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Year 2016, Volume: 4 Issue: 2, 72 - 89, 01.03.2016

Asim Hussain Muhammad Shabir

Abstract

References

  • J. Ahsan, fully Idempotent Semirings, Proc. Japan Acad. 69, Ser. A (1993)185-188
  • J. Ahsan, Semirings Characterized by Their Fuzzy Ideals, J. Fuzzy Math. 6 (1998), 181-192.
  • J. Ahsan, K. Saifullah, M. F. Khan, Fuzzy semirings, Fuzzy Sets and Systems 60 (1993) 309-320
  • K. Atanassov; Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986) 87-96.
  • S.K. Bhakat, P. Das, (22 _q)-fuzzy subgroups, Fuzzy Sets and Systems 80 (1996) 359-368. D. Coker, M. Demirci, On intuitionistic fuzzy points, Notes IFS 1 (2) (1995) 79-84.
  • W.A. Dudek, Special types of intuitionistic fuzzy left h-ideals of hemirings, Soft Comput. 12 (2008) 359-364.
  • W.A. Dudek, M. Shabir, I. Ali, (ab )-fuzzy ideals of hemirings, Comput. Math. Appl. 58 (2) (2009) 310-321.
  • J. S. Golan, Semirings and their Applications, Kluwer Acad. Publ. , 1999
  • U. Hebisch, H.J. Weinert, Semirings: Algebraic Theory and Applications in the Computer Science, World Scientific, 1998.
  • A. Hussain, M. Shabir, Soft Finite State Machine, Journal of Intelligent and Fuzzy System, 2015, ( Accepted).
  • A. Hussain, M. Shabir, Cubic Finite State Machine, Annals of Fuzzy Mathematics and Informatics, 2015, ( Accepted).
  • Y.B. Jun, Generalization of (22 _q)-fuzzy subalgebras in BCK/BCI-algebras, Comput. Math. Appl. 58 (2009) 1383-1390.
  • Y.B. Jun, On (ϕ y)-intuitionistic fuzzy fubgroups, KYUNGPOOK Math. J. 45 (2005) 87-94.
  • Y.B. Jun, W.A. Dudek, M. Shabir, Generalizations of (ab )-fuzzy ideals of hemirings.
  • A. Khan, M. Shabir, (ab )-fuzzy interior ideals in ordered semigroups, Lobachevskii J. Math. 30 (2009) 30-39.
  • A. Khan, Y.B Jun, N.H. Sarmin, F.M. Khan, Ordered semigroups characterized by(22 _qk)-fuzzy generalized bi-ideals, Neural Comput & Applic (2011).
  • V.N. Mishra, Some Problems on Approximations of Functions in Banach Spaces, Ph.D. Thesis (2007), Indian Institute of Technology, Roorkee - 247 667, Uttarakhand, India.
  • J.N. Mordeson, D.S. Malik, Fuzzy Automata and Languages, Theory and Applications, in: Computational Mathematics Series, Chapman and Hall/CRC, Boca Raton, 2002.
  • V. Murali, Fuzzy points of equivalent fuzzy subsets, Information Science 158 (2004) 277-288.
  • P.M. Pu, Y.M. Liu, Fuzzy topology I, neighborhood 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.
  • M. Shabir, Y.B. Jun, Y. Nawaz, Characterizations of regular semigroups by (ab )-fuzzy ideals, Comput. Math. Appl. 59 (2010) 161-175.
  • M. Shabir, Y.B. Jun, Y. Nawaz, Semigroups characterized by (2 2 _qk)-fuzzy ideals, Comput. Math. Appl. 60 (2010) 1473-1493.
  • H.S. Vandiver, Note on a simple type of algebra in which cancellation law of addition does not hold, Bull. Amer. Math. Soc. 40 (1934) 914-920.
  • L. A. Zadeh, Fuzzy sets, Inform. Control 8 (1965) 338-353.

Generalized intuitionistic fuzzy ideals of hemirings

Year 2016, Volume: 4 Issue: 2, 72 - 89, 01.03.2016

Asim Hussain Muhammad Shabir

Abstract

In this paper we generalize the concept of quasi-coincident of an intuitionistic fuzzy point with an intuitionistic fuzzy set and define (2; 2 _qk)-intuitionistic fuzzy ideals of hemirings and characterize different classes of hemirings by the properties of these ideals.


