Level subsets and translations of QFST(G)
Keywords:Fuzzy algebraic structures, Group Theory, Norms, Q-fuzzy subgroups, nNormal Q-fuzzy subgroups, Homomorphisms
First, we introduce level subsets and translations of QFST(G) and study their properties. Secondly, we prove that the union and intersection of two-level subsets of QTST(G) are subgroups of G. Also we prove that translations of QTST(G) are also QFST(G). Finally, we define fuzzy image and fuzzy pre-image of translations of QFST(G) under group homomorphisms and anti group homomorphisms and investigate properties of them.
M. T. Abu Osman, on some products of fuzzy subgroups, Fuzzy Sets and Systems, 24 (1987), 79-86.
C. Alsina et al, On some logical connectives for fuzzy set theory, J. Math. Anal. Appl, 93 (1983), 15-26
J. J. Buckley and E. Eslami, introduction to fuzzy logic and fuzzy sets, Springer-Verlag Berlin Heidelbe GmbH, (2002).
Z. Bonikowaski, Algebraic structures of rough sets, in W. P. Ziarko (Ed.), Rough Sets, Fuzzy Sets and Knowledge Discovery, Springer-Verlag, Berlin, (1995), 242-247.
E. Hendukolaie , On fuzzy homomorphism between hypernear-rings, JMCS, 2 (2011), 702-716.
E. Hendukolaie, M. Aliakbarnia. omran and Y. Nasabi, On fuzzy isomorphism theorems of Γ - hyperpnea rings, JMCS, 7 (2013), 80-88.
U. Hohle, Probabilistic uniformization of fuzzy topologies, Fuzzy Sets and Systems, 1 (1978), 311-332.
T. Hungerford, Algebra, Graduate Texts in Mathematics. Springer (2003).
T. Iwinski, Algebraic approach to rough sets, Bull. PolishAcad. Sci. Math.35, (1987), 673-683.
D. S. Malik and J. N. Mordeson, Fuzzy Commutative Algebra, World Science Publishing Co.Pte.Ltd., (1995)
E. Ranjbar-Yanehsari and M. Asghari-Larimi , Union and intersection fuzzy sub hypergroups, JMCS, (2012), 82-90.
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.
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 Set 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.
R. Rasuli, Characterizations of intuitionistic fuzzy sub semirings of semirings and their homomorphisms norms, Journal of New Theory, 18(2017), 39-52.
R. Rasuli, Intuitionistic fuzzy subrings and ideals of a ring under norms, LAP LAMBERT Academic Publishing, 2017, ISBN: 978-620-2-06926-7.
R. Rasuli, Characterization of Q-Fuzzy subrings (Anti Q-Fuzzy Subrings) with respect to a T-norm (TConorms), Journal of Information and Optimization Science, 31(2018), 1-11.
R. Rasuli, T -Fuzzy Submodules of R × M, Journal of New Theory, 22(2018), 92-102.
R. Rasuli, Fuzzy subgroups over a T -norm, Journal of Information and Optimization Science, 39 (2018) 1757-1765.
R. Rasuli, Fuzzy Sub-vector Spaces and Sub-bivector Spaces under t-Norms, General Letters in Mathematics, 5(2018), 47-57.
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 Journal of Mathematics and Statistics (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.
R. Rasuli, Norms over anti fuzzy G-submodules, MathLAB Journal, 2(2019), 56-64.
R. Rasuli, Norms over bi-fuzzy bi-ideals with operators in semigroups, Notes on Intuitionistic Fuzzy Sets, 25(2019), 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 Journal of Mathematical Sciences, 27(1)(2019), 241-263.
R. Rasuli, Some Results of Anti Fuzzy Subrings Over t-Conorms, MathLAB Journal, 4(2019), 25-32.
R. Rasuli, Anti Fuzzy Equivalence Relation on Rings with respect to t-conorm C, Earthline Journal of Mathematical Sciences, 3(1) (2020), 1-19.
R. Rasuli, t-norms over Fuzzy Multi groups, Earthline Journal of Mathematical Sciences, 3(2)(2020), 207-228.
A. Rosenfled, Fuzzy groups, Journal of Mathematical Analysis and Application, 35 (1971), 512-517.
A. Solairaju and R. Nagarajan, A New structure and constructions of Q- fuzzy group, Advances in Fuzzy Mathematics, 4 (2009), 23-29.
How to Cite
Copyright (c) 2020 rasul rasuli
This work is licensed under a Creative Commons Attribution 4.0 International License.