TY - JOUR T1 - ALGEBRAIC HYPERSTRUCTURES OF SOFT SETS ASSOCIATED TO N-ARY POLYGROUPS AU - Yılmaz, Şerife AU - , Osmankazanci PY - 2013 DA - December JF - Mathematical Sciences and Applications E-Notes JO - Math. Sci. Appl. E-Notes PB - Murat TOSUN WT - DergiPark SN - 2147-6268 SP - 63 EP - 71 VL - 1 IS - 2 LA - en AB - This paper concerns a relationship between soft sets and n-arypolygroups. We consider the notion of an n-ary polygroup as a generalization ofa polygroup and apply the notion of soft sets to n-ary polygroups. Some relatednotions are defined and several basic properties are discussed by using the softset theory. Furthermore, we propose the homomorphism of n-ary polygroupsand investigate the properties which are preserved under the homomorphism KW - n-ary polygroup KW - soft set KW - strong homomorphism CR - Ali, M.I., Feng, F., Liu, X., Min, W.K. and Shabira, M., On some new operations in soft set theory, Computers and Mathematics with Applications 57 (9) (2009), 1547-1553. CR - Comer, S. D., Polygroups derived from cogroups, Journal of Algebra 89 (1984), 397-405. CR - Corsini, P. and Leoreanu, V., Applications of Hyperstructure Theory, in: Advances in Math- ematics, vol. 5, Kluwer Academic Publishers Boston, Mass, 2003. CR - Davvaz, B. and Vougiouklis, T., n-ary hypergroups, Iran. J. Sci. Technol. Trans. A, 30 (2006), 165-1 CR - Dresher, M. and Ore, O., Theory of multigroups, American Journal of Mathematics 60 (1938), 705-733. CR - Feng, F., Jun, Y.B. and Zhao, X., Soft semirings, Computers and Mathematics with Appli- cations 56 (10) (2008), 2621-2628. CR - Gau, W.L. and Buehrer, D. J., Vague sets, IEEE Transactions on Systems, Man and Cyber- netics 23(2) (1993), 610-614. CR - Ghadiri, M. and Waphare, B. N., n-ary polygroups, Iran. J. Sci. Technol. Trans. A, 33, No. A Gorzalzany, M. B., A method of inference in approximate reasoning based on interval-valued fuzzy sets, Fuzzy Sets and Systems 21 (1987), 1-17. CR - Jun, Y.B., Lee, K.J. and Khan, A., Soft ordered semigroups, Mathematical Logic Quarterly 56 (1) (2010), 42-50. CR - Kazancı, O., Yılmaz, S¸. and Yamak, S., Soft sets and Soft BCH-algebras, Hacettepe J. Math. Stst. 39(2) (2010), 205-217. CR - Maji, P.K., Biswas, R. and Roy, A.R., Soft set theory, Computers and Mathematics with Applications 45 (2003), 555-562. CR - F. Marty, Sur une generalization de la notion de group, in: Proc. 8th Congress Math. Scan- denaves Stockholm, (1934) 45-49. CR - Molodtsov, D., Soft set theory-first results, Computers and Mathematics with Applications 37 (1999), 19-31. CR - Molodtsov, D., The Theory of Soft Sets, URSS Publishers Moscow, 2004 (in Russian). CR - Pawlak, Z., Rough sets, International Journal of Information and Computer Sciences 11 (1982), 341-356. CR - Pawlak, Z., Rough Sets: Theoretical Aspects of Reasoning About Data, Kluwer Academic Publishers Boston, MA, 1991. CR - Xiao, Z., Gong, K., Xia, S.S. and Zou, Y., Exclusive disjunctive soft sets, Computers and Mathematics with Applications 59 (2010), 2128-2137. CR - Zadeh, L. A., Fuzzy sets, Information and Control 8 (1965), 338-353. CR - Department of Mathematics, Karadeniz Technical University, 61080, Trabzon, Turkey CR - E-mail address: serifeyilmaz@ktu.edu.tr E-mail address: kazancio@yahoo.com UR - https://dergipark.org.tr/en/pub/mathenot/issue//207646 L1 - https://dergipark.org.tr/en/download/article-file/182479 ER -