Direct Sum of Intuitionistic Fuzzy Submodules of G-module

Authors

  • Poonam K. Sharma D.A.V.College, Jalandhar , Punjab, India

Keywords:

Intuitionistic fuzzy submodules, G-modules, direct sum

Abstract

In 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.

Author Biography

Poonam K. Sharma, D.A.V.College, Jalandhar , Punjab, India

Asscoaite Professor in Mathematics

References

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,

ISBN: 978-3-8443-9147-3

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,

INC, (1962).

B. Davvaz, W.A. Dudek, Y.B. Jun, Intuitionistic fuzzy Hv-submodules, Information Sciences,

(2006), 285-300.

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,

Basel, (1975).

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-

cated).

P.K.Sharma, Exact sequence of intuitionistic fuzzy G-modules, (Under preparation).

L.A. Zadeh, Fuzzy Sets, Inform. Control, 8 (1965) 338-353.

Downloads

Published

2016-09-01

How to Cite

Sharma, P. K. (2016). Direct Sum of Intuitionistic Fuzzy Submodules of G-module. Asian Journal of Fuzzy and Applied Mathematics, 4(4). Retrieved from https://www.ajouronline.com/index.php/AJFAM/article/view/4079

Issue

Vol. 4 No. 4 (2016): August 2016

Section

Articles

License

  • Papers must be submitted on the understanding that they have not been published elsewhere (except in the form of an abstract or as part of a published lecture, review, or thesis) and are not currently under consideration by another journal published by any other publisher.
  • It is also the authors responsibility to ensure that the articles emanating from a particular source are submitted with the necessary approval.
  • The authors warrant that the paper is original and that he/she is the author of the paper, except for material that is clearly identified as to its original source, with permission notices from the copyright owners where required.
  • The authors ensure that all the references carefully and they are accurate in the text as well as in the list of references (and vice versa).
  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Attribution-NonCommercial 4.0 International that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
  • The journal/publisher is not responsible for subsequent uses of the work. It is the author's responsibility to bring an infringement action if so desired by the author.