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The characterizations of hemirings in terms of fuzzy soft h-ideals

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Abstract

Maji et al. introduced the concept of a fuzzy soft set, which is an extension to the concept of a soft set. In this paper, we apply the concept of a fuzzy soft set to hemiring theory. The concepts of \((\in_{\gamma},\in_{\gamma} \! \vee { q_{\delta}})\)-fuzzy soft left h-ideals (right h-ideals, h-bi-ideals, and h-quasi-ideals) are introduced, and some related properties are obtained. The notion of left (right) h-hemiregular hemirings is provided. Some characterization theorems of (left) h-hemiregular and (left) duo hemirings are derived in terms of \((\in_{\gamma},\in_{\gamma} \! \vee { q_{\delta}})\)-fuzzy soft left (right) h-ideals, \((\in_{\gamma},\in_{\gamma} \! \vee { q_{\delta}})\)-fuzzy soft h-bi-ideals, and \((\in_{\gamma},\in_{\gamma} \! \vee { q_{\delta}})\)-fuzzy soft h-quasi-ideals.

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References

  1. Aktaş H, Çğman N (2007) Soft sets and soft groups. Inform Sci 177:2726–2735

    Article  MathSciNet  MATH  Google Scholar 

  2. Irfan Ali M, Feng F, Liu X, Min WK, Shabir M (2009) On some new operations in soft set theory. Comput Math Appl 57:1547–1553

    Article  MathSciNet  MATH  Google Scholar 

  3. Irfan Ali M, Shabir M (2010) Comments on De Morgan’s law in fuzzy soft sets. J Fuzz Math 18(3):679–686

    MathSciNet  MATH  Google Scholar 

  4. Aygünoğlu A, Aygün H (2009) Introduction to fuzzy soft groups. Comput Math Appl 58:1279–1286

    Article  MathSciNet  MATH  Google Scholar 

  5. Çǎgman N, Enginǒlu S (2010) Soft matrix theory and its decision making. Comput Math Appl 59((10):3308–3314

    Article  MathSciNet  Google Scholar 

  6. Çǎman N, Enginǒlu S (2010) Soft set theory and uni-int decision making. Eur J Oper Res 207((2):848–855

    Google Scholar 

  7. Chen D, Tsang ECC, Yeung DS, Wang X (2005) The parameterization reduction of soft sets and its applications. Comput Math Appl 49:757–763

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  9. Dutta TK, Biswas BK (1995) Fuzzy k-ideals of semirings. Bull Cal Math Soc 87:91–96

    MathSciNet  MATH  Google Scholar 

  10. Molodtsov D (1999) Soft set theory-First results. Comput Math Appl 37(4–5):19–31

    Article  MathSciNet  MATH  Google Scholar 

  11. Feng F, Jun YB, Liu X, Li L (2010) An adjustable approach to fuzzy soft set based decision making. J Comput Appl Math 234((1):10–20

    Article  MathSciNet  MATH  Google Scholar 

  12. Feng F, Jun YB, Zhao X (2008) Soft semirings. Comput Math Appl 56:2621–2628

    Article  MathSciNet  MATH  Google Scholar 

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

    Google Scholar 

  14. Huang X, Li H, Yin Y (2007) The h-hemiregular fuzzy duo hemirings. Int J Fuzzy Syst 9:105–109

    MathSciNet  Google Scholar 

  15. Iizuka K (1959) On the Jacobson radical of a semiring. Tohoku Math J 11(2):409–421

    Article  MathSciNet  MATH  Google Scholar 

  16. Jiang Y, Tang Y, Chen Q (2011) An adjustable approach to intuitionistic fuzzy soft sets based decision making. Appl Math Model 35:824–836

    Article  MathSciNet  MATH  Google Scholar 

  17. Jun YB (2008) Soft BCK/BCI-algebras. Comput Math Appl 56:1408–1413

    Article  MathSciNet  MATH  Google Scholar 

  18. Jun YB, Lee KJ, Park CH (2009) Soft set theory applied to ideals in d-algebras. Comput Math Appl 57:367–378

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  20. Jun YB, Park CH (2008) Applications of soft sets in ideal theory of BCK/BCI-algebras. Inform Sci 178:2466–2475

