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Soft Rings Related to Fuzzy Set Theory ABSTRACT | FULL TEXT

Year 2013, Volume: 42 Issue: 1 , 51 - 66 , 01.01.2013

Xianping Liu Dajing Xiang K. P. Shum Jianming Zhan

https://izlik.org/JA88UC26BH

Abstract

We deal with soft rings based on some fuzzy sets, in particular, byusing the so called ∈ −soft sets and q-soft sets. Some characterizationtheorems of soft rings defined on soft sets are given and soft regularrings are hence characterized by special soft sets.

Keywords

Soft rings Idealistic soft rings Bi-idealistic soft rings Quasi-idealistic softrings (∈ ∈ ∨q)-fuzzy subrings (∈ ∈ ∨ q)-fuzzy subrings regular rings soft regularrings.

References

  • H. Aktas, N. Ca˘ gman, Soft sets and soft groups, Inform. Sci. 177, 2726-2735, 2007.
  • S. K. Bhakat, P. Das, Fuzzy subrings and ideals redefined, Fuzzy Sets and Systems 81,383– 393, 1996.
  • D. Chen, E. C. C. Tsang, D. S. Yeung, X. Wang, The parametrization reduction of soft sets and its applications, Comput. Math. Appl. 49, 757-763, 2005.
  • F. Feng, Y. B. Jun, X. Zhao, Soft semirings, Comput. Math. Appl. 56, 2621-2628, 2008.
  • Y. B. Jun, Soft BCK/BCI-algebras, Comput. Math. Appl. 56, 1408-1413, 2008.
  • Y. B. Jun, C. H. Park, Applications of soft sets in ideal theory of BCK/BCI-algebras, Inform. Sci. 178, 2466-2475, 2008.
  • N. Kuroki, Regular fuzzy duo rings, Inform. Sci. 94, 119-139, 1996.
  • X. Liu, D. Xiang, K. P. Shum, J. Zhan, Isomorphism theorems for soft rings, Algebra Colloquium, 19, 391-397, 2012.
  • X. Ma, J. Zhan, On fuzzy h-ideals of hemirings, J. Syst. Sci. Complexity 20, 470-478, 2007. X. Ma, J. Zhan, Generalized fuzzy h-bi-ideals and h-quasi-ideals of hemirings, Inform. Sci. 179, 1249-1268, 2009.
  • P. K. Maji, A. R. Roy, R. Biswas, An application of soft sets in a decision making problem, Comput. Math. Appl. 44, 1077-1083, 2002.
  • P. K. Maji, A. R. Roy, R. Biswas, Soft set theory, Comput. Math. Appl. 45, 555-562, 2003. D. Molodstov, Soft set theory-first results, Comput. Math. Appl. 37, 19-31, 1999.
  • T. K. Mukherjee, M. K. Sen, On fuzzy ideals on a ring I, Fuzzy Sets and Systems 21, 99-104, 1987.
  • O. Steinfeld, Quasi-ideals in rings and semigroups, Akad. Kiado, Budapest, 1978.
  • Y. Yin, H. Li, The characterizations of h-hemiregular hemirings and h-intra-hemiregular hemirings, Inform. Sci. 178, 3451-3464, 2008.
  • Y. Yin, X. Huang, D. Xu, F. Li, The characterization of h-semisimple hemirings, Int. J. Fuzzy Syst. 11, 116-122, 2009.
  • L. A. Zadeh, Fuzzy sets, Inform. Control 8, 338-353, 1965.
  • L. A. Zadeh, Toward a generalized theory of uncertainty (GTU)-an outline, Inform. Sci. 172, 1-40, 2005.
  • J. Zhan, B. Davvaz, K. P. Shum, Generalized fuzzy hyperideals of hyperrings, Comput. Math. Appl. 56, 1732-1740, 2008.
  • J. Zhan, W. A. Dudek, Fuzzy h-ideal of hemirings, Inform. Sci. 177, 876-886, 2007.
  • J. Zhan, Y. Xu, Soft lattice implication algebras based on fuzzy sets, Hacet. J. Math. Stat. 40, 483-492, 2011.

