitionistic fuzzy sets in semigroups,
- Sci. Math. Jpn. Online, e-2007, 37-42.
- Schein B.M., 1992. Difference semigroups, Communications in Algebra 20, No.8, 2153-2169.
- Williams D.R.P., 2008. Fuzzy ideals in near-subtraction semigroups, World
- Academy of Science, Engineering and Technology, Vol. 2, Issue 1, 39-46. Zadeh L.A., 1965. Fuzzy Sets, Information and Control 8, No.3, 338-353.
- Zelinka B., 1995. Subtraction semigroups, Math. Bohemica 120, No.4, 445-447.
- Zekiye Çiloğlu e-mail: zekiyeciloglu@sdu.edu.tr
Abstract
Bu makalede, çıkarma yarıgruplarında bulanık iç ideal, bulanık bi-ideal, sezgisel bulanık iç ideal ve sezgisel bulanık bi-ideal kavramlarının tanımları verilmiştir. Bir X çıkarma yarıgrubunun boş olmayan bir alt kümesinin bulanık iç ideal, bulanık bi-ideal, sezgisel bulanık iç ideal ve sezgisel bulanık bi-ideal olması için bazı karakterizasyonlar verilmiştir. Ayrıca bu kavramlarla ilgili bazı denk koşullar elde edilmiştir.
Keywords
çıkarma yarıgruplar bulanık iç ideal bulanık bi-ideal sezgisel bulanık iç ideal sezgisel bulanık bi-ideal
References
- Atanassov K.T., 1986. Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20, 87-96.
- Atanassov K.T., 1994. New operations defined over the intuitionistic fuzzy sets,
- Fuzzy Sets and Systems 61, 137-142. Abbott J.C., 1969. Sets, Lattices and Boolean Algebras, Allyn and Bacon, Boston.
- Dheena P., Satheesh Kumar G., 2007. On strongly regular near-subtraction semigroups, Commun. Korean Math. Soc. 22, No.3, 323-330.
- Dheena P., Mohanraj G., 2012. Fuzzy weakly prime ideals of near-subtraction semigroups, Annals of Fuzzy Mathematics and Informatics, Vol.4, No.2, 235-242.
- Jun Y.B., Kim H.S., Roh E.H., 2004. Ideal theory of subtraction algebras, Sci. Math. Jpn. Online e-2004, 397-402.
- Jun Y.B., Kim H.S., 2006. On ideals in subtraction algebras, Sci. Math. Jpn. Online e-2006, 1081-1086.
- Kim H.S., Jun Y.B., 2002. Intuitionistic fuzzy ideals of semigroups, Indian J. Pure Appl. Math., 33(4), 443-449.
- Lee K.J., Park C.H., 2007. Some questions on fuzzifications of ideals in subtraction algebras, Commun. Korean Math. Soc. 22, No.3, 359-363.
- Öztürk M.A., Çeven Y., Jun Y.B., 2007. Intuitionistic fuzzy sets in semigroups,
- Sci. Math. Jpn. Online, e-2007, 37-42.
- Schein B.M., 1992. Difference semigroups, Communications in Algebra 20, No.8, 2153-2169.
- Williams D.R.P., 2008. Fuzzy ideals in near-subtraction semigroups, World
- Academy of Science, Engineering and Technology, Vol. 2, Issue 1, 39-46. Zadeh L.A., 1965. Fuzzy Sets, Information and Control 8, No.3, 338-353.
- Zelinka B., 1995. Subtraction semigroups, Math. Bohemica 120, No.4, 445-447.
- Zekiye Çiloğlu e-mail: zekiyeciloglu@sdu.edu.tr
Details
| Primary Language | English |
|---|---|
| Subjects | Mathematical Sciences |
| Journal Section | Makaleler |
| Authors | |
| Publication Date | June 3, 2014 |
| Published in Issue | Year 2014 Volume: 9 Issue: 1 |