Keywords

Intuitionistic fuzzy sub-hemiring intuitionistic fuzzy ideal fully idemotent hemiring

References

  • J. Ahsan, fully Idempotent Semirings, Proc. Japan Acad. 69, Ser. A (1993)185-188
  • J. Ahsan, Semirings Characterized by Their Fuzzy Ideals, J. Fuzzy Math. 6 (1998), 181-192.
  • J. Ahsan, K. Saifullah, M. F. Khan, Fuzzy semirings, Fuzzy Sets and Systems 60 (1993) 309-320
  • K. Atanassov; Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986) 87-96.
  • S.K. Bhakat, P. Das, (22 _q)-fuzzy subgroups, Fuzzy Sets and Systems 80 (1996) 359-368. D. Coker, M. Demirci, On intuitionistic fuzzy points, Notes IFS 1 (2) (1995) 79-84.
  • W.A. Dudek, Special types of intuitionistic fuzzy left h-ideals of hemirings, Soft Comput. 12 (2008) 359-364.
  • W.A. Dudek, M. Shabir, I. Ali, (ab )-fuzzy ideals of hemirings, Comput. Math. Appl. 58 (2) (2009) 310-321.
  • J. S. Golan, Semirings and their Applications, Kluwer Acad. Publ. , 1999
  • U. Hebisch, H.J. Weinert, Semirings: Algebraic Theory and Applications in the Computer Science, World Scientific, 1998.
  • A. Hussain, M. Shabir, Soft Finite State Machine, Journal of Intelligent and Fuzzy System, 2015, ( Accepted).
  • A. Hussain, M. Shabir, Cubic Finite State Machine, Annals of Fuzzy Mathematics and Informatics, 2015, ( Accepted).
  • Y.B. Jun, Generalization of (22 _q)-fuzzy subalgebras in BCK/BCI-algebras, Comput. Math. Appl. 58 (2009) 1383-1390.
  • Y.B. Jun, On (ϕ y)-intuitionistic fuzzy fubgroups, KYUNGPOOK Math. J. 45 (2005) 87-94.
  • Y.B. Jun, W.A. Dudek, M. Shabir, Generalizations of (ab )-fuzzy ideals of hemirings.
  • A. Khan, M. Shabir, (ab )-fuzzy interior ideals in ordered semigroups, Lobachevskii J. Math. 30 (2009) 30-39.
  • A. Khan, Y.B Jun, N.H. Sarmin, F.M. Khan, Ordered semigroups characterized by(22 _qk)-fuzzy generalized bi-ideals, Neural Comput & Applic (2011).
  • V.N. Mishra, Some Problems on Approximations of Functions in Banach Spaces, Ph.D. Thesis (2007), Indian Institute of Technology, Roorkee - 247 667, Uttarakhand, India.
  • J.N. Mordeson, D.S. Malik, Fuzzy Automata and Languages, Theory and Applications, in: Computational Mathematics Series, Chapman and Hall/CRC, Boca Raton, 2002.
  • V. Murali, Fuzzy points of equivalent fuzzy subsets, Information Science 158 (2004) 277-288.
  • P.M. Pu, Y.M. Liu, Fuzzy topology I, neighborhood 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.
  • M. Shabir, Y.B. Jun, Y. Nawaz, Characterizations of regular semigroups by (ab )-fuzzy ideals, Comput. Math. Appl. 59 (2010) 161-175.
  • M. Shabir, Y.B. Jun, Y. Nawaz, Semigroups characterized by (2 2 _qk)-fuzzy ideals, Comput. Math. Appl. 60 (2010) 1473-1493.
  • H.S. Vandiver, Note on a simple type of algebra in which cancellation law of addition does not hold, Bull. Amer. Math. Soc. 40 (1934) 914-920.
  • L. A. Zadeh, Fuzzy sets, Inform. Control 8 (1965) 338-353.
There are 25 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Asim Hussain This is me

Muhammad Shabir This is me

Publication Date March 1, 2016
Published in Issue Year 2016 Volume: 4 Issue: 2

Cite

APA Hussain, A., & Shabir, M. (2016). Generalized intuitionistic fuzzy ideals of hemirings. New Trends in Mathematical Sciences, 4(2), 72-89.
AMA Hussain A, Shabir M. Generalized intuitionistic fuzzy ideals of hemirings. New Trends in Mathematical Sciences. March 2016;4(2):72-89.
Chicago Hussain, Asim, and Muhammad Shabir. “Generalized Intuitionistic Fuzzy Ideals of Hemirings”. New Trends in Mathematical Sciences 4, no. 2 (March 2016): 72-89.
EndNote Hussain A, Shabir M (March 1, 2016) Generalized intuitionistic fuzzy ideals of hemirings. New Trends in Mathematical Sciences 4 2 72–89.
IEEE A. Hussain and M. Shabir, “Generalized intuitionistic fuzzy ideals of hemirings”, New Trends in Mathematical Sciences, vol. 4, no. 2, pp. 72–89, 2016.
ISNAD Hussain, Asim - Shabir, Muhammad. “Generalized Intuitionistic Fuzzy Ideals of Hemirings”. New Trends in Mathematical Sciences 4/2 (March 2016), 72-89.
JAMA Hussain A, Shabir M. Generalized intuitionistic fuzzy ideals of hemirings. New Trends in Mathematical Sciences. 2016;4:72–89.
MLA Hussain, Asim and Muhammad Shabir. “Generalized Intuitionistic Fuzzy Ideals of Hemirings”. New Trends in Mathematical Sciences, vol. 4, no. 2, 2016, pp. 72-89.
Vancouver Hussain A, Shabir M. Generalized intuitionistic fuzzy ideals of hemirings. New Trends in Mathematical Sciences. 2016;4(2):72-89.
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