The chain structure of intuitionistic level subgroups in cyclic groups of order pq

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DOI:

https://doi.org/10.26637/MJM0804/0081

Abstract

It is well known that the set of all level subgroups of any fuzzy subgroup of a finite group forms a chain. In this paper we prove that this result does not extend to Intuitionistic Fuzzy Subgroups (IFSGs) by providing a counter-example. For any two distinct prime numbers p and q, we prove that the cyclic group Zpq has 36 non-isomorphic IFSGs. The Intuitionistic Level Subgroups (ILSGs) of only 28 of them form chains, while those of remaining 8 do not form chains. The list of all the 36 distinct IFSGs is also provided; and those whose ILSGs form a chain, and not, are identified. The case is illustrated using a specific example. We have also obtained a characterisation of IFSGs of Zpq, whose ILSGs form a chain.

Keywords:

Intuitionistic fuzzy set, intuitionistic fuzzy subgroup, level subgroup, isomorphism, cyclic group

Mathematics Subject Classification:

Mathematics
  • S. Divya Mary Daise Department of Mathematics, St. Albert’s College, Ernakulam (Affiliated to Mahatma Gandhi University), Cochin-682018, India.
  • S. Deepthi Mary Tresa Department of Mathematics, St. Albert’s College, Ernakulam (Affiliated to Mahatma Gandhi University), Cochin-682018, India.
  • Shery Fernandez Department of Mathematics, Cochin University of Science and Technology, Cochin-682022, India.
  • Pages: 1818-1823
  • Date Published: 01-01-2020
  • Vol. 8 No. 04 (2020): Malaya Journal of Matematik (MJM)

Atanassov K. T., Intuitionistic Fuzzy Sets, Fuzzy Sets and Systems, 20(1) (1986), 87-96.

Biswas R., Intuitionistic Fuzzy Subgroups, Mathematical Forum, X (1996), 39 - 44

Burton. David M., Elementary Number Theory, Seventh Edition, Mc Graw Hill, New York, (2011)

Daise S. D. M. and Tresa S. D. M., On Level Subgroups of Intuitionistic Fuzzy Groups, J. Comp. Math. Sci., 7(11) (2016), 606 - 612

Daise S. D. M., Tresa S. D. M., Fernandez S., Intuitionistic Level Subgroups of Intuitionistic Fuzzy Groups, Pro ceedings of International Conference of Mathematics (ICM 2018), (2018), 78-82

Daise S. D. M., Tresa S. D. M., Fernandez S., On Isomorphism of Intuitionistic Fuzzy Sets (Communicated).

Daise S. D. M., Tresa S. D. M., Fernandez S., Intuitionistic Level Subgoups in Cyclic Groups of Order $p^n$ (Communicated).

Das P. S., Fuzzy Groups and Level Subgroups, J. Math. Anal. Appl., 84 (1981), 264 - 269.

Palaniappan N, Naganathan S, Arjunan K, A Study on Intuitionistic L-Fuzzy Subgroups, Applied Mathematical Sciences, 3(53)(2009), 2619 - 2624

Rosenfeld A., Fuzzy Groups, J. Math. Anal. Appl., 35 (1971), 512 - 517.

Sebastian S., Babu Sunder, Fuzzy groups and group homomorphisms, Fuzzy Sets and Systems, 81(1996), 397 401.

Sharma P. K., Intuitionistic Fuzzy Groups, International Journal of Data Warehousing and Mining, 1(1)(2011), $1-10$.

Tae-Chon. Ahn, Hur. Kul, Jang. Kyung-Won, Intuitionistic Fuzzy Subgroups and Level Subgroups, International Journal of Fuzzy Logic and Intelligent Systems, 6(3)(2006), 240 - 246.

Zadeh L. A., Fuzzy Sets, Information and Control, 8 (1965), 338-353.

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Published

01-01-2020

How to Cite

S. Divya Mary Daise, S. Deepthi Mary Tresa, and Shery Fernandez. “The Chain Structure of Intuitionistic Level Subgroups in Cyclic Groups of Order pq”. Malaya Journal of Matematik, vol. 8, no. 04, Jan. 2020, pp. 1818-23, doi:10.26637/MJM0804/0081.