T-Fuzzy Submodules of RxM

Abstract

In this paper, we introduce the concept of T-fuzzy submodule of RxM and give new results on this subject. Next we study the concept of the extension of T-fuzzy submodule of RxM and prove some results on these. Also we investigate T-fuzzy submodule of RxM under homomorphisms or R-modules.

Keywords

• Theory of modules,extensions,homomorphism,fuzzy set theory,norms

References

1. [1] C. Alsina et al, On some logical connectives for fuzzy set theory, J. Math. Anal. Appl, 93 (1983), 15-26.
2. [2] J. M. Anthony and H. Sherwood, Fuzzy groups rede¯ned, Journal of Mathemat- ical Analysis and Application, 69 (1977), 124-130.
3. [3] M. M. Gupta and J. Qi, Theory of T-norms and fuzzy inference methods, Fuzzy Sets and System, 40 (1991), 431-450.
4. [4] U. Hohle, Probabilistic uniformization of fuzzy topologies, Fuzzy Sets and Sys- tems, 1 (1978), 311-332.
5. [5] A. Solairaju and R. Nagarajan, Q-Fuzzy left R-subgroups of near rings with respect to t-norms, Antarctica Journal of Mathematics 5(2008), 59-63.
6. [6] A. Solairaju and R. Nagarajan, A New Structure and Construction of Q-Fuzzy Groups, Advances in fuzzy mathematics 4(2009), 23-29.
7. [7] R. Rasuli, Fuzzy Ideals of Subtraction Semigroups with Respect to A t-norm and A t-conorm, The Journal of Fuzzy Mathematics Los Angeles, 24 (4) (2016), 881-892.
8. [8] R. Rasuli, Fuzzy modules over a t-norm, Int. J. Open Problems Compt. Math., 9 (3) (2016), 12-18.

9. [9] R. Rasuli, Fuzzy Subrings over a t-norm , The Journal of Fuzzy Mathematics Los Angeles, 24 (4) (2016), 995-1000.
10. [10] R. Rasuli, Norms over intuitionistic fuzzy subrings and ideals of a ring, Notes on Intuitionistic Fuzzy Sets, 22 (5) (2016), 72-83.
11. [11] R. Rasuli, Norms over fuzzy Lie algebra, Journal of New Theory, 15(2017), 32-38.
12. [12] R. Rasuli, Fuzzy subgroups on direct product of groups over a t-norm, Journal of Fuzzy Set Valued Analysis, 3(2017), 96-101.
13. [13] R. Rasuli, Characterizations of intuitionistic fuzzy subsemirings of semirings and their homomorphisms by norms, Journal of New Theory, 18(2017), 39-52.
14. [14] R. Rasuli, intuitionistic fuzzy subrings and ideals of a ring under norms, LAP LAMBERT Academic publishing, 2017, ISBN: 978-620-2-06926-7.
15. [15] R. Rasuli, Characterization of Q-Fuzzy subrings (Anti Q-Fuzzy Subrings) with respect to a T-norm (T-Conorms), Journal of Information and Optimization Science, 31(2018), 1-11.
16. [16] Y. Yandong, Triangular norms and TNF-sigma algebras,, Fuzzy Sets and Sys- tem, 16 (1985), 251-264.
17. [17] L. A. Zadeh, Fuzzy sets, inform. and Control, 8(1965), 338-353.