Original Research Article

Article volume = 2023 and issue = 1

Pages: 39–54

Article publication Date: December 27, 2022

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# Norms Over Intuitionistic Fuzzy Subgroups on Direct Product of Groups

#### Rasul Rasuli

Department of Mathematics, Payame Noor University (PNU), P. O. Box 19395-3697, Tehran, Iran.

##### Abstract:

In this paper, by using norms (t-norm T and s-norm S), the notion of intuitionistic fuzzy subgroups on direct product of groups will be introduced. Also intersection and normality of them will be defined and investigated some properties of them. Finally, some results of them under group homomorphisms will be provided.

##### Keywords:

Group theory, theory of fuzzy sets, intuitionistic fuzzy groups, norms, homomorphisms, intersection.

##### References:

- [1] M. T. Abu Osman, On some products of fuzzy subgroups, Fuzzy Sets and Systems, 24 (1987), 79-86. 1, 2.10
- [2] J. M. Anthony and H. Sherwood, A characterization of fuzzy subgroups, Fuzzy Sets and Systems, 7(1982), 297-305. 1
- [3] K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1986), 87-96. 1, 2.3, 2.4
- [4] K. T. Atanassov, New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems, 61(1994), 137-142. 2.5
- [5] J. J. Buckley and E. Eslami, An introduction to fuzzy logic and fuzzy sets, Springer-Verlag Berlin Heidelberg GmbH, (2002). 2.6, 2.7, 2.8, 2.9
- [6] T. Hungerford, Algebra, Graduate Texts in Mathematics. Springer (2003). 2.1
- [7] D. S. Malik and J. N. Mordeson, Fuzzy Commutative Algebra, World Science publishing Co.Pte.Ltd.,(1995). 2.2
- [8] R. Rasuli, Norms over intuitionistic fuzzy subrings and ideals of a ring, Notes on Intuitionistic Fuzzy Sets, 22(5)(2016), 72-83. 1, 2.11, 2.12
- [9] R. Rasuli, t-norms over fuzzy ideals (implicative, positive implicative) of BCK-algebras, Mathematical Analysis and its Contemporary Applications, 4(2)(2022), 17-34. 1
- [10] R. Rasuli, T-fuzzy subbigroups and normal T-fuzzy subbigroups of bigroups, J. of Ramannujan Society of Mathematics and Mathematical Sciences, 9(2)(2022), 165-184. 1
- [11] R. Rasuli, M. A. Hashemi and B. Taherkhani, S-norms and Anti fuzzy ideals of BCI-algebras, 10th National Mathematics Conference of the Payame Noor University, Shiraz, May, 2022. 1
- [12] R. Rasuli, B. Taherkhani and H. Naraghi, T-fuzzy SU-subalgebras, 10th National Mathematics Conference of the Payame Noor University, Shiraz, May, 2022. 1
- [13] R. Rasuli, A study of T-fuzzy multigroups and direct preoduct of them, 1th National Conference on Applied Reserches in Basic Sciences( Mathematics, Chemistry and Physics) held by University of Ayatolla Boroujerdi, Iran, during May 26-27, 2022. 1
- [14] R. Rasuli, S - (M,N)-fuzzy subgroups, 1th National Conference on Applied Reserches in Basic Sciences( Mathematics, Chemistry and Physics) held by University of Ayatolla Boroujerdi, Iran, during May 26-27, 2022. 1
- [15] R. Rasuli, Intuitionistic fuzzy BCI-algebras (implicative ideals, closed implicative ideals, commutative ideals) under norms, Mathematical Analysis and its Contemporary Applications, 4(3)(2022), 17-34. 1
- [16] R. Rasuli, Fuzzy d-algebras under t-norms, Eng. Appl. Sci. Lett. (EASL), 5(1)(2022), 27-36. 1
- [17] R. Rasuli, Fuzzy vector spaces under norms, Annals of Mathematics and Computer Science, 9(2022), 7-24. 1
- [18] R. Rasuli, T-fuzzy G-submodules, Scientia Magna, 17(1)(2022), 107-118. 1
- [19] R. Rasuli, Anti Fuzzy Congruence on Product Lattices, 7th International Congerence on Combinatotcs, Crytography, Computer Science and Computing held by Iran University of Science and Technology, Iran,Tehran, during November 16-17, 2022. 1
- [20] R. Rasuli, Anti complex fuzzy Lie subalgebras under S-norms, Mathematical Analysis and its Contemporary Applications, 4(4)(2022), 13-26. 1
- [21] R. Rasuli, t-conorms over anti fuzzy subgroups on direct product of groupos, Annals of Mathematics and Computer Science, 10(2022), 8-18. 1
- [22] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35(1971), 512-519. 1
- [23] S. Sessa, On fuzzy subgroups and fuzzy ideals under triangular norms: short communiction, Fuzzy Sets and Systems, 13(1984), 95-100. 1
- [24] L. A. Zadeh, Fuzzy sets, inform. and Control, 8(1965), 338-353. 1
- [25] P. Zhan and Tan, Intuitionistic M-fuzzy subgroups, Soochow Journal of Mathematics, 30(2004), 85-90. 1

##### Cite this article as:

- Rasul Rasuli, Norms Over Intuitionistic Fuzzy Subgroups on Direct Product of Groups, Communications in Combinatorics, Cryptography & Computer Science, 2023(1), PP.39–54, 2022
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