Direct Product of Fuzzy Multigroups

Abstract

The paper introduces direct product in fuzzy multigroup setting as an extension of  direct product of fuzzy subgroups.   Some properties of  direct product of fuzzy multigroups are explicated. It is established that the direct product of fuzzy multigroups is a fuzzy multigroup.  The notion of homomorphism and some of its properties in the context of direct product of fuzzy multigroups are introduced.

Keywords

• Fuzzy multisets,Fuzzy multigroups,Direct product of fuzzy multigroups

References

1. L.A. Zadeh, Fuzzy sets, Information and Control 8 (1965) 338-353.
2. A. Rosenfeld, Fuzzy subgroups, Journal of Mathematical Analysis and Applications 35 (1971) 512-517.
3. J.M. Mordeson, K.R. Bhutani and A. Rosenfeld, Fuzzy group theory, Springer-Verlag Berlin Heidelberg, 2005.
4. B. Seselja, A. Tepavcevic, A note on fuzzy groups, Yugoslav Journal of Operation Research 7(1) (1997) 49-54.
5. A. Syropoulos, Mathematics of multisets, Springer-Verlag Berlin Heidelberg (2001) 347-358.
6. N.J. Wildberger, A new look at multisets, School of Mathematics, UNSW Sydney 2052, Australia, 2003.
7. D. Singh, A.M. Ibrahim, T. Yohanna, and J.N. Singh, An overview of the applications of multisets, Novi Sad Journal of Mathematics 37(2) (2007) 73-92.
8. R.R. Yager, On the theory of bags, International Journal of General Systems 13 (1986) 23-37.

9. P.A. Ejegwa, Correspondence between fuzzy multisets and sequences, Global Journal Science Frontier Research: F Mathematics and Decision Science 14(7) (2014) 61-66.
10. S. Miyamoto, Basic operations of fuzzy multisets, Journal of Japan Society of Fuzzy Theory and Systems 8(4) (1996) 639-645.
11. A. Syropoulos, On generalized fuzzy multisets and their use in computation, Iranian Journal of Fuzzy Systems 9(2) (2012) 113-125.
12. T.K. Shinoj, A. Baby and J.J. Sunil, On some algebraic structures of fuzzy multisets, Annals of Fuzzy Mathematics and Informatics 9(1) (2015) 77-90.
13. A. Baby, T.K. Shinoj and J.J. Sunil, On abelian fuzzy multigroups and order of fuzzy multigroups, Journal of New Theory 5(2) (2015) 80-93.
14. P.A. Ejegwa, On abelian fuzzy multigroups, Journal of Fuzzy Mathematics 26(3) (2018) 655-668.
15. P.A. Ejegwa, On fuzzy multigroups and fuzzy submultigroups, Journal of Fuzzy Mathematics 26(3) (2018) 641-654.
16. P.A. Ejegwa, On normal fuzzy submultigroups of a fuzzy multigroup, Theory and Applications of Mathematics and Computer Science 8(1) (2018) 64-80.
17. P.A. Ejegwa, Homomorphism of fuzzy multigroups and some of its properties, Applications and Applied Mathematics 13(1) (2018) 114-129.
18. A.K. Ray, On product of fuzzy subgroups, Fuzzy Sets and Systems 105 (1999) 181-183.
19. S. Miyamoto and K. Mizutani, Fuzzy multiset model and methods for nonlinear document clustering for information retrieval, Springer-Verlag Berlin Heidelberg (2004) 273-283.
20. R. Biswas, An application of Yager's bag theory in multicriteria based decision making problems, International Journal of Intelligent Systems 14 (1999) 1231-1238.
21. K. Mizutani, R. Inokuchi and S. Miyamoto, Algorithms of nonlinear document clustering based on fuzzy multiset model, International Journal of Intelligent Systems 23 (2008) 176-198.