BibTex RIS Kaynak Göster

A New Type of Interval Valued Fuzzy Normal Subgroups of Groups

Yıl 2015, Cilt: 3 Sayı: 3, 62 - 77, 26.06.2015

Öz

In this paper we are using the notions of not belonging (∈) and non quasi-k-coincidenceqk ( ) of an interval valued fuzzypoint with an interval valued fuzzy set, we define the concepts of interval valued (∈,∈ ∨ qk)-fuzzy normal subgroups and interval valued(∈,∈ ∨ qk)-fuzzy cosets which is a generalization of fuzzy normal subgroups, fuzzy coset, interval valued fuzzy normal subgroups,interval valued fuzzy coset, interval valued (∈,∈ ∨ q)-fuzzy normal subgroups and interval valued (∈,∈ ∨ q)-fuzzy cosets. We givesome characterizations of an interval valued (∈,∈ ∨ qk)-fuzzy normal subgroup and interval valued (∈,∈ ∨ qk)-fuzzy coset, and dealwith several related properties. The important achievement of the study with an interval valued (∈,∈ ∨ qk)-fuzzy normal subgroupand interval valued (∈,∈ ∨ qk)-fuzzy cosets is the generalization of that the notions of fuzzy normal subgroups, fuzzy coset, intervalvalued fuzzy normal subgroups, interval valued fuzzy coset, interval valued (∈,∈ ∨ q)-fuzzy normal subgroups and interval valued(∈,∈ ∨ q)-fuzzy cosets. We prove that the set of all interval valued (∈,∈ ∨ qk)-fuzzy cosets of G is a group, where the multiplicationis defined byλx·λy=λxyfor all x, y∈ G. Ifµ : F → D[0,1] is defined by µ←−←−(←−)λx =λ (x) for all x ∈ G. Then µ is an interval valued( )-fuzzy normal subgroup of F

Kaynakça

  • S. Abdullah, A new type of interval valued fuzzy subgroups of groups, Submitted. S. Abdullah, M.Aslam, T. Ahmad and M. Naeem, A new typ fuzzy normal subgroups and fuzzy cosets, Journal of Intelligent and Fuzzy Systems, 2012, 10.3233/IFS-2012-0612.
  • M. Aslam, S. Abdullah and N. Amin, Characterizations of gamma LA-semigroups by generalized fuzzy gamma ideals, International J. of Mathematics and Statistics, 12 (2012): 29-50.
  • M. Akram, K.H. Dar, , K.P. Shum, Interval-valued (α,β)-fuzzy K-algebras, Applied Soft Computing, 11, 1, (2011), 1213-1222.
  • S. K. Bhakat, (∈,∈ ∨q)-Level subset, Fuzzy Sets and System 103 (1999) 529-533.
  • S. K. Bhakat, (∈,∈ ∨q)-fuzzy normal, quasinormal and maximal subgroups, Fuzzy Sets and System 112 (2000) 299-312.
  • S. K. Bhakat, P. Das, (∈,∈ ∨q)-fuzzy subgroup, Fuzzy Sets and System 80 (1996) 359-368.
  • S. K. Bhakat, P. Das, On the definition of a fuzzy subgroup, Fuzzy Sets and System 51 (1992) 235-241.
  • R. Biswas, Rosenfeld’s fuzzy subgroups with interval-valued membership functions, Fuzzy Sets and Systems, 63, 1, (1994), 87-90.
  • P. S. Das, Fuzzy groups and level subgroups, J. Math. Anal. Appl. 85 (1981) 264-269.
  • B. Davvaz, Interval-valued fuzzy subhypergroups, Korean Journal of Computational and Applied Mathematics, 6, 1, (1999), 197- 20
  • Y. B. Jun, Generalizations of (∈,∈ ∨q)-fuzzy subalgebras in BCK/BCI-algebras, Comput. Math. Appl. , 58 (2009): 1383 1390
  • Y. B. Jun, M. S. Kang, and C. H. Park, Fuzzy subgroups based on fuzzy points, Commun. Korean Math. Soc. 26 (2011), No. 3, pp. 349-3
  • K.B. Latha, D.R. P. Williams and E.Chandrasekar, Interval valued (α,β)-fuzzy subgroups, Mamthematica, Tome 52, (75), 2, (2010), 177-184
  • W.-J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems 8 (1982), no. 2, 133–139.
  • Mukherjee and P. Bhattacharya, Fuzzy normal subgroups and fuzzy cosets, Inform. Sci. 34 (1984), no. 3, 225–239.
  • V. Murali, Fuzzy points of equivalent fuzzy subsets, Inform. Sci. 158 (2004) 277-288.
  • P. M. Pu, Y.M. Liu, Fuzzy topology I, neighbourhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl. 76 (1980) 571-599.
  • A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35 (1971) 512-517.
  • J. S. Rose, A Course on Group Theory, Cambridge University Press, 1978.
  • M. Shabir, Y.B. Jun, Y. Nawaz, Characterizations of regular semigroups by (α,β)-fuzzy ideals, Comput. Math. Appl. , 59 (2010) 161-1
  • M. Shabir, Y.B. Jun and Y. Nawaz, Semigroups characterized by (∈,∈ ∨q)-fuzzy ideals, Comput. Math. Appl. , 60 (2010) 1473- 14
  • X. Yuan, C. Zhang, and Y. Ren, Generalized fuzzy groups and many-valued implications, Fuzzy Sets and Systems 138 (2003), no. 1, 205–211.
  • L.A. Zadeh, Fuzzy sets, Inform. and Control 8 (1965) 338-353.
  • L.A.Zadeh, The concept of a linguistic variable and its application to approximate reasoning-I, Information Sciences, 8, (1975), 199-2
  • J. Zhan, B. Davvaz and K.P. Shum, A new view of fuzzy hypernear-rings, Information Sciences, 178, (2008), 425-438.
  • J. Zhan, B. Davvaz and K.P. Shum, A new view of fuzzy hyperquasigroups, Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology, 20(4, 5), 147-157.

