Main Article Content
The uni-soft type of bi-ideals in ordered semigroup is considered. The notion of a uni-soft bi-ideal is introduced and the related properties are investigated. The concept of Î´-exclusive set is given and the relations between uni-soft bi-ideals and Î´-exclusive set are discussed. The concepts of two types of prime uni-soft bi-ideals of an ordered semigroup S are given and it is proved that, a non-constant uni-soft bi-ideal of S is prime in the second sense if and only if each of its proper Î´-exclusive set is a prime bi-ideal of S. The characterizations of left and right simple ordered semigroups are considered. Using the notion of uni-soft bi-ideals, some semilattices of left and right simple semigroups are provided. By using the properties of uni-soft bi-ideals, the characterization of a regular ordered semigroup is provided. In the last section of this paper, the characterizations of both regular and intra-regular ordered semigroups are provided.
- U. Acar, F. Koyuncu, and B. Tanay, Soft sets and soft rings, Computers Math. Appl. 59 (11) (2010), 3458-3463.
- N. Kehayopulu and M. Tsingelis, Regular ordered semigroups in terms of fuzzy subsets, Inform. Sci. 176 (24) (2006), 3675-3693.
- N. Kehayopulu, On completely regular ordered semigroups, Sci. Math. 1 (1) (1998), 27-32.
- N. Kehayopulu, On semilattices of simple poe-semigroups, Math. Japon. 38 (2) (1993), 305-318.
- N. Kehayopulu, On weakly prime ideals of ordered semigroups, Math. Japon. 35 (6) (1990), 1051-1056.
- A. Khan, Y. B. Jun, S. I. A, Shah and R. Khan, Applications of soft sets in ordered semigroups via uni-soft quasi-ideals, J. Intell. Fuzzy Syst. 30 (2016), 97-107.
- A. Khan, R. Khan, Y.B. Jun, Uni-soft structure applied to ordered semigroups, Soft Comput. 21 (2017), 1021-1030.
- A. Khan, Y. B. Jun and R. Khan, Characterizations of ordered semigroups in terms of int-soft ideals, submitted.
- H. Aktas and N. Ca˘gman, Soft sets and soft groups, Inform. Sci. 177 (13) (2007), 2726-2735.
- A. O. Atagun and A. Sezgin, Soft substructures of rings, fields and modules, Computers Math. Appl. 61 (3) (2011), 592-601.
- F. Feng, Y. B. Jun, and X. Zhao, Soft semirings, Computers Math. Appl. 56 (10) (2008), 2621-2628.
- F. Feng, M. I. Ali, and M. Shabir, Soft relations applied to semigroups, Filomat, 27 (7) (2013), 1183-1196.
- F. Feng, H. Fujita, Y. B. Jun, and M. Khan, Decomposition of fuzzy soft sets with finite value spaces, Sci. World J. 2014 (2014), Article ID 902687.
- F. Feng and Y.M. Li, Soft subsets and soft product operations, Inform. Sci. 232 (2013), 44-57.
- Y. B. Jun, S. Z. Song, and G. Muhiuddin, Concave soft sets, critical soft points, and union-soft ideals of ordered semigroups, Sci. World J. 2014 (2104), Article ID 467968.
- Y. B. Jun, K. J. Lee, and A. Khan, Soft ordered semigroups, Math. Log. Q. 56 (1) (2010), 42-50.
- N. Cagman and S. Enginoglu, Soft set theory and uni-int decision making, Eur. J. Oper. Res. 207 (2) (2010), 848-855.
- M. Shabir and A. Khan, Characterizations of ordered semigroups by their fuzzy ideals, Comput. Math. Appl. 59 (2010), 539-549.
- X. Ma and J. Zhan, Characterizations of three kinds of hemirings by fuzzy soft h-ideals, J. Intell. Fuzzy Syst. 24 (2013), 535-548.
- D. Molodtsov, Soft set theory””first results, Computers Math. Appl. 37 (4-5) (1999), 19-31.
- L. A. Zadeh, Fuzzy sets, Inform. Control 8 (1965), 338-353.
- J. Zhan, N. Ca˘gman and A. S. Sezer, Applications of soft union sets to hemirings via ˇ SU-h-ideals, J. Intell. Fuzzy Syst. 26 (2014), 1363-1370.