Direct sum of Intuitionistic fuzzy quasi injective s-act
DOI:
https://doi.org/10.24237/ASJ.03.02.840BKeywords:
fuzzy, Direct sumAbstract
In order to define the intuitionistic fuzzy s-act of the direct sum Ai ⨁ Aj, we first introduce the idea of the direct sum of intuitionistic fuzzy s-act (L = Li ⨁ Lj) of A and go over a few associated properties if Li and Lj are intuitionistic fuzzy s-acts of Ai and Aj s-acts, respectively. Next, we expand the definition of intuitionistic fuzzy s-act Li and Lj. It is demonstrated that the direct sum of the supported of intuitionistic fuzzy s-act Li and Lj equals the support of the direct sum of those supports. Additionally, we have obtained some results by analyzing the direct sum of an arbitrary family of intuitionistic fuzzy s-act. Additionally, we present and demonstrate the concepts of intuitionistic fuzzy s-act decomposability and indecomposility
References
L.A.Zadeh, Fuzzy Sets, In form. Control, 8,338-353, (1965).
A.Rosenfeld, Fuzzy group, J. Math-Anal. and Appl-35,512-517,(1971).
C.V.Negoita, D.A.Ralescu, Applications. of Fuzzy Sets and System Analysis, Birkhauser, Basel, (1975).
S. Fernadde Z, Astudy of fuzzy G-modules, Ph.D Thesis, St. Albert's College, Rev. Dr.Konnully Memorial Research Centre and P-G-Department of Mathematics, (2004).
K.T.Atanassov, Intuitionistic fuzzy Sets, Fuzzy sets and Systems, 20(1), 87-96-(1986).
K.T. Atanassov, New operation defined over the intuitionistic fuzzy Sets, Fuzzy Sets and Systems, 61,137-142, (1994).
K.T. Atanassov, Intuitionistic Fuzzy Sets Theory and Applications, studies on fuzziness and Soft Computing, 35, physica - Verlag, Heidelberg (1999).
R.Biswas, Intuitionistic fuzzy subgroup, Mathematical Forum "X, 37-46, (1989).
B.DavvaZ, W. A. Dudek, Y. B.Jun, Intuitionistic fuzzy HV-Submodules, Information Sciences, 176, 285-300, (2006)
p.k. Sharma and Tarandeep Kaur, Intuitionistic fuzzy G-modules, Notes on Intuitionistic Fuzzy Sets, 21(1), 6-23, (2015).
p.K. Sharma and Tarandeep Kaur, on intuitionistic fuzzy representation of intuitionistic fuzzy G-modules, Annals of fuzzy Mathematics and Informatics 11(4),557-569, (2016).
p.K.Sharma, Reducibility and complete Reducibility of intuitionistial fuzzy G-modules, Annals of Fuzzy Mathematic and Informatics, 11 (6), 885-898, (2016)
p.K.Sharma, Semi-Simple Intuitionistic Fuzzy G-Modules, International Journal of pure and Applied Researches, 1(2), 101-108, (2016).
p.K. Sharma, Isomorphism Theorems for Intuitionistic Fuzzy Submodules of G-Modules, Notes on Intuitionistic Fuzzy Sets, 22(3),(2016).
p.K.Sharma and Simpi chopra, Injectivily of intuitionistic fuzzy G-modules, Annals of fuzzy Mathematics and Informatics (accepted).
p.k. Sharma and Simip chopra, projectivity of intuitionistic fuzzy G-modules, (Communicated).
M.kilp, U. Knanuer and A.V.Kikhalev monoids acts and categories with application to wreath products and graphs, Walter de Gruyter-Berlin New York, (2000).
J.Ahsan and M.Shabir, fuzzy divisible Semi groups, Annals of fuzzy Mathemeties and Informatics, Vol. 10, 193-202, (2015).
A.s. Abdul Kareem and eta fuzzy injective S-act over monoids, TWMS Journal of applied and engineering mathematics, 11 (4),1072-1079, (2021).
A.M. Lopez, Jr. and J.K. Lueed man, Quasi injective S-System and their S-endomorphism semigroup, Czechoslovak Mathematical Journal, Vol. 29, No.L, 97-104, (1979).
T.F. Abdul Lateef and A-S-Abdul Kareem, Some general Zations of fuzzy quasi injective S-act, MSc. Thesis, (2021).
L. Zhong Kui and J. Ahsan .on relative quasi-projective acts over monoids. Arabian Journal for science and Engineering 35(2D), 225-233, (2010).
A.S.J.Sabah, Intuitionistic fuzzy injective and intuitionistic fuzzy quasi injective s-act, about (to appear), (2023).
H. Liu, Morita theory for the category of fuzzy S-acts. IAENG International Journal of computer Science, 42(1), 54-58, (2015)
M.Shabir M.S. Arif-characterizations of Monoids By the properties of their intuitionistic fuzzy Subact New Mathematics and Natural computation, 6(01),31-48, (2010).
T.Abraham.on studies on fuzzy Representation of fuzzy Groups (PhD Thesis). Mahatma Gandhi University, Faculty of Science (2007).
K.T. Atanassor. Intuitionistic fuzzy sets. Fuzzy sets and System, 20(1), 87-96, Retrieved from https://www Science direct.com /science article/pii/So165011486800343.
Downloads
Published
Issue
Section
License
Copyright (c) 2025 CC BY 4.0
This work is licensed under a Creative Commons Attribution 4.0 International License.