A new type of interval valued fuzzy normal subgroups of groups

Yıl 2015, Cilt: 3 Sayı: 3, 62 - 77, 26.06.2015

Öz

Kaynakça

  • S. Abdullah, A new type of interval valued fuzzy subgroups of groups, Submitted. S. Abdullah, M.Aslam, T. Ahmad and M. Naeem, A new typ fuzzy normal subgroups and fuzzy cosets, Journal of Intelligent and Fuzzy Systems, 2012, 10.3233/IFS-2012-0612.
  • M. Aslam, S. Abdullah and N. Amin, Characterizations of gamma LA-semigroups by generalized fuzzy gamma ideals, International J. of Mathematics and Statistics, 12 (2012): 29-50.
  • M. Akram, K.H. Dar, , K.P. Shum, Interval-valued (α,β)-fuzzy K-algebras, Applied Soft Computing, 11, 1, (2011), 1213-1222.
  • S. K. Bhakat, (∈,∈ ∨q)-Level subset, Fuzzy Sets and System 103 (1999) 529-533.
  • S. K. Bhakat, (∈,∈ ∨q)-fuzzy normal, quasinormal and maximal subgroups, Fuzzy Sets and System 112 (2000) 299-312.
  • S. K. Bhakat, P. Das, (∈,∈ ∨q)-fuzzy subgroup, Fuzzy Sets and System 80 (1996) 359-368.
  • S. K. Bhakat, P. Das, On the definition of a fuzzy subgroup, Fuzzy Sets and System 51 (1992) 235-241.
  • R. Biswas, Rosenfeld’s fuzzy subgroups with interval-valued membership functions, Fuzzy Sets and Systems, 63, 1, (1994), 87-90.
  • P. S. Das, Fuzzy groups and level subgroups, J. Math. Anal. Appl. 85 (1981) 264-269.
  • B. Davvaz, Interval-valued fuzzy subhypergroups, Korean Journal of Computational and Applied Mathematics, 6, 1, (1999), 197- 20
  • Y. B. Jun, Generalizations of (∈,∈ ∨q)-fuzzy subalgebras in BCK/BCI-algebras, Comput. Math. Appl. , 58 (2009): 1383 1390
  • Y. B. Jun, M. S. Kang, and C. H. Park, Fuzzy subgroups based on fuzzy points, Commun. Korean Math. Soc. 26 (2011), No. 3, pp. 349-3
  • K.B. Latha, D.R. P. Williams and E.Chandrasekar, Interval valued (α,β)-fuzzy subgroups, Mamthematica, Tome 52, (75), 2, (2010), 177-184
  • W.-J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy Sets and Systems 8 (1982), no. 2, 133–139.
  • Mukherjee and P. Bhattacharya, Fuzzy normal subgroups and fuzzy cosets, Inform. Sci. 34 (1984), no. 3, 225–239.
  • V. Murali, Fuzzy points of equivalent fuzzy subsets, Inform. Sci. 158 (2004) 277-288.
  • P. M. Pu, Y.M. Liu, Fuzzy topology I, neighbourhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl. 76 (1980) 571-599.
  • A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35 (1971) 512-517.
  • J. S. Rose, A Course on Group Theory, Cambridge University Press, 1978.
  • M. Shabir, Y.B. Jun, Y. Nawaz, Characterizations of regular semigroups by (α,β)-fuzzy ideals, Comput. Math. Appl. , 59 (2010) 161-1
  • M. Shabir, Y.B. Jun and Y. Nawaz, Semigroups characterized by (∈,∈ ∨q)-fuzzy ideals, Comput. Math. Appl. , 60 (2010) 1473- 14
  • X. Yuan, C. Zhang, and Y. Ren, Generalized fuzzy groups and many-valued implications, Fuzzy Sets and Systems 138 (2003), no. 1, 205–211.
  • L.A. Zadeh, Fuzzy sets, Inform. and Control 8 (1965) 338-353.
  • L.A.Zadeh, The concept of a linguistic variable and its application to approximate reasoning-I, Information Sciences, 8, (1975), 199-2
  • J. Zhan, B. Davvaz and K.P. Shum, A new view of fuzzy hypernear-rings, Information Sciences, 178, (2008), 425-438.
  • J. Zhan, B. Davvaz and K.P. Shum, A new view of fuzzy hyperquasigroups, Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology, 20(4, 5), 147-157.
Toplam 26 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Bölüm Articles
Yazarlar

