New submissions to International Journal "Notes on Intuitionistic Fuzzy Sets" are temporarily suspended from 1 June until 1 September 2026.
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Issue:Intuitionistic fuzzy G-modules: Difference between revisions

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| issue          = [[Notes on Intuitionistic Fuzzy Sets/21/1|"Notes on Intuitionistic Fuzzy Sets", Volume 21, 2015, Number 1]], pages 6—23
| issue          = [[Notes on Intuitionistic Fuzzy Sets/21/1|"Notes on Intuitionistic Fuzzy Sets", Volume 21, 2015, Number 1]], pages 6—23
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# Atanassov, K. T. (1986) Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1), 87–96.
# Atanassov, K. T. (1986) Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1), 87–96.
# Atanassov, K. T. (1994) New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems, 61(2), 1994, 137–142.
# Atanassov, K. T. (1994) New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems, 61(2), 1994, 137–142.
# Atanassov, K. T. (1999) Intuitionistic Fuzzy Sets: Theory and Applications, Studies on Fuzziness and Soft Computing, 35, Physica-Verlag, Heidelberg.
# Atanassov, K. T. (1999) [[Intuitionistic Fuzzy Sets: Theory and Applications]], Studies on Fuzziness and Soft Computing, 35, Physica-Verlag, Heidelberg.
# Biswas, R. (1989) Intuitionistic fuzzy subgroups, Mathematical Forum, 10, 37–46.
# Biswas, R. (1989) Intuitionistic fuzzy subgroups, Mathematical Forum, 10, 37–46.
# Curties, C.W. & Reiner, I. (1962) Representation Theory of Finite Groups and Associated Algebras, INC.
# Curties, C.W. & Reiner, I. (1962) Representation Theory of Finite Groups and Associated Algebras, INC.
Line 40: Line 38:
# Fernadez, S. (2002) Fuzzy G-modules and fuzzy representations, TAJOPAM, 1, 107–114.
# Fernadez, S. (2002) Fuzzy G-modules and fuzzy representations, TAJOPAM, 1, 107–114.
# Isaac, P., & John, P. P. (2011) On Intuitionistic Fuzzy Submodules of a Module, Int. J. of Mathematical Sciences and Applications, 1(3), 1447–1454.
# Isaac, P., & John, P. P. (2011) On Intuitionistic Fuzzy Submodules of a Module, Int. J. of Mathematical Sciences and Applications, 1(3), 1447–1454.
# Jose, S., & Kuriakose, S. (2012) Decomposition theorems of an intuitionistic fuzzy set, Notes on intuitionistic Fuzzy Sets, 18(2), 31–36.
# Jose, S., & Kuriakose, S. (2012) [[Issue:Decomposition theorems of an intuitionistic fuzzy set|Decomposition theorems of an intuitionistic fuzzy set]], Notes on intuitionistic Fuzzy Sets, 18(2), 31–36.
# Naegoita, C.V., & Ralescu, D.A. (1975) Application of Fuzzy Sets in System Analysis, Birkhauser, Basel.
# Naegoita, C.V., & Ralescu, D.A. (1975) Application of Fuzzy Sets in System Analysis, Birkhauser, Basel.
# Rahman, S., & Saikia, H.K. (2012) Some aspects of Atanassov’s intuitionistic fuzzy submodules, Int. J. Pure and Appl. Mathematics, 77(3), 369–383.
# Rahman, S., & Saikia, H.K. (2012) Some aspects of Atanassov’s intuitionistic fuzzy submodules, Int. J. Pure and Appl. Mathematics, 77(3), 369–383.

Latest revision as of 12:32, 20 May 2026

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http://ifigenia.org/wiki/issue:nifs/21/1/6-23
Title of paper: Intuitionistic fuzzy G-modules
Author(s):
P. K. Sharma
Post Graduate Department of Mathematics, D. A. V. College, Jalandhar, Punjab, India
pksharma@davjalandhar.com
Tarandeep Kaur
Post Graduate Department of Mathematics, D. A. V. College, Jalandhar, Punjab, India
tarandeepkaur41@yahoo.com
Published in: "Notes on Intuitionistic Fuzzy Sets", Volume 21, 2015, Number 1, pages 6—23
Download:  PDF (208  Kb, File info)
Abstract: In this paper, the notion of intuitionistic fuzzy G-modules on a G-module M over a field K is introduced. The quotient intuitionistic fuzzy G-modules are defined and discussed. A homomorphism of G-module M onto M* is established. Also we introduced (weak) intuitionistic fuzzy G-homomorphism (isomorphism). Intersection, Sum, Product and Cartesian product of two intuitionistic fuzzy G-modules are also discussed.
Keywords: Intuitionistic fuzzy set, Intuitionistic fuzzy G-module, (α, β)–cut set, Support, Quotient intuitionistic fuzzy G-module.
AMS Classification: 03F55, 08A72, 16D10
References:
  1. Abraham, T. & Sebastian, S. (2010) On fuzzy representation of fuzzy G-modules, J. Comp. & Math. Sci., 1(5), 592-597.
  2. Atanassov, K. T. (1986) Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20(1), 87–96.
  3. Atanassov, K. T. (1994) New operations defined over the intuitionistic fuzzy sets, Fuzzy Sets and Systems, 61(2), 1994, 137–142.
  4. Atanassov, K. T. (1999) Intuitionistic Fuzzy Sets: Theory and Applications, Studies on Fuzziness and Soft Computing, 35, Physica-Verlag, Heidelberg.
  5. Biswas, R. (1989) Intuitionistic fuzzy subgroups, Mathematical Forum, 10, 37–46.
  6. Curties, C.W. & Reiner, I. (1962) Representation Theory of Finite Groups and Associated Algebras, INC.
  7. Davvaz, B., Dudek, W.A., & Jun, Y.B. (2006) Intuitionistic fuzzy Hv-submodules, Information Sciences, 176, 285–300.
  8. Fernadez, S. (2002) Fuzzy G-modules and fuzzy representations, TAJOPAM, 1, 107–114.
  9. Isaac, P., & John, P. P. (2011) On Intuitionistic Fuzzy Submodules of a Module, Int. J. of Mathematical Sciences and Applications, 1(3), 1447–1454.
  10. Jose, S., & Kuriakose, S. (2012) Decomposition theorems of an intuitionistic fuzzy set, Notes on intuitionistic Fuzzy Sets, 18(2), 31–36.
  11. Naegoita, C.V., & Ralescu, D.A. (1975) Application of Fuzzy Sets in System Analysis, Birkhauser, Basel.
  12. Rahman, S., & Saikia, H.K. (2012) Some aspects of Atanassov’s intuitionistic fuzzy submodules, Int. J. Pure and Appl. Mathematics, 77(3), 369–383.
  13. Sharma, P. K. (2013) (α, β)-Cut of intuitionistic fuzzy modules, Int. J. of Mathematical Sciences and Applications, 3(1), 11–17.
  14. Sharma, P. K. (2011) (α, β)-Cut of Intuitionistic fuzzy modules - II, Int. J. of Mathematical Sciences and Applications, 1(3), 1489–1492.
  15. Sharma, P. K. On intuitionistic fuzzy Abelian subgroups- II, Advances in Fuzzy Sets and Systems (communicated)
  16. Sharma, P. K., & Kaur, T. On intuitionistic fuzzy representation of intuitionistic fuzzy Gmodules, (under preparation)
  17. Zadeh, L. A. (1965) Fuzzy Sets, Inform. control., 8, 338–353.
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