ALGEBRAIC HYPERSTRUCTURES OF SOFT SETS ASSOCIATED TO N-ARY POLYGROUPS
Year 2013,
Volume: 1 Issue: 2, 63 - 71, 01.12.2013
Şerife Yılmaz
Osmankazanci
Abstract
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
References
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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.
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Comer, S. D., Polygroups derived from cogroups, Journal of Algebra 89 (1984), 397-405.
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Corsini, P. and Leoreanu, V., Applications of Hyperstructure Theory, in: Advances in Math- ematics, vol. 5, Kluwer Academic Publishers Boston, Mass, 2003.
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Davvaz, B. and Vougiouklis, T., n-ary hypergroups, Iran. J. Sci. Technol. Trans. A, 30 (2006), 165-1
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Dresher, M. and Ore, O., Theory of multigroups, American Journal of Mathematics 60 (1938), 705-733.
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Feng, F., Jun, Y.B. and Zhao, X., Soft semirings, Computers and Mathematics with Appli- cations 56 (10) (2008), 2621-2628.
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Gau, W.L. and Buehrer, D. J., Vague sets, IEEE Transactions on Systems, Man and Cyber- netics 23(2) (1993), 610-614.
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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.
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Jun, Y.B., Lee, K.J. and Khan, A., Soft ordered semigroups, Mathematical Logic Quarterly 56 (1) (2010), 42-50.
-
Kazancı, O., Yılmaz, S¸. and Yamak, S., Soft sets and Soft BCH-algebras, Hacettepe J. Math. Stst. 39(2) (2010), 205-217.
-
Maji, P.K., Biswas, R. and Roy, A.R., Soft set theory, Computers and Mathematics with Applications 45 (2003), 555-562.
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F. Marty, Sur une generalization de la notion de group, in: Proc. 8th Congress Math. Scan- denaves Stockholm, (1934) 45-49.
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Molodtsov, D., Soft set theory-first results, Computers and Mathematics with Applications 37 (1999), 19-31.
-
Molodtsov, D., The Theory of Soft Sets, URSS Publishers Moscow, 2004 (in Russian).
-
Pawlak, Z., Rough sets, International Journal of Information and Computer Sciences 11 (1982), 341-356.
-
Pawlak, Z., Rough Sets: Theoretical Aspects of Reasoning About Data, Kluwer Academic Publishers Boston, MA, 1991.
-
Xiao, Z., Gong, K., Xia, S.S. and Zou, Y., Exclusive disjunctive soft sets, Computers and Mathematics with Applications 59 (2010), 2128-2137.
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Zadeh, L. A., Fuzzy sets, Information and Control 8 (1965), 338-353.
-
Department of Mathematics, Karadeniz Technical University, 61080, Trabzon, Turkey
-
E-mail address: serifeyilmaz@ktu.edu.tr E-mail address: kazancio@yahoo.com
Year 2013,
Volume: 1 Issue: 2, 63 - 71, 01.12.2013
Şerife Yılmaz
Osmankazanci
References
-
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.
-
Comer, S. D., Polygroups derived from cogroups, Journal of Algebra 89 (1984), 397-405.
-
Corsini, P. and Leoreanu, V., Applications of Hyperstructure Theory, in: Advances in Math- ematics, vol. 5, Kluwer Academic Publishers Boston, Mass, 2003.
-
Davvaz, B. and Vougiouklis, T., n-ary hypergroups, Iran. J. Sci. Technol. Trans. A, 30 (2006), 165-1
-
Dresher, M. and Ore, O., Theory of multigroups, American Journal of Mathematics 60 (1938), 705-733.
-
Feng, F., Jun, Y.B. and Zhao, X., Soft semirings, Computers and Mathematics with Appli- cations 56 (10) (2008), 2621-2628.
-
Gau, W.L. and Buehrer, D. J., Vague sets, IEEE Transactions on Systems, Man and Cyber- netics 23(2) (1993), 610-614.
-
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.
-
Jun, Y.B., Lee, K.J. and Khan, A., Soft ordered semigroups, Mathematical Logic Quarterly 56 (1) (2010), 42-50.
-
Kazancı, O., Yılmaz, S¸. and Yamak, S., Soft sets and Soft BCH-algebras, Hacettepe J. Math. Stst. 39(2) (2010), 205-217.
-
Maji, P.K., Biswas, R. and Roy, A.R., Soft set theory, Computers and Mathematics with Applications 45 (2003), 555-562.
-
F. Marty, Sur une generalization de la notion de group, in: Proc. 8th Congress Math. Scan- denaves Stockholm, (1934) 45-49.
-
Molodtsov, D., Soft set theory-first results, Computers and Mathematics with Applications 37 (1999), 19-31.
-
Molodtsov, D., The Theory of Soft Sets, URSS Publishers Moscow, 2004 (in Russian).
-
Pawlak, Z., Rough sets, International Journal of Information and Computer Sciences 11 (1982), 341-356.
-
Pawlak, Z., Rough Sets: Theoretical Aspects of Reasoning About Data, Kluwer Academic Publishers Boston, MA, 1991.
-
Xiao, Z., Gong, K., Xia, S.S. and Zou, Y., Exclusive disjunctive soft sets, Computers and Mathematics with Applications 59 (2010), 2128-2137.
-
Zadeh, L. A., Fuzzy sets, Information and Control 8 (1965), 338-353.
-
Department of Mathematics, Karadeniz Technical University, 61080, Trabzon, Turkey
-
E-mail address: serifeyilmaz@ktu.edu.tr E-mail address: kazancio@yahoo.com