Saleem Abdullah Bu kişi benim

Muhammad Naeem Bu kişi benim

Yayımlanma Tarihi 26 Haziran 2015
Yayımlandığı Sayı Yıl 2015 Cilt: 3 Sayı: 3

Kaynak Göster

APA Abdullah, S., & Naeem, M. (2015). A New Type of Interval Valued Fuzzy Normal Subgroups of Groups. New Trends in Mathematical Sciences, 3(3), 62-77.
AMA Abdullah S, Naeem M. A New Type of Interval Valued Fuzzy Normal Subgroups of Groups. New Trends in Mathematical Sciences. Haziran 2015;3(3):62-77.
Chicago Abdullah, Saleem, ve Muhammad Naeem. “A New Type of Interval Valued Fuzzy Normal Subgroups of Groups”. New Trends in Mathematical Sciences 3, sy. 3 (Haziran 2015): 62-77.
EndNote Abdullah S, Naeem M (01 Haziran 2015) A New Type of Interval Valued Fuzzy Normal Subgroups of Groups. New Trends in Mathematical Sciences 3 3 62–77.
IEEE S. Abdullah ve M. Naeem, “A New Type of Interval Valued Fuzzy Normal Subgroups of Groups”, New Trends in Mathematical Sciences, c. 3, sy. 3, ss. 62–77, 2015.
ISNAD Abdullah, Saleem - Naeem, Muhammad. “A New Type of Interval Valued Fuzzy Normal Subgroups of Groups”. New Trends in Mathematical Sciences 3/3 (Haziran 2015), 62-77.
JAMA Abdullah S, Naeem M. A New Type of Interval Valued Fuzzy Normal Subgroups of Groups. New Trends in Mathematical Sciences. 2015;3:62–77.
MLA Abdullah, Saleem ve Muhammad Naeem. “A New Type of Interval Valued Fuzzy Normal Subgroups of Groups”. New Trends in Mathematical Sciences, c. 3, sy. 3, 2015, ss. 62-77.
Vancouver Abdullah S, Naeem M. A New Type of Interval Valued Fuzzy Normal Subgroups of Groups. New Trends in Mathematical Sciences. 2015;3(3):62-77.