Soft Interior-Hyperideals in Left Regular LA-Semihypergroups


Download PDF

Authors: M. Y. ABBASI, S. A. KHAN, A. F. TALEE AND A. KHAN

DOI: 10.46793/KgJMat2002.217A

Abstract:

This paper is a contribution to the study of the effective content of LA-hyperstructure. In this paper, we introduce the notion of soft interior-hyperideals. Further, we give several basic properties of these notions and provide different important characterizations in terms of soft interior hyperideals.



Keywords:

LA-semihypergroups, soft interior-hyperideals, left regular LA-semihypergroups.



References:

[1]   H. Aktas and N. Cagman, Soft sets and soft groups, Inform. Sci. 177 (2007), 2726–2735.

[2]   V. Amjad, K. Hila and F. Yousafzai, Generalized hyperideals in locally associative left almost semihypergroups, New York J. Math. 20 (2014), 1063–1076.

[3]   V. Amjad and F. Yousafzai, On pure LA-semihypergroups, Konuralp J. Math. 2 (2014), 53–63.

[4]   S. M. Anvariyeh, S. Mirvakili, O. Kazanci and B. Davvaz, Algebraic hyperstructures of soft sets associated to semihypergroups, Southeast Asian Bull. Math. 35 (2011), 911–925.

[5]   M. Aslam, T. Aroob and N. Yaqoob, On cubic G-hyperideals in left almost G-semihypergroups, Ann. Fuzzy Math. Inform. 5 (2013), 169–182.

[6]   M. Azhar, M. Gulistan, N. Yaqoob and S. Kadry, On fuzzy ordered LA-semihypergroups, International Journal of Analysis and Applications 16 (2018), 276–289.

[7]   N. Cagman, F. Citak and H. Aktas, Soft int-group and its applications to group theory, Neural Computing and Applications 21 (2012), 151–158.

[8]   N. Cagman and S. Enginoglu, Soft set theory and uni-int decision making, European J. Oper. Res. 207 (2010), 848–855.

[9]   P. Corsini, Prolegomena of Hypergroup Theory, Second Edition, Aviani Editore, Aviani, 1993.

[10]   B. Davvaz and V. L. Fotea, Hyperring Theory and Applications, International Academic Press, Gulf Breeze, Fla, USA, 2007.

[11]   M. Farooq, A. Khan, and B. Davvaz, Characterizations of ordered semihypergroups by the properties of their intersectional-soft generalized bi-hyperideals, Soft Computing 9(22) (2018), 3001–3010.

[12]   F. Feng, Y. B. Jun and X. Zhao, Soft semirings, Comput. Math. Appl. 56 (2008), 2621–2628.

[13]   M. Gulistan, M. Khan, N. Yaqoob and M. Shahzad, Structural properties of cubic sets in regular LA-semihypergroups, Fuzzy Inf. Eng. 9 (2017), 93–116.

[14]   M. Gulistan, N. Yaqoob and M. Shahzad, A note on Hv-LA-semigroups, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys. 77 (2015), 93–106.

[15]   A. Hasankhani, Ideals in a semihypergroup and greens relations, Ratio Mathematica 13 (1999), 29–36.

[16]   K. Hila and J. Dine, On hyperideals in left almost semihypergroups, ISRN Algebra 2011 (2011), Article ID 953124, 8 pages.

[17]   M. A. Kazim and M. Naseeruddin, On almost semigroups, Aligarh Bull. Math. 2 (1972), 1–7.

[18]   A. Khan, M. Farooq, M. Izhar and B. Davvaz, Fuzzy hyperideals of left almost semihypergroups, International Journal of Analysis and Applications 15 (2016), 155–171.

[19]   M. Khan, N. Y. M. Gulistan and F. Hussain, General cubic hyperideals of LA-semihypergroups, Afr. Mat. 27 (2016), 731–751.

[20]   M. Khan, N. Y. M. Gulistan and F. Hussain, General cubic hyperideals of LA-semihypergroups, Afr. Mat. 27 (2016), 731–751.

[21]   S. A. Khan, M. Y. Abbasi and A. F. Talee, A new approach to soft hyperideals in LA-semihypergroups, in: N. Yadav, A. Yadav, J. C. Bansal, K. Deep and J. H. Kim (Eds.), Harmony Search and Nature Inspired Optimization Algorithm, Theory and Applications, ICHSA-2018, Advances in Intelligent System and Computing 29 (2019), 293–303, DOI 10.1007/978-981-13-0761-4-29.

[22]   P. K. Maji, R. Biswas and A. R. Roy, Soft set theory, Comput. Math. Appl. 45 (2003), 555–562.

[23]   F. Marty, Sur une generalization de la notion de group, in: Proceedings of 8th Congress Math. Scandinaves, Stockholm, Sweden, 1934, 45–49.

[24]   D. Molodtsov, Soft set theory-first results, Comput. Math. Appl. 37 (1999), 19–31.

[25]   S. Naz and M. Shabir, On soft semihypergroups, Journal of Intelligent and Fuzzy Systems 26 (2014), 2203–2213.

[26]   A. Sezgin, A new approach to LA-semigroup theory via the soft sets, Journal of Intelligent and Fuzzy Systems 26 (2014), 2483–2495.

[27]   A. Sezgin and A. O. Atagun, On operations of soft sets, Comput. Math. Appl. 61 (2011), 1457–1467.

[28]   N. Yaqoob, M. Akram and M. Aslam, Intuitionistic fuzzy soft groups induced by (t,s)-norm, Indian Journal of Science and Technology 6 (2013), 4282–4289.

[29]   N. Yaqoob, M. Aslam and Faisal, On soft G-hyperideals over left almost G-semihypergroups, Journal of Advanced Research in Dynamical and Control Systems 4 (2012), 1–12.

[30]   N. Yaqoob, P. Corsini and F. Yousafzai, On intra-regular left almost semihypergroups with pure left identity, J. Math. 2013 (2013), Article ID 510790, 10 pages.

[31]   N. Yaqoob and M. Gulistan, Partially ordered left almost semihypergroups, J. Egyptian Math. Soc. 23 (2015), 231–235.

[32]   F. Yousafzai, K. Hila, P. Corsini and A. Zeb, Existence of non-associative algebraic hyper-structures and related problems, Afr. Mat. 26 (2015), 981–995.

[33]   F. Yousafzai and C. Piersiulio, Some characterization problems in LA-semihypergroups, Journal of Algebra, Number Theory: Advances and Applications 10 (2013), 41–55.

[34]   F. Yousafzai, N. Yaqoob and A. Ghareeb, Left regular AG-groupoids in terms of fuzzy interior ideals, Afr. Mat. 24 (2013), 577–587.

[35]   L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338–353.