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

R. Nagarajan; K. Balamurugan

doi:doi:10.11648/j.acm.20140306.13

| Peer-Reviewed

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

R. Nagarajan, K. Balamurugan

Published in Applied and Computational Mathematics (Volume 3, Issue 6)

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

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

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.

Published in	Applied and Computational Mathematics (Volume 3, Issue 6)
DOI	10.11648/j.acm.20140306.13
Page(s)	303-306
Creative Commons	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), 2014. 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.

Cite This Article

Plain Text BibTeX RIS

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

Copy | Download

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

Copy | Download

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

Copy | Download

@article{10.11648/j.acm.20140306.13,
  author = {R. Nagarajan and K. Balamurugan},
  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},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140306.13},
  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}
}

Copy | Download

TY  - JOUR
T1  - (α, β)- Infimum and Supremum of Q- Fuzzy Subgroups over Implication Operator of M* ([0,1])
AU  - R. Nagarajan
AU  - K. Balamurugan
Y1  - 2014/12/23
PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140306.13
DO  - 10.11648/j.acm.20140306.13
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 303
EP  - 306
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140306.13
AB  - 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.
VL  - 3
IS  - 6
ER  -

Copy | Download

Author Information

R. Nagarajan

Department of Mathematics, J. J College of Engineering &Technology, Tiruchirappalli-09, India
K. Balamurugan

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

Download PDF

Submit an Article

Sections

Plain Text BibTeX RIS

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

Copy | Download

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

Copy | Download

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

Copy | Download

@article{10.11648/j.acm.20140306.13,
  author = {R. Nagarajan and K. Balamurugan},
  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},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20140306.13},
  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}
}

Copy | Download

TY  - JOUR
T1  - (α, β)- Infimum and Supremum of Q- Fuzzy Subgroups over Implication Operator of M* ([0,1])
AU  - R. Nagarajan
AU  - K. Balamurugan
Y1  - 2014/12/23
PY  - 2014
N1  - https://doi.org/10.11648/j.acm.20140306.13
DO  - 10.11648/j.acm.20140306.13
T2  - Applied and Computational Mathematics
JF  - Applied and Computational Mathematics
JO  - Applied and Computational Mathematics
SP  - 303
EP  - 306
PB  - Science Publishing Group
SN  - 2328-5613
UR  - https://doi.org/10.11648/j.acm.20140306.13
AB  - 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.
VL  - 3
IS  - 6
ER  -

Copy | Download