Anti Q-fuzzy Subgroups under t-conorms
Abstract
In this paper we introduce the notion of anti Q-fuzzy subgroups of G with respect to t‑conorm C and study their important properties. Next we define the union, normal and direct product of two anti Q-fuzzy subgroups of G with respect to t-conorm C and we show that the union, normal and direct product of them is again an anti Q-fuzzy subgroup of G with respect to t-conorm C. It is also shown that the homomorphic image and pre image of anti Q-fuzzy subgroup of G with respect to t-conorm C is again an anti Q-fuzzy subgroup of G with respect to t-conorm C.
References
M. T. Abu Osman, On some products of fuzzy subgroups, Fuzzy Sets and Systems 24 (1987), 79-86. https://doi.org/10.1016/0165-0114(87)90115-1
J. J. Buckley and E. Eslami, Introduction to Fuzzy Logic and Fuzzy Sets, Springer-Verlag Berlin, Heidelberg, GmbH, 2002. https://doi.org/10.1007/978-3-7908-1799-7
T. Hungerford, Algebra, Graduate Texts in Mathematics, Springer, 2003.
D. S. Malik and J. N. Mordeson, Fuzzy Commutative Algebra, World Science Publishing Co. Pte. Ltd., 1995.
K. Menger, Statistical metrics, Proc. Nat. Acad. Sci. U.S.A. 28 (1942), 535-537. https://doi.org/10.1073/pnas.28.12.535
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.
R. Rasuli, Fuzzy modules over a t-norm, Int. J. Open Problems Compt. Math. 9(3) (2016), 12-18. https://doi.org/10.12816/0033740
R. Rasuli, Fuzzy Subrings over a t-norm, The Journal of Fuzzy Mathematics Los Angeles 24(4) (2016), 995-1000.
R. Rasuli, Norms over intuitionistic fuzzy subrings and ideals of a ring, Notes on Intuitionistic Fuzzy Sets 22(5) (2016), 72-83.
R. Rasuli, Norms over fuzzy Lie algebra, Journal of New Theory 15 (2017), 32-38.
R. Rasuli, Fuzzy subgroups on direct product of groups over a t-norm, Journal of Fuzzy Set Valued Analysis 3 (2017), 96-101. https://doi.org/10.5899/2017/jfsva-00339
R. Rasuli, Characterizations of intuitionistic fuzzy subsemirings of semirings and their homomorphisms by norms, Journal of New Theory 18 (2017), 39-52.
R. Rasuli, Intuitionistic Fuzzy Subrings and Ideals Under Norms, LAP LAMBERT Academic Publishing, 2017.
R. Rasuli, Characterization of Q-fuzzy subrings (anti Q-fuzzy subrings) with respect to a t-norm (t-conorms), J. Inf. Optim. Sci. 39 (2018), 827-837.
R. Rasuli, T-fuzzy submodules of R M, Journal of New Theory 22 (2018), 92-102.
R. Rasuli, Fuzzy subgroups over a t-norm, J. Inf. Optim. Sci. 39 (2018), 1757-1765. https://doi.org/10.1080/02522667.2018.1427028
R. Rasuli, Fuzzy sub-vector spaces and sub-bivector spaces under t-norms, General Letters in Mathematics 5 (2018), 47-57. https://doi.org/10.31559/glm2018.5.1.6
R. Rasuli, Anti fuzzy submodules over a t-conorm and some of their properties, The Journal of Fuzzy Mathematics Los Angles 27 (2019), 229-236.
R. Rasuli, Artinian and Noetherian fuzzy rings, Int. J. Open Problems Compt. Math. 12 (2019), 1-7.
R. Rasuli and H. Narghi, T-norms over Q-fuzzy subgroups of group, Jordan J. Math. Stat. (JJMS) 12 (2019), 1-13.
R. Rasuli, Fuzzy equivalence relation, fuzzy congruence relation and fuzzy normal subgroups on group G over t-norms, Asian Journal of Fuzzy and Applied Mathematics 7 (2019), 14-28. https://doi.org/10.24203/ajfam.v7i2.5736
R. Rasuli, Norms over anti fuzzy G-submodules, MathLAB Journal 2 (2019), 56-64.
R. Rasuli, Norms over bifuzzy bi-ideals with operators in semigroups, Notes on Intuitionistic Fuzzy Sets 25 (2019), 1-11. https://doi.org/10.7546/nifs.2019.25.1.1-11
R. Rasuli, Norms over basic operations on intuitionistic fuzzy sets, The Journal of Fuzzy Mathematics Los Angles 27(3) (2019), 561-582.
R. Rasuli, T-fuzzy bi-ideals in semirings, Earthline J. Math. Sci. 2(1) (2019), 241-263. https://doi.org/10.34198/ejms.2119.241263
R. Rasuli, Anti fuzzy equivalence relation on rings with respect to t-conorm C, Earthline J. Math. Sci. 3(1) (2020), 1-19. https://doi.org/10.34198/ejms.3120.119
A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35 (1971), 512-517. https://doi.org/10.1016/0022-247X(71)90199-5
B. Schweizer and A. Sklar, Probabilistic Metric Space, North-Holland, Amsterdam, 1983.
A. Solairaju and R. Nagarajan, A New structure and constructions of Q-fuzzy group, Advances in Fuzzy Mathematics 4 (2009), 23-29.
X. H. Yuan and E. S. Lee, A fuzzy algebraic system based on the theory of falling shadows, J. Math. Anal. Appl. 208 (1997), 243-251. https://doi.org/10.1006/jmaa.1997.5331
L. A. Zadeh, Fuzzy sets, Information and Control 8 (1965), 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
This work is licensed under a Creative Commons Attribution 4.0 International License.
.jpg){kind=logo}
