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Fuzzy h-ideals in h-hemiregular and h-semisimple \(\Upgamma\)-hemirings

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Abstract

In this paper, we introduce the concepts of some kinds of fuzzy h-ideals in \(\Upgamma\)-hemirings and obtain some of their related properties. In particular, the characterizations of prime fuzzy h-ideals in \(\Upgamma\)-hemirings are discussed. Finally, we show that the h-hemiregular and h-semisimple \(\Upgamma\)-hemirings can be described by using these kinds of fuzzy h-ideals.

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References

  1. Barnes WE (1966) On the \(\Upgamma\)-rings of Nobusawa. Pac J Math 18:411–422

    MATH  MathSciNet  Google Scholar 

  2. Dudek WA (2008) Special types of intuitionistic fuzzy left h-ideals of hemirings. Soft Comput 12:359–364

    Article  MATH  Google Scholar 

  3. Dudek WA (2006) Intuitionistic fuzzy h-ideals of hemirings. WSEAS Trans Math 12:1315–1331

    MathSciNet  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  5. Dutta TK, Chanda T (2005) Structures of fuzzy ideals of \(\Upgamma\)-rings. Bull Malays Math Sci Soc 28(1):9–15

    MATH  MathSciNet  Google Scholar 

  6. Dutta TK, Chanda T (2005) Fuzzy prime ideals in \(\Upgamma\)-rings. Bull Malays Math Sci Soc 30(1):65–73

    MathSciNet  Google Scholar 

  7. Dutta TK, Sardar SK (2002) On the operator semirings of a \(\Upgamma\)-semirings. SEA Bull Math 26:203–213

    Article  MATH  MathSciNet  Google Scholar 

  8. Dutta TK, Sardar SK (2000) Semiprime ideals and irreducible ideals of \(\Upgamma\)-semirings. Novi Sad J Math 30:97–108

    MATH  MathSciNet  Google Scholar 

  9. Glazek K (2002) A guide to the literature on semirings and their applications in mathematics and information sciences: with complete bibliography. Kluwer, Dodrecht

    MATH  Google Scholar 

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

    Google Scholar 

  11. Hong SM, Jun YB (1995) A note on fuzzy ideals in gamma-rings. Bull Honam Math Soc 12:39–48

    Google Scholar 

  12. Jonathan S, Golan JS (1999) Semirings and their applications. Kluwer, Dodrecht

    MATH  Google Scholar 

  13. Jun YB (1995) On fuzzy prime ideals of \( \Upgamma\)-rings. Soochow J Math 21(1):41–48

    MATH  MathSciNet  Google Scholar 

  14. Jun YB, Kim HS, Öztürk MA (2005) Fuzzy k-ideals in semirings. J Fuzzy Math 13:351–364

    MATH  MathSciNet  Google Scholar 

  15. Jun YB, Lee CY (1992) Fuzzy \(\Upgamma\)-rings. Pusan Kyongnan Math J (presently, East Asian Math J) 8(2):163–170

    Google Scholar 

  16. Jun YB, Lee CY (1993) Fuzzy prime ideals of \(\Upgamma\)-rings. Pusan Kyongnan Math J (presently, East Asian Math J) 9(1):105–111

    Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  18. Kondo M, Dudek WA (2005) On the Transfer Principle in fuzzy theory. Mathware Soft Comput 12:41–55

    MATH  MathSciNet  Google Scholar 

  19. Kyuno S, Nobusawa N, Sith NB (1987) Regular gamma rings. Tsukuba J. Math 11(2):371–382

    MATH  MathSciNet  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  MATH  MathSciNet  Google Scholar 

  22. Rao MK (1995) \(\Upgamma\)-semirings-1. SEA Bull Math 19:49–54

    MATH  Google Scholar 

  23. Sardar SK, Dasgupta U (2004) On primitive \(\Upgamma\)-semirings. Novi Sad J Math 34:1–12

    MathSciNet  Google Scholar 

  24. Wechler W (1978) The concept of fuzziness in automata and language theory. Akademie-Verlag, Berlin

    MATH  Google Scholar 

  25. Yin Y, Huang X, Xu D, Li H (2009) The characterization of h-semisimple hemirings. Int J Fuzzy Syst 11:116–122

    Google Scholar 

  26. Yin Y, Li H (2008) The characterization of h-hemiregular hemirings and h-intra-hemiregular hemirings. Inform Sci 178:3451–3464

    Article  MATH  MathSciNet  Google Scholar 

  27. Zadeh LA (2005) Toward a generalized theory of uncertainty (GTU)-an outline. Inform Sci 172:1–40

    Article  MATH  MathSciNet  Google Scholar 

  28. Zadeh LA (2008) Is there a need for fuzzy logic? Inform Sci 178:2751–2779

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  30. Zhan J, Tan Z (2003) T-fuzzy k-ideals of semirings. Sci Math Japon 58:597–601

    MathSciNet  Google Scholar 

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Acknowledgments

This research of the first author is partially supported by a grant of National Natural Science Foundation of China # 60875034; a grant of the Natural Science Foundation of Education Committee of Hubei Province, China, # D20092901; # Q20092907; # D20082903 and # B200529001 and also a grant of the Natural Science Foundation of Hubei Province, China # 2008CDB341; # 2009CDB340.

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  1. Department of Mathematis, Hubei Institute for Nationalities, 445000, Enshi, Hubei, China

    Xueling Ma & Jianming Zhan

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  1. Xueling Ma
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  2. Jianming Zhan
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Correspondence to Jianming Zhan.

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Ma, X., Zhan, J. Fuzzy h-ideals in h-hemiregular and h-semisimple \(\Upgamma\)-hemirings. Neural Comput & Applic 19, 477–485 (2010). https://doi.org/10.1007/s00521-010-0341-4

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