Applied and Computational Mathematics

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(α, β)- Infimum and Supremum of Q- Fuzzy Subgroups over Implication Operator of M* ([0,1])

Received: 25 August 2014    Accepted: 18 December 2014    Published: 23 December 2014
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Abstract

In this paper, the concept of (α,β)- inf-sup Q-fuzzy set is generalized and there after we defined (α,β)- inf-sup Q-fuzzy group and a few of its properties are discussed. On the other hand we give the definition of the upper normal Q- fuzzy subgroups, and study the main theorem for this. We also give new results on this subject. Characterization of inf-sup normal Q-fuzzy subgroups also investigated.

DOI 10.11648/j.acm.20140306.13
Published in Applied and Computational Mathematics (Volume 3, Issue 6, December 2014)
Page(s) 303-306
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Fuzzy Set, (α,β)- Inf-Sup Q-Fuzzy Group, (α,β)- Inf-Sup Q-Fuzzy Normal Subgroups, Q-Fuzzy Subset, Fuzzy Group

References
[1] J.H.Anthony and H.sherwood,(1979) Fuzzy groups redefined . J.Hath. Anal. Appl .69.124-130.
[2] N.P.Mukherjee and P.Bhattacharya. Fuzzy normal subgroups and fuzzy cosets, Information Sciences, Vol.34, (1984), pp 225-239.
[3] N.P.Mukherjee and P.Bhattacharya Fuzzy groups: Some group theoretic analogs Information Sciences, Vol.39. (1986) pp247-269.
[4] Massadeh.M(2008). Properties of fuzzy subgroups in particular the normal subgroups”. Damacus University - Syrian Arab Republic, Doctorate thesis
[5] V.Murali. and B.B Makamba (2006). ”Counting the number of fuzzy subgroups of on abelian groop of order pnq, Fuzzy sets and systems ,44. 459-470.
[6] V.Murali. and B.B Makamba (2004) Fuzzy subgroups of finite abelian groups Far East journal of Mathematical Science, (EJMC),14.360-371.
[7] N.P.Mukherjee and P.Bhattacharya (1984). Fuzzy normal subgroups and fuzzy Cosets, Information Sciences,34,225-239.
[8] R.Nagarajan & S.V.Manemaran, Constructions of M-fuzzy factor groups, International Journal of Mathematical Archive Vol.4, No.7, (2013) 253-256.
[9] A.Rosenfield. Fuzzy groups J.Math.Anal.Appl.Vol.35(1965), 521-517.
[10] A.Solairaju, P.Saragapany, R.Nagarajan, New Structures on upper flexible Q-fuzzy groups, Applied Mathematical Sciences ,Accepted For Publication,(2013).
[11] A.Solairaju, P.Saragapany, R.Nagarajan ,Max-Norm interval valued subgroups of near rings, International Journal of Mathematics Trends and Technology,Vol.4, No.8, (2013) 136-140.
[12] G.Subbiah & R.Nagarajan, Degrees of Q-fuzzy group over implication Operator [0,1], Elixir Applied Mathematics ,Vol.63(2013) 18350-18352
[13] L.A.Zadeh, Fuzzy Sets, Information and Control ,Vol.8,(1965),338-353.
[14] W.H.Wu,Normal fuzzy subgroups. Fuzzy Math,1,(1981)21-30.
[15] H.J Zimmerman (1997). Fuzzy set theory and its applications, Kluwer Academic publishers London, third edition.
Author Information
  • Department of Mathematics, J. J College of Engineering &Technology, Tiruchirappalli-09, India

  • Department of Mathematics, M. A. M. School of Engineering, Trichirappalli-105, India

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  • APA Style

    R. Nagarajan, K. Balamurugan. (2014). (α, β)- Infimum and Supremum of Q- Fuzzy Subgroups over Implication Operator of M* ([0,1]). Applied and Computational Mathematics, 3(6), 303-306. https://doi.org/10.11648/j.acm.20140306.13

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    ACS Style

    R. Nagarajan; K. Balamurugan. (α, β)- Infimum and Supremum of Q- Fuzzy Subgroups over Implication Operator of M* ([0,1]). Appl. Comput. Math. 2014, 3(6), 303-306. doi: 10.11648/j.acm.20140306.13

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    AMA Style

    R. Nagarajan, K. Balamurugan. (α, β)- Infimum and Supremum of Q- Fuzzy Subgroups over Implication Operator of M* ([0,1]). Appl Comput Math. 2014;3(6):303-306. doi: 10.11648/j.acm.20140306.13

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  • @article{10.11648/j.acm.20140306.13,
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      title = {(α, β)- Infimum and Supremum of Q- Fuzzy Subgroups over Implication Operator of M* ([0,1])},
      journal = {Applied and Computational Mathematics},
      volume = {3},
      number = {6},
      pages = {303-306},
      doi = {10.11648/j.acm.20140306.13},
      url = {https://doi.org/10.11648/j.acm.20140306.13},
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      abstract = {In this paper, the concept of (α,β)- inf-sup Q-fuzzy set is generalized and there after we defined (α,β)- inf-sup Q-fuzzy group and a few of its properties are discussed. On the other hand we give the definition of the upper normal Q- fuzzy subgroups, and study the main theorem for this. We also give new results on this subject. Characterization of inf-sup normal Q-fuzzy subgroups also investigated.},
     year = {2014}
    }
    

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