International Journal of Analysis and Applications ISSN 2291-8639 (Online)

Research Article

Generalized Complex Fuzzy and Anti-Fuzzy H_v-Subgroups

  • M. Al Tahan
  • B. Davvaz1*
  1. Yazd University

* Corresponding author

Abstract

In this paper, we introduce the concept of generalized complex fuzzy subhypergroup ($H_{v}$-subgroup) as well as the generalized concept of complex anti-fuzzy subhypergroup ($H_{v}$-subgroup). We investigate their properties and their relations with the generalized traditional fuzzy (anti-fuzzy) subhypergroup ($H_{v}$-subgroup).

How to Cite

M. Al Tahan, B. Davvaz, Generalized Complex Fuzzy and Anti-Fuzzy H_v-Subgroups, Int. J. Anal. Appl. 16 (2018), 628–642. https://doi.org/10.28924/2291-8639-16-2018-628

BibTeX
@article{Tahan2018,
  author  = {Al Tahan, M. and Davvaz, B.},
  title   = {Generalized Complex Fuzzy and Anti-Fuzzy H_v-Subgroups},
  journal = {Int. J. Anal. Appl.},
  volume  = {16},
  year    = {2018},
  pages   = {628--642},
  doi     = {10.28924/2291-8639-16-2018-628}
}

References

  • [1] M. Al-Tahan, B. Davvaz, Complex fuzzy Hv-subgroups of an Hv-group, submitted.
  • [2] P. Corsini, Join spaces, power sets, fuzzy sets, Proceedings of the Fifth Int. Congress of Algebraic Hyperstructures and Appl., 1993, Iasi, Romania, Hadronic Press, 1994.
  • [3] P. Corsini, A new connection between hypergroups and fuzzy sets, Southeast Asian Bull. Math. 27(2003), 221-229.
  • [4] P. Corsini and V. Leoreanu, Applications of Hyperstructures Theory, Advances in Mathematics, Kluwer Academic Pub- lisher, 2003.
  • [5] B. Davvaz, Fuzzy Hv-groups, Fuzzy sets Syst. 101 (1999), 191-195.
  • [6] B. Davvaz, Polygroup Theory and Related Systems, World Scientific Publishing Co. Pte. Ltd., Hackensack, NJ, 2013. viii+200 pp.
  • [7] B. Davvaz and I. Cristea, Fuzzy Algebraic Hyperstructures- An introduction, Studies in Fuzziness and Soft Computing 321. Cham: Springer, 2015.
  • [8] F. Marty, Sur une generalization de la notion de group, In 8th Congress Math. Scandenaves, (1934), 45-49.
  • [9] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35 (1971), 512?17.
  • [10] D. Ramot, R. Milo, M. Friedman and A. Kandel, Complex fuzzy logic, IEEE trans. fuzzy syst. 10(2) (2002), 171-186.
  • [11] D. Ramot, M. Friedman, G. Langholz and A. Kandel, Complex fuzzy sets, IEEE trans. fuzzy syst. 11(4) (2003), 450-461.
  • [12] T. Vougiouklis, Hyperstructures and Their Representations, Aviani editor. Hadronic Press, Palm Harbor, USA, 1994.
  • [13] T. Vougiouklis, A new class of hyperstructures, J. Combin. Inform. Syst. Sci. 20 (1995), 229?35.
  • [14] T. Vougiouklis, The fundamental relation in hyperrings. The general hyperfield, In: Proc of the 4th int. congress on algebraic hyperstructures and appl. (A.H.A 1990). World Sientific, Xanthi, Greece, pp 203-211.
  • [15] L. A. Zadeh, Fuzzy sets, Inf. Control 8 (1965), 338-353.