Direct Sum of Intuitionistic Fuzzy Submodules of G-module
Keywords:Intuitionistic fuzzy submodules, G-modules, direct sum
AbstractIn this paper, we introduce the notion of direct sum ofintuitionistic fuzzy submodules of G-module M and discuss some relatedproperties. If B and C are intuitionistic fuzzy submodules of G-module Mand G-module N respectively, then we extend the denition of intuitionisticfuzzy submodules B and C to formulate intuitionistic fuzzy submodules ofthe direct sum M N: It is proved that the support of the direct sumof intuitionistic fuzzy submodules B and C is equal to the direct sumof supports of intuitionistic fuzzy submodules B and C: Also we analyzethe direct sum of arbitrary family of intuitionistic fuzzy submodules andobtained some results. We also introduce the notion of decomposability andindecomposility of intuitionistic fuzzy G-modules and prove some results.
K.T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1) (1986), 87-96.
K.T. Atanassov, New operation dened over the intuitionistic fuzzy sets, Fuzzy Sets and
Systems, 61 (1994), 137-142.
K.T. Atanassov, Intuitionistic Fuzzy Sets Theory and Applications, Studies on Fuzziness and
Soft Computing, 35, Physica-Verlag, Heidelberg (1999).
D.K. Basnet, Topics in intuitionistic fuzzy algebra, Lambert Academic Publishing, 2011,
R. Biswas, Intuitionistic fuzzy subgroup, Mathematical Forum X (1989), 37-46.
C.W. Curties and I. Reiner, Representation Theory of nite groups and associated algebras,
B. Davvaz, W.A. Dudek, Y.B. Jun, Intuitionistic fuzzy Hv-submodules, Information Sciences,
S. Fernadez, A study of fuzzy G-modules, Ph.D Thesis, St. Albert's College, Rev. Dr.
Konnully Memorial Research Centre and P.G. Department of Mathematics, 2004.
Paul Isaac, Pearly P. John, On Intuitionistic Fuzzy Submodules of a Module, Int. J. of Math-
ematical Sciences and Applications, 1(3) (2011), 1447-1454.
C.V. Negoita, D.A. Ralescu, Applications of Fuzzy sets and systems Analysis, Birkhauser,
A. Rosenfeld, Fuzzy group, J. Math. Anal. and Appl., 35(1971), 512-517.
S. Rahman, H.K. Saikia, Some aspects of Atanassov
s intuitionistic fuzzy submodules, Int. J.
Pure and Appl. Mathematics, 77(3) (2012), 369-383.
P.K. Sharma, (,)-Cut of intuitionistic fuzzy modules-II, Int. J. of Mathematical Sciences
and Applications 3(1) (2013), 11-17.
P.K.Sharma and Gagandeep Kaur, Intuitionistic fuzzy super
uous submodule, Notes of Intu-
itionistic Fuzzy Sets, 22(4)(2016) (to appear)
P.K. Sharma and Tarandeep Kaur, Intuitionistic fuzzy G-modules, Notes on Intuitionistic
Fuzzy Sets, 21(1) (2015), 6-23.
P.K. Sharma and Tarandeep Kaur, On intuitionistic fuzzy representation of intuitionistic fuzzy
G-modules, Annals of Fuzzy Mathematics and Informatics, 11(4) (2016), 557-569.
P.K.Sharma, Reducibility and Complete Reducibility of intuitionistic fuzzy G-modules, Annals
of Fuzzy Mathematics and Informatics, 11(6) (2016), 885-898.
P.K Sharma, Semi-simple Intuitionistic Fuzzy G- Modules, International Journal of Pure and
Applied Researches, 1(2) 2016, 101- 108.
P.K.Sharma, Isomorphism Theorems for Intuitionistic Fuzzy Submodules of G-Modules, Notes
on Intuitionistic Fuzzy Sets, 22(3) (2016) (to appear)
P.K. Sharma and Simpi Chopra, Injectivity of intuitionistic fuzzy G-modules, Annals of Fuzzy
Mathematics and Informatics (accepted)
P.K. Sharma and Simpi Chopra, projectivity of intuitionistic fuzzy G-modules, (communi-
P.K.Sharma, Exact sequence of intuitionistic fuzzy G-modules, (Under preparation).
L.A. Zadeh, Fuzzy Sets, Inform. Control, 8 (1965) 338-353.
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