    MathSciNet  MATH  Google Scholar 

  21. Koyuncu F, Tanay B (2010) Soft sets and soft rings. Comput Math Appl 59:3458–3463

    Article  MathSciNet  MATH  Google Scholar 

  22. 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 

  23. Maji PK, Biswas R, Roy AR (2001) Fuzzy soft sets. J Fuzzy Math 9(3):589–602

    MathSciNet  MATH  Google Scholar 

  24. Maji PK, Biswas R, Roy AR (2001) Intuitionistic fuzzy soft sets. J Fuzzy Math 9(3):677–692

    MathSciNet  MATH  Google Scholar 

  25. Maji PK, Biswas R, Roy AR (2003) Soft set theory. Comput Math Appl 45((4C5):555–562

    Article  MathSciNet  MATH  Google Scholar 

  26. Maji PK, Roy AR, Biswas R (2002) An application of soft sets in a decision making problem. Comput Math Appl 44:1077–1083

    Article  MathSciNet  MATH  Google Scholar 

  27. Maji PK, Roy AR, Biswas R (2004) On intuitionistic fuzzy soft sets. J Fuzzy Math 12(3):669–683

    MathSciNet  MATH  Google Scholar 

  28. Majumdar P, Samanta SK (2010) Generalised fuzzy soft sets. Comput Math Appl 59(4):1425–1432

    Article  MathSciNet  MATH  Google Scholar 

  29. Qin K, Hong Z (2010) On soft equality. J Comput Appl Math 234:1347–1355

    Article  MathSciNet  MATH  Google Scholar 

  30. Roy AR, Maji PK (2007) A fuzzy soft set theoretic approach to decision making problems. J Comput Appl Math 203:412–418

    Article  MATH  Google Scholar 

  31. Xiao Z, Gong K, Zou Y (2009) A combined forecasting approach based on fuzzy soft sets. J Comput Appl Math 228(1):326–333

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    MathSciNet  Google Scholar 

  34. Zadeh LA (1965) Fuzzy sets. Inform Cont 8:338–358

    Article  MathSciNet  MATH  Google Scholar 

  35. Zhan J, Dudek W (2007) Fuzzy h-ideal of hemirings. Inform Sci 177:876–886

    Article  MathSciNet  MATH  Google Scholar 

  36. Zhan J, Jun YB (2010) Soft BL-algebras based on fuzzy sets. Comput Math Appl 59:2037–2046

    Article  MathSciNet  MATH  Google Scholar 

  37. Zou Y, Xiao Z (2008) Data analysis approaches of soft sets under incomplete information. Knowl Based Syst 21(8):941–945

    Article  Google Scholar 

Download references

Acknowledgments

We are grateful to the Editor and the referees for their constructive comments on an earlier version of our paper. This paper was supported in part by the Natural Science Foundation for Young Scholars of Jiangxi, China (2010GQS0003); in part by the Science Foundation of Education Committee for Young Scholars of Jiangxi, China (GJJ11143) and in part by the Innovation Team of Higher Education of Huibei Province, China (T201109).

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Authors and Affiliations

  1. Key Laboratory of Radioactive Geology and Exploration Technology Fundamental Science for National Defense East China Institute of Technology, 344000, Fuzhou, Jiangxi, China

    Yunqiang Yin

  2. School of Mathematics and Information Sciences, East China Institute of Technology, 344000, Fuzhou, Jiangxi, China

    Yunqiang Yin

  3. Department of Mathematics, Hubei University for Nationalities, 445000, Enshi, Hubei Province, China

    Jianming Zhan

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  1. Yunqiang Yin
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  2. Jianming Zhan
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Correspondence to Yunqiang Yin.

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Yin, Y., Zhan, J. The characterizations of hemirings in terms of fuzzy soft h-ideals. Neural Comput & Applic 21 (Suppl 1), 43–57 (2012). https://doi.org/10.1007/s00521-011-0591-9

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  • DOI: https://doi.org/10.1007/s00521-011-0591-9

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