The Norms Over Anti Fuzzy G-submodules
In this study, we define anti fuzzy-submodules with respect to investigate some of their algebraic properties. Later we introduce the union and direct sum of them and finally, we prove that the union, direct sum, homomorphic images and pre images of them are also anti fuzzy
 C. Alsina, E. Trillas and L. Valverde, On some logical connectives for fuzzy set theory, J. Math. Anal.
Appi., 93(1983), 15-26.
 I. Beg, Fuzzy multivalued functions, Bull. Allahabad Math. Soc., 21(2006), 41-104.
 I. Beg and S. Ashraf, Fuzzy similarity and measure of similarity with Lukasiewicz implicator, New Math.
Natural Computation, 4(2008), 191-206.
 I. Beg and S. Ashraf, Fuzzy inclusion and fuzzy similarity with Godel implication operator, New Math.
Natural Computation, 5(2009), 617-633.
 I. Beg and S. Ashraf, Fuzzy dissimilarity measures and distance functions, Fuzzy Information and Engineering, 1(2009), 205-217.
 I. Beg and S. Ashraf, Similarity measures for fuzzy sets, Appl. and Comput. Math., 8(2009), 192-202.
 V. V. Cross and T.A. Sudkamp, Similarity and Compatibility in Fuzzy Set Theory, Springer-Verlag, Heidelberg 2002.
 C. W. Curtles and I. Reiner, Representation Theory of finite group and Associative algebra, INC, 1962.
 J. Dombi, A general class of fuzzy operators, the De Morgan class of fuzzy operators and fuzziness induced
by fuzzy operators, Fuzzy Setsand Systems, 8(1982), 149-163.
 D. Dubois and H. Prade, Fundamentals of Fuzzy Sets, Kluwer Academic Publishers, Dordrecht 2000.
 S. Gottwald, Fuzzy Sets and Fuzzy Logic, Vieweg, Wiesbaden, 1993.
 U. Hohle, Probabilistie uniformization of fuzzy topologies, Fuzzy Sets and System, 1(1978), 311-332.
 U. Hohle and S.E. Rodabaugh, Mathematics of Fuzzy Sets: Logic, Topology, and Measure Theory, The
Hand book of Fuzzy Mathematics Series, 1998.
 A. J. Kamble and T. Venkatesh, A note on some fuzzy algebraic structures, Inter. J. Fuzzy Math. Sys. ,
 A. Kaufmann and M. M. Gupta, Fuzzy Mathematics Models in Engineering and management Science,
North-Holland, Amsterdam, 1988.
 E. E. Kerre, Introduction to the Basic Principles of Fuzzy Set Theory and some of its Applications, Communication and Cognition, 1991.
 H. X. Li and V. C. Yen, Fuzzy Sets and Fuzzy Decision-Making, CRC Press. Inc., London, 1995.
 J. Lukasiewicz, A numerical interpretation of the theory of propositions, Ruch Filozoficzny, 23(1922),
 D. S. Malik, J. N. Mordeson and M. K. Sen, Fundamentals of Abstract Algebra, McGraw Hill, (1997).
 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.
 H.T . Nguyen and E. A. Walker, Fuzzy Logic, (Third Edition) CRC Press, Boston, 2006.
 K. Peeva and Y. Kyosev, Fuzzy Relational Calculus, World Scientific, New Jersey 2004.
 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),
 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,
 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 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),
 A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35(1971), 512-517.
 B. Russell, Vagueness, Australian J. Phil., 1(1923), 84-92.
 B. Schweizer and A. Sklar, Probabilistic Metric Space, North-Holland, Amsterdam, 1983.
 P. K. Sharma, Anti fuzzy submodule of a module, Advances in Fuzzy Sets and Systems, 12 (2012), 49-57.
 S. Weber, A general concept of fuzzy connectives, negations and implications based on t-norms and tconorms, Fuzzy Setsand Systems, 11(1983), 115-134.
 R. R. Yager, On a general class of fuzzy connectives, Fuzzy Setsand Systems, 4(1980), 235-242.
 L. A. Zadeh, Fuzzy sets, Inform. Control., 8(1965), 338-353.
 L. A. Zadeh, Generalized theory of uncertainty (GTU)principal concepts and ideas, Comput. Statist. Data
Anal., 51(2006), 15-46.
 H. J. Zimmermann, Fuzzy Set Theory and its Applications, Kluwer Academic Publishers, Boston, 1991.
Copyright (c) 2019 rasul rasuli
This work is licensed under a Creative Commons Attribution 4.0 International License.
Please find the rights and licenses into Chemistry Journal
All articles published in this journal are licensed under a Creative Commons Attribution 4.0 International License.
2. Author’s Warranties
The author warrants that the article is original, written by stated author(s), has not been published before, contains no unlawful statements, does not infringe the rights of others, is subject to copyright that is vested exclusively in the author and free of any third party rights, and that any necessary written permissions to quote from other sources have been obtained by the author(s).
3. User Rights
To Chemistry Journal's spirit is to disseminate articles published are as free as possible. Under the Creative Commons Attribution 4.0 International License., which permits unrestricted use, distribution, and reproduction in any medium, provided that the original work is properly cited.
4. Rights of Authors
Authors retain the following rights:
- Copyright, and other proprietary rights relating to the article, such as patent rights,
- The right to use the substance of the article in future own works, including lectures and books,
- The right to reproduce the article for own purposes,
- The right to self-archive the article,
- the right to enter into separate, additional contractual arrangements for the non-exclusive distribution of the article's published version (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal (To Chemistry Journal ).
If the article was jointly prepared by other authors, the signatory of this form warrants that he/she has been authorized by all co-authors to sign this agreement on their behalf, and agrees to inform his/her co-authors of the terms of this agreement.
This agreement entitles the author to no royalties or other fees. To such extent as legally permissible, the author waives his or her right to collect royalties relative to the article in respect of any use of the article by To Chemistry Journal or its sublicensee.
To Chemistry Journal will publish the article (or have it published) in the journal if the article’s editorial process is successfully completed and To Chemistry Journal has become obligated to have the article published. To Chemistry Journal may conform the article to a style of punctuation, spelling, capitalization, referencing and usage that it deems appropriate. The author acknowledges that the article may be published so that it will be publicly accessible and such access will be free of charge for the readers.