| Title of paper:
|
Norms over bifuzzy bi-ideals with operators in semigroups
|
| Author(s):
|
| Rasul Rasuli
|
| Department of Mathematics, Payame Noor University, Tehran, Iran
|
| rasulirasul@yahoo.com
|
|
| Published in:
|
Notes on Intuitionistic Fuzzy Sets, Volume 25 (2019), Number 1, pages 1–11
|
| DOI:
|
https://doi.org/10.7546/nifs.2019.25.1.1-11
|
| Download:
|
 PDF (185 Kb, File info)
|
| Abstract:
|
In this paper, by using norms (T and C) we introduce the concepts of Ω-bifuzzy subsemigroups, Ω-bifuzzy ideals and Ω-bifuzzy bi-ideals of semigroup S and consider some of their properties and structured characteristics.
|
| Keywords:
|
Theory of groups, Ideals, Norms, Intuitionistic mathematics, Fuzzy set theory, Lattice.
|
| AMS Classification:
|
05B10, 06B10, 03B45, 03F55, 03E72, 06D50
|
| References:
|
- Abbott, J. C. (1969). Sets, Lattices and Boolean Algebras, Allyn and Bacon, Boston.
- Atanassov, K. T. (1986). Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1), 87–96.
- Atanassov, K. T. (1994). New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems, 61, 137–142.
- Buckley, J. J. & Eslami, E. (2002). An Introduction to Fuzzy Logic and Fuzzy Sets, Springer-Verlag Berlin Heidelberg GmbH.
- Dubois, D. & Prade, H. (1988). Fuzzy Sets and Systems, Academic Press, New York.
- Gerstenkorn, T. & Manko, J. (1995). Bifuzzy probabilistic sets, Fuzzy Sets and Systems, 71, 207–214.
- Hong, S. M., Jun, Y. B. & Meng, J. (1995). Fuzzy interior ideals in semigroups, Indian J. Pure Appl. Math., 26(9), 859–863.
- Howie, J. (1995). Fundamentals of Semigroup Theory, London Mathematical Society Monographs. New Series, 12. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York.
- Hur, K., Jun, Y. B. & Kim, H. S. (2005). Ω-bifuzzy subsemigroups in semigroups, Honam Math. J., 27(1), 31–41.
- Klaua, D. (2010). An early approach toward graded identity and graded membership in set theory, Fuzzy Sets and Systems, 161, 2369–2379.
- Kuroki, N. (1982). Fuzzy semiprime ideals in semigroups, Fuzzy Sets and Systems, 8, 71–79.
- Kuroki, N. (1991). On fuzzy semigroups, Inform. Sci., 53, 203–236.
- Kuroki, N. (1992). Fuzzy generalized bi-ideals in semigroups, Inform. Sci., 66, 235–243.
- Lajos, S. (1972). On generalized bi-ideals in semigroups, Coll. Math. Soc. Janos Bolyai, Algebraic Theory of Semigroups, (G. Pollak, Ed.) North-Holland, 20, 335–340.
- Lajos, S. (1972). A note on semilattice of groups, Acta. Sci. Math. (Szeged), 33, 315–317.
- Liang, R., Lu, S., Wang, X. Lu, Y., Mandal, V., Patacsil, D. & Kumar, D. (2006). A Fuzzy-Set-Theory-Based Approach to Differential Gene Expression Data Analysis, BMC Bioinformatics, 7 (Suppl 4): S7.
- Mo, Z. W. & Wang, X. P. (1993). On pointwise depiction of fuzzy regularity of semigroups, Inform. Sci., 74, 265–274.
- Petrich, M. (1973). Introduction to Semigroups, Columbus, Ohio.
- Rasuli, R. (2016). Fuzzy Ideals of Subtraction Semigroups with Respect to a t-norm and a t-conorm, The Journal of Fuzzy Mathematics Los Angeles, 24(4), 881–892.
- Rasuli, R. (2016). Fuzzy modules over a t-norm, Int. J. Open Problems Compt. Math., 9(3), 12–18.
- Rasuli, R. (2016). Fuzzy Subrings over a t-norm, The Journal of Fuzzy Mathematics Los Angeles, 24(4), 995–1000.
- Rasuli, R. (2016). Norms over intuitionistic fuzzy subrings and ideals of a ring, Notes on Intuitionistic Fuzzy Sets, 22(5), 72–83.
- Samhan, M. A. (1993). Fuzzy congruences on semigroups, Inform. Sci., 74, 165–175.
- Wang, X. P. & Liu, W. J. (1993). Fuzzy regular subsemigroups in semigroups, Inform. Sci., 68, 225–231.
- Zadeh, L. A. (1965). Fuzzy sets, Inform. Control., 8, 338–353.
|
| Citations:
|
The list of publications, citing this article may be empty or incomplete. If you can provide relevant data, please, write on the talk page.
|
|
