INTERSECTIONAL SOFT SETS IN ORDERED GROUPOIDS

Abstract

In this note, the notions of soft int-ordered groupoids and soft left (resp., right) ideals are introduced. The characterization of int-soft ordered groupoids in terms of characteristic and inclusive sets is discussed. The concepts of soft prime ideals and soft int-filters are also introduced, and the relation between them is investigated.

Keywords

• Ordered groupoids,soft sets,int-soft filters,soft prime ideals

References

1. [1] H. Aktas, N. Cagman, Soft sets and soft groups, Inform. Sci. 177 (2007) 2726-2735.
2. [2] N. Cagman, F. C. Tak, H. Aktas, Soft int-group and its applications to group theory, Neural. Comput. Appl. 21(2012) 151-158.
3. [3] K. Kaygsz, On soft int-groups, Ann. Fuzzy Math. Inform. 4 (2) (2012). 365-375.
4. [4] N. Kehayopulu, On weakly commutative poe-semigroups, Semigroup Forum 34 (1987) 367– 370.
5. [5] N. Kehayopulu, On weakly prime ideals of ordered semigroups, Math. Japonica 35(1990) 1051–1056.
6. [6] N. Kehayopulu, M. Tsingelis, Fuzzy sets in ordered groupoids, Semigroup Forum 65(2002) 128 – 132.
7. [7] A. Khan, N. Sarmin, F. Khan, B. Davvaz, A study of fuzzy soft interior ideals of ordered semigroups, Iranian Journal of Science & Technology, 37A3: (2013) 237-249
8. [8] D. A. Molodtsov, Soft set theory first results, Computers and Mathematics with Applications 37 (1999) 19-31.

9. [9] A. Sezgin, A. Atagun, Soft groups and normalistic soft groups, Computers and Mathematics with Applications 62(2) (2011) 685-698.
10. [10] I. Simsek, N. Cagman, K. Kaygisiz, On normal soft intersection groups, Contemp. Analy. And Appl. Math.,Vol.2, No.2 ( 2014) 258-267.
11. [11] S. Song, H. Kim, Y. Jun, Ideal theory in semigroups based on intersectional soft sets, The Scientific World J. Vol.2014, Article ID136424, (2014) 7 pages.
12. [12] G. Sun, Y. Li, Y. Yin Y, New characterizations of regular ordered semigroups in terms of fuzzy soft ideals, Mathematica Aeterna, Vol. 3, , no.7 (2013) 545 – 554
13. [13] S. Yuksela, T. Dizman, G. Yildizdan, U. Sertc, Application of soft sets to diagnose the prostate cancer Risk, Journal of Inequalities and Applications 2013, 2013:229
14. [14] L. A. Zadeh, Fuzzy sets, Inf. Control 8 (1965) 338-353.