Soft intersection abel-grassmann’s groups

Document Type : Research Paper

Authors

1 Department of Mathematics, University of Malakand, Chakdara Dir Lower, KP, Pakistan

2 Department of Mathematics, University of Malakand, Chakdara Dir Lower, KP, Pakistan.

3 Department of Mathematics, University of C¸ ankırı Karatekin, 18100, C¸ ankırı, Turkey.

Abstract

This paper is a bridging among soft set theory, set theory and AG-groups, in which soft intersection AG-group (abbreviated by soft int-AG-group) is defined and investigated. The concept of soft int-AG-group is further extended to define the notions of conjugates soft int-AG-group, normal soft int AG-group, e-set and α-inclusion of soft int-AG-groups. Various properties of these notions are investigated and supported by relevant examples that are produced by GAP.

Keywords


[1] M. I. Ali, F. Feng, X. Lui. W. K. Min and M. Shabir, On some new operations in soft set theory, Computers and Mathematics with Applications, 57 (2009),1547-1553.
[2] H. Akta¸s & N. C¸ a˘gman, Soft sets and soft groups, Information Sciences,177(13)(2007), 2726-2735.
[3] A. Ayg¨uno˘glu, H. Ayg¨un, Introduction to fuzzy soft groups, Computer and Math-ematics with Applications, 58 (2009), 1279-1286.
[4] I. Ahmad, Amanullah, M. Shah, Fuzzy AG-subgroups, Life Science Journal, 9(4)(2012), 3931-3936.
[5] Amanullah, Imtiaz Ahmad, and Faruk Karaaslan, Cubic Abel-grassmann’s sub-groups, Journal of Computational and Theoretical Nanoscience, 13(1) (2016),628-635,.
[6] Amanullah, I. Ahmad, M. Shah, On the equal-height elements of fuzzy AG-subgroups, Life Science Journal, 10(4) (2013), 3143-3146, .
[7] N. C¸ a˘gman, F. C¸ ıtak and H. Akta¸s, Soft int-group and its applications to group theory, Neural Computing and Applications, 21(1) (2012), 151-158.
[8] N. C¸ a˘gman, S. Engino˘glu, Soft set theory and uni-int decision making, European Journal of Operation Research, 207 (2010), 848-855.
[9] F. Feng, M.I. Ali, M. Shabir, Soft relations applied to semigroups, Filomat, 27(7)(2013), 1183-1196.
[10] K. Kaygısız, On soft int-groups, Annals of Fuzzy Mathematics and Informatics,4(2) (2012), 365-375.
[11] F. Karaaslan, I. Ahmad, Amanullah, Bipolar soft groups, Journal of Intelligent and Fuzzy system, 31(1) (2016), 651-662.
[12] X. Ma, J. Zhan, B. Davvaz, Applications of soft intersection sets to hemirings via Si-h-Bi-ideals and Si-h-Quasi-ideals, Filomat, 30(8) (2016), 2295-2313.
[13] P. K. Maji, A.R. Roy and R. Biswas, An application of soft sets in a deci-sion making problem, Computers and Mathematics with Applications, 44 (2002),1077-1083.
[14] P. K. Maji, R. Biswas and A.R. Roy, Soft set theory, Computer and Mathematics with Application, 45 (2003), 555-562.
[15] M. S. Kamran, Conditions for LA-semigroups to resemble associative structures, PhD thesis, Quaid-i-Azam University, Islamabad 1993.
[16] D. Molodtsov, Soft set theory-first results, Computers and Mathematics with Applications, 37 (1999), 19-31.
[17] A. Rosenfeld, Fuzzy group, Journal of Mathematical Analysis and Applications, 35 (1971), 512-517.
[18] A. S. Sezer, A new approach to LA-semigroup theory via the soft sets, Journal of Intelligent and Fuzzy Systems, 26 (2014), 2483-2495.
[19] A. Sezgin, N. C¸ a˘gman, A.O. Atag¨un, M.I. Ali, E. T¨urkmen, Soft Intersection Semigroups, Ideals and Bi-Ideals;a New Application on Semigroup Theory I, Filo-mat 29(5) (2015), 917-946.
[20] T. Shah, I. Rehman and A. Razzaq, Soft ordered Abel-Grassman’s groupoid (AG-groupoid), International Journal of the Physical Sciences, 6(25) (2011), 6118-6126.
[21] M. Shah and A. Ali, Some structural properties of AG-groups, InternationalMathematical Forum,6(34)(2011),1661-1667.
[22] M. Shah, C. Gretton, V. Sorge, Enumerating AG-groups with a study of smaran-dache AG-groups, International Mathematical Forum, 6(62) (2011), 3079-3086.
[23] N. Sultana, N. Rani, M.I. Ali, A. Hussain, Soft translations and soft extensions of BCI/BCK-algebras, Applied Soft Computing, 36 (2015), 499-505.
[24] H. Zhang, J. Zhan, Rough soft lattice implication algebras and corresponding decision making methods , International Journal of Machine Learning and Cy-bernetics, 8(4) (2016),1301-1308.
[25] J. Zhan, K. Zhu, A novel soft rough fuzzy set: Z-soft rough fuzzy ideals of hemir-ings and corresponding decision making, Soft Computing, 21(8) (2017), 1923-1936.
[26] J. Zhan, X. Zhou, D.Xiang, Rough soft n-ary semigroups based on a novel con-gruence relation and corresponding decision making, Journal of Intelligent and Fuzzy Systems, 33(2) (2017), 693-703.
[27] K. Zhu, J. Zhan, A study on soft Z-congruence relations over hemirings, Journal of Intelligent and Fuzzy Systems, 30(1) (2015), 467-474.