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Journals / New Trends in Mathematical Sciences / 2026 / Cilt: 4 Sayı: 2

Generalized intuitionistic fuzzy ideals of hemirings

Asim Hussain(Quaid-i-Azam University)
Muhammad Shabir(Quaid-i-Azam University)
Pages
72–89
Publication Date
2016-03-01
DOI
—
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AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

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

📌 3 Key Takeaways

🎯
Objective & Hypothesis:In this paper we generalize the concept of quasi-coincident of an intuitionistic fuzzy point with an intuitionistic fuzzy set and define ( 2 ; 2 _ q k )  -intuitionistic fuzzy ideals of hemirings and characterize different classes of hemirings by the properties of these ideals.
📊
Key Findings & Data:In this paper we generalize the concept of quasi-coincident of an intuitionistic fuzzy point with an intuitionistic fuzzy set and define ( 2 ; 2 _ q k )  -intuitionistic fuzzy ideals of hemirings and characterize different classes of hemirings by the properties of these ideals.
💡
Conclusion & Impact:In this paper we generalize the concept of quasi-coincident of an intuitionistic fuzzy point with an intuitionistic fuzzy set and define ( 2 ; 2 _ q k )  -intuitionistic fuzzy ideals of hemirings and characterize different classes of hemirings by the properties of these ideals.
🔬Design:Araştırma Makalesi
📍Scope:Comprehensive Sample
⚙️Variables:Intuitionistic fuzzy sub-hemiring · intuitionistic fuzzy ideal · fully idemotent hemiring

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 _ q k )  -intuitionistic fuzzy ideals of hemirings and characterize different classes of hemirings by the properties of these ideals.

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Cite This Article

Hussain, A., Shabir, M. (2016). Generalized intuitionistic fuzzy ideals of hemirings. New Trends in Mathematical Sciences, Cilt: 4 Sayı: 2, 72–89. https://ajindex.com/articles/1657758

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References (26)

  1. J. Ahsan, fully Idempotent Semirings, Proc. Japan Acad. 69, Ser. A (1993)185-188
  2. J. Ahsan, Semirings Characterized by Their Fuzzy Ideals, J. Fuzzy Math. 6 (1998), 181-192.
  3. J. Ahsan, K. Saifullah, M. F. Khan, Fuzzy semirings, Fuzzy Sets and Systems 60 (1993) 309-320
  4. K. Atanassov; Intuitionistic fuzzy sets, Fuzzy Sets and Systems, 20 (1986) 87-96.
  5. 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.
  6. W.A. Dudek, Special types of intuitionistic fuzzy left h-ideals of hemirings, Soft Comput. 12 (2008) 359-364.
  7. W.A. Dudek, M. Shabir, I. Ali, (ab )-fuzzy ideals of hemirings, Comput. Math. Appl. 58 (2) (2009) 310-321.
  8. J. S. Golan, Semirings and their Applications, Kluwer Acad. Publ., 1999
  9. U. Hebisch, H.J. Weinert, Semirings: Algebraic Theory and Applications in the Computer Science, World Scientific, 1998.
  10. A. Hussain, M. Shabir, Soft Finite State Machine, Journal of Intelligent and Fuzzy System, 2015, ( Accepted).
  11. A. Hussain, M. Shabir, Cubic Finite State Machine, Annals of Fuzzy Mathematics and Informatics, 2015, ( Accepted).
  12. Y.B. Jun, Generalization of (22 _q)-fuzzy subalgebras in BCK/BCI-algebras, Comput. Math. Appl. 58 (2009) 1383-1390.
  13. Y.B. Jun, On (ϕ y)-intuitionistic fuzzy fubgroups, KYUNGPOOK Math. J. 45 (2005) 87-94.
  14. Y.B. Jun, W.A. Dudek, M. Shabir, Generalizations of (ab )-fuzzy ideals of hemirings.
  15. A. Khan, M. Shabir, (ab )-fuzzy interior ideals in ordered semigroups, Lobachevskii J. Math. 30 (2009) 30-39.
  16. 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).
  17. 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.
  18. J.N. Mordeson, D.S. Malik, Fuzzy Automata and Languages, Theory and Applications, in: Computational Mathematics Series, Chapman and Hall/CRC, Boca Raton, 2002.
  19. V. Murali, Fuzzy points of equivalent fuzzy subsets, Information Science 158 (2004) 277-288.
  20. 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.
  21. A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35 (1971) 512-517.
  22. M. Shabir, Y.B. Jun, Y. Nawaz, Characterizations of regular semigroups by (ab )-fuzzy ideals, Comput. Math. Appl. 59 (2010) 161-175.
  23. M. Shabir, Y.B. Jun, Y. Nawaz, Semigroups characterized by (2 2 _qk)-fuzzy ideals, Comput. Math. Appl. 60 (2010) 1473-1493.
  24. 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.
  25. L. A. Zadeh, Fuzzy sets, Inform. Control 8 (1965) 338-353.
  26. J. S. Golan, Semirings and their Applications, Kluwer Acad. Publ., 1999