On anti-fuzzy subgroup

Authors

  • Sudipta Gayen Department of Mathematics, National Institute of Technology Jamshedpur, India
  • Sripati Jha Department of Mathematics, National Institute of Technology Jamshedpur, India
  • Manoranjan Kumar Singh Department of Mathematics, Magadh University, Bodh Gaya, India
  • Ashish Kumar Prasad School of Advanced Sciences, Vellore Institute of Technology, Vellore, India

DOI:

https://doi.org/10.2298/YJOR200717043G

Keywords:

Fuzzy subgroup, Anti-fuzzy subgroup, Lower level set, Lower level subgroup

Abstract

In this paper, efforts have been taken to generalise the notion of anti-fuzzy subgroup. Proposed definition was supported by graphical comparison with our previous result and suitably constructed examples. Based on the introduced definition, we derive not only some results of anti-fuzzy subgroup but also we redefine lower level set and lower level subgroup, and derive some essential theorems to study some algebraic characteristics. Further, a modified notion of lower level subgroup is given.

References

Atanassov, K.T., “Intuitionistic fuzzy sets”, Fuzzy Sets and Systems, 20 (1) (1986) 87–96.

Biswas, R., “Fuzzy Subgroups and Anti Fuzzy Subgroups”, Fuzzy Sets and Systems, 35 (1) (1990) 121–124.

Rosenfeld, A., “Fuzzy Groups”, Journal of Mathematical Analysis and Applications, 35 (3) (1971) 512–517.

Das, P.S., “Fuzzy Groups and Level Subgroups”, Journal of Mathematical Analysis and Applications, 84 (1) (1981) 264-269.

Kandasamy, W.B.V., Smarandache Fuzzy Algebra, American Research Press, Rehoboth, New Mexico, 2003.

Kilr, G.J., Yuan, B., Fuzzy Sets And Fuzzy Logic: Theory and Applications, Pearson, Upper Saddle River, New Jersey, 1995.

Li, D., Zhang, C., Ma, S., “The Intuitionistic Anti-fuzzy Subgroup in Group G”, Fuzzy Information and Engineering, 54 (1) (2009) 145-151.

Mukherjee, N.P., “Fuzzy Normal Subgroups and Fuzzy Cosets”, Information Science, 34 (3) (1984) 225–239.

Rasuli, R., “Some Results of Anti Fuzzy Subrings Over t-Conorms”, MathLAB Journal, 4 (2019) 25–32.

Singh, M., Theory of Fuzzy Structures and Applications, Lambert Academic Publishing, Saarbrücken, Germany, 2010.

Gayen S., Jha, S., Singh, M., Kumar, R., “On a Generalized Notion of Anti-fuzzy Subgroup and Some Characterizations”, International Journal of Engineering and Advanced Technology, 8 (3) (2019) 385–390.

Zadeh, L.A., “Fuzzy Sets”, Information and Control, 8 (3) (1965) 338–353.

Downloads

Published

2021-11-01

Issue

Vol. 31 No. 4 (2021)

Section

Research Articles

License

Copyright (c) 2021 YUJOR

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.