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Characterizations of hemirings by \((\overline{\varvec{\in}},\overline{\varvec{\in}} \vee \overline{\varvec{q}})\)-fuzzy ideals

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Abstract

In this paper, we characterize different classes of hemirings by the properties of their \((\overline{\in}, \overline{\in} \vee \overline{q})\)-fuzzy ideals, \((\overline{\in}, \overline{\in} \vee \overline{q})\)-fuzzy quasi-ideals and \((\overline{\in}, \overline{\in} \vee \overline{q}) \)-fuzzy bi-ideals.

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References

  1. Aho AW, Ullman JD (1979) Introduction to automata theory, languages and computation. Addison Wesley, Reading

    Google Scholar 

  2. Ahsan J (1998) Semirings characterized by their fuzzy ideals. J Fuzzy Math 6:181–192

    MathSciNet  MATH  Google Scholar 

  3. Ahsan J, Saifullah K, Khan MF (1993) Fuzzy semirings. Fuzzy Sets Syst 60:309–320

    Article  MathSciNet  MATH  Google Scholar 

  4. Bhakat SK (1999) \(\left( \in \vee q\right) \)-level subset. Fuzzy Sets Syst 103:529–533

    Article  MathSciNet  MATH  Google Scholar 

  5. Bhakat SK (2000) \(\left( \in ,\in \vee q\right) \)-fuzzy normal, quasinormal and maximal subgroups. Fuzzy Sets Syst 112:299–312

    Article  MathSciNet  MATH  Google Scholar 

  6. Bhakat SK, Das P (1992) On the definition of a fuzzy subgroup. Fuzzy Sets Syst 51:235–241

    Article  MathSciNet  MATH  Google Scholar 

  7. Bhakat SK, Das P (1996) \(\left( \in ,\in \vee q\right) \)-fuzzy subgroups. Fuzzy Sets Syst 80:359–368

    Article  MathSciNet  MATH  Google Scholar 

  8. Bhakat SK, Das P (1996) Fuzzy subrings and ideals redefined. Fuzzy Sets Syst 81:383–393

    Article  MathSciNet  MATH  Google Scholar 

  9. Davvaz B (2006) \(\left( \in ,\in \vee q\right) \)-fuzzy subnearrings and ideals. Soft Comput 10:206–211

    Article  MATH  Google Scholar 

  10. Dudek WA, Shabir M, Irfan Ali M (2009) (α , β)-Fuzzy ideals of hemirings. Comput Math Appl 58:310–321

    Article  MathSciNet  MATH  Google Scholar 

  11. Ghosh S (1998) Fuzzy k-ideals of semirings. Fuzzy Sets Syst 95:103–108

    Article  MATH  Google Scholar 

  12. Glazek K (2002) A guide to litrature on semirings and their applications in mathematics and information sciences: with complete bibliography. Kluwer, The Netherlands

    Google Scholar 

  13. Golan JS (1999) Semirings and their applications. Kluwer, Dordrecht

    MATH  Google Scholar 

  14. Hebisch U, Weinert HJ (1998) Semirings: algebraic theory and applications in the computer science. World Scientific, Singapore

    MATH  Google Scholar 

  15. Henriksen M (1958) Ideals in semirings with commutative addition. Am Math Soc Notices 6:321

    Google Scholar 

  16. Iizuka K (1959) On Jacobson radical of a semiring. Tohoku Math J 11:409–421

    Article  MathSciNet  MATH  Google Scholar 

  17. Jun YB, Özürk MA, Song SZ (2004) On fuzzy h-ideals in hemirings. Inform Sci 162:211–226

    Article  MathSciNet  MATH  Google Scholar 

  18. Jun YB, Song SZ (2006) Generalized fuzzy interior ideals in semigroups. Inform Sci 176:3079–3093

    Article  MathSciNet  MATH  Google Scholar 

  19. La Torre DR (1965) On h-ideals and k-ideals in hemirings. Publ Math Debrecen 12:219–226

    MathSciNet  MATH  Google Scholar 

  20. Ma X, Zhan J (2007) On fuzzy h-ideals of hemirings. J Syst Sci Complex 20:470–478

    Article  MathSciNet  Google Scholar 

  21. Ma X, Zhan J (2009) Generalized fuzzy h-bi-ideals and h-quasi-ideals of hemirings. Inform Sci 179:1249–1268

    Article  MathSciNet  MATH  Google Scholar 

  22. Mordeson JN, Malik DS (2002) Fuzzy automata and languages, theory and applications, computational mathematics series. Chapman and Hall/CRC, Boca Raton

    Book  Google Scholar 

  23. Murali V (2004) Fuzzy points of equivalent fuzzy subsets. Inform Sci 158:277–288

    Article  MathSciNet  MATH  Google Scholar 

  24. Pu PM, Liu YM (1980) Fuzzy topology I, neighborhood structure of a fuzzy point and Moore-Smith convergence. J Math Anal Appl 76:571–599

    Article  MathSciNet  MATH  Google Scholar 

  25. Shabir M, Mahmood T (2010) Hemirings characterized by the properties of their fuzzy ideals with thresholds. Quasigroups Relat Syst 18:195–212

    MathSciNet  MATH  Google Scholar 

  26. Vandiver HS (1934) Note on a simple type of algebra in which cancellation law of addition does not hold. Bull Am Math Soc 40:914–920

    Article  MathSciNet  Google Scholar 

  27. Yin YQ, Li H (2008) The charatecrizations of h-hemiregular hemirings and h-intra-hemiregular hemirings. Inform Sci 178:3451–3464

    Article  MathSciNet  MATH  Google Scholar 

  28. Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353

    Article  MathSciNet  MATH  Google Scholar 

  29. Zhan J, Dudek WA (2007) Fuzzy h-ideals of hemirings. Inform Sci 177:876–886

    Article  MathSciNet  MATH  Google Scholar 

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Authors and Affiliations

  1. Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan

    Muhammad Shabir & Yasir Nawaz

  2. Department of Mathematics, International Islamic University, Islamabad, Pakistan

    Tahir Mahmood

Authors
  1. Muhammad Shabir
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  2. Yasir Nawaz
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  3. Tahir Mahmood
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Correspondence to Tahir Mahmood.

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Shabir, M., Nawaz, Y. & Mahmood, T. Characterizations of hemirings by \((\overline{\varvec{\in}},\overline{\varvec{\in}} \vee \overline{\varvec{q}})\)-fuzzy ideals. Neural Comput & Applic 21 (Suppl 1), 93–103 (2012). https://doi.org/10.1007/s00521-011-0693-4

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  • DOI: https://doi.org/10.1007/s00521-011-0693-4

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