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ALGEBRAIC HYPERSTRUCTURES OF SOFT SETS ASSOCIATED TO N-ARY POLYGROUPS

Year 2013, Volume: 1 Issue: 2, 63 - 71, 01.12.2013

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

  • 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

Year 2013, Volume: 1 Issue: 2, 63 - 71, 01.12.2013

Abstract

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
There are 20 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Şerife Yılmaz This is me

Osmankazanci This is me

Publication Date December 1, 2013
Submission Date March 9, 2015
Published in Issue Year 2013 Volume: 1 Issue: 2

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