Soft Rings Related to Fuzzy Set Theory ABSTRACT | FULL TEXT

Year 2013, Volume: 42 Issue: 1 , 51 - 66 , 01.01.2013

Xianping Liu Dajing Xiang K. P. Shum Jianming Zhan

https://izlik.org/JA88UC26BH

Abstract

-

Keywords

-

References

  • H. Aktas, N. Ca˘ gman, Soft sets and soft groups, Inform. Sci. 177, 2726-2735, 2007.
  • S. K. Bhakat, P. Das, Fuzzy subrings and ideals redefined, Fuzzy Sets and Systems 81,383– 393, 1996.
  • D. Chen, E. C. C. Tsang, D. S. Yeung, X. Wang, The parametrization reduction of soft sets and its applications, Comput. Math. Appl. 49, 757-763, 2005.
  • F. Feng, Y. B. Jun, X. Zhao, Soft semirings, Comput. Math. Appl. 56, 2621-2628, 2008.
  • Y. B. Jun, Soft BCK/BCI-algebras, Comput. Math. Appl. 56, 1408-1413, 2008.
  • Y. B. Jun, C. H. Park, Applications of soft sets in ideal theory of BCK/BCI-algebras, Inform. Sci. 178, 2466-2475, 2008.
  • N. Kuroki, Regular fuzzy duo rings, Inform. Sci. 94, 119-139, 1996.
  • X. Liu, D. Xiang, K. P. Shum, J. Zhan, Isomorphism theorems for soft rings, Algebra Colloquium, 19, 391-397, 2012.
  • X. Ma, J. Zhan, On fuzzy h-ideals of hemirings, J. Syst. Sci. Complexity 20, 470-478, 2007. X. Ma, J. Zhan, Generalized fuzzy h-bi-ideals and h-quasi-ideals of hemirings, Inform. Sci. 179, 1249-1268, 2009.
  • P. K. Maji, A. R. Roy, R. Biswas, An application of soft sets in a decision making problem, Comput. Math. Appl. 44, 1077-1083, 2002.
  • P. K. Maji, A. R. Roy, R. Biswas, Soft set theory, Comput. Math. Appl. 45, 555-562, 2003. D. Molodstov, Soft set theory-first results, Comput. Math. Appl. 37, 19-31, 1999.
  • T. K. Mukherjee, M. K. Sen, On fuzzy ideals on a ring I, Fuzzy Sets and Systems 21, 99-104, 1987.
  • O. Steinfeld, Quasi-ideals in rings and semigroups, Akad. Kiado, Budapest, 1978.
  • Y. Yin, H. Li, The characterizations of h-hemiregular hemirings and h-intra-hemiregular hemirings, Inform. Sci. 178, 3451-3464, 2008.
  • Y. Yin, X. Huang, D. Xu, F. Li, The characterization of h-semisimple hemirings, Int. J. Fuzzy Syst. 11, 116-122, 2009.
  • L. A. Zadeh, Fuzzy sets, Inform. Control 8, 338-353, 1965.
  • L. A. Zadeh, Toward a generalized theory of uncertainty (GTU)-an outline, Inform. Sci. 172, 1-40, 2005.
  • J. Zhan, B. Davvaz, K. P. Shum, Generalized fuzzy hyperideals of hyperrings, Comput. Math. Appl. 56, 1732-1740, 2008.
  • J. Zhan, W. A. Dudek, Fuzzy h-ideal of hemirings, Inform. Sci. 177, 876-886, 2007.
  • J. Zhan, Y. Xu, Soft lattice implication algebras based on fuzzy sets, Hacet. J. Math. Stat. 40, 483-492, 2011.
There are 20 citations in total.

Details

Primary Language Turkish
Authors

Xianping Liu This is me

Dajing Xiang This is me

K. P. Shum This is me

Jianming Zhan This is me

Publication Date January 1, 2013
IZ https://izlik.org/JA88UC26BH
Published in Issue Year 2013 Volume: 42 Issue: 1

Cite

APA Liu, X., Xiang, D., Shum, K. P., & Zhan, J. (2013). Soft Rings Related to Fuzzy Set Theory ABSTRACT | FULL TEXT. Hacettepe Journal of Mathematics and Statistics, 42(1), 51-66. https://izlik.org/JA88UC26BH
AMA 1.Liu X, Xiang D, Shum KP, Zhan J. Soft Rings Related to Fuzzy Set Theory ABSTRACT | FULL TEXT. Hacettepe Journal of Mathematics and Statistics. 2013;42(1):51-66. https://izlik.org/JA88UC26BH
Chicago Liu, Xianping, Dajing Xiang, K. P. Shum, and Jianming Zhan. 2013. “Soft Rings Related to Fuzzy Set Theory ABSTRACT | FULL TEXT”. Hacettepe Journal of Mathematics and Statistics 42 (1): 51-66. https://izlik.org/JA88UC26BH.
EndNote Liu X, Xiang D, Shum KP, Zhan J (January 1, 2013) Soft Rings Related to Fuzzy Set Theory ABSTRACT | FULL TEXT. Hacettepe Journal of Mathematics and Statistics 42 1 51–66.
IEEE [1]X. Liu, D. Xiang, K. P. Shum, and J. Zhan, “Soft Rings Related to Fuzzy Set Theory ABSTRACT | FULL TEXT”, Hacettepe Journal of Mathematics and Statistics, vol. 42, no. 1, pp. 51–66, Jan. 2013, [Online]. Available: https://izlik.org/JA88UC26BH
ISNAD Liu, Xianping - Xiang, Dajing - Shum, K. P. - Zhan, Jianming. “Soft Rings Related to Fuzzy Set Theory ABSTRACT | FULL TEXT”. Hacettepe Journal of Mathematics and Statistics 42/1 (January 1, 2013): 51-66. https://izlik.org/JA88UC26BH.
JAMA 1.Liu X, Xiang D, Shum KP, Zhan J. Soft Rings Related to Fuzzy Set Theory ABSTRACT | FULL TEXT. Hacettepe Journal of Mathematics and Statistics. 2013;42:51–66.
MLA Liu, Xianping, et al. “Soft Rings Related to Fuzzy Set Theory ABSTRACT | FULL TEXT”. Hacettepe Journal of Mathematics and Statistics, vol. 42, no. 1, Jan. 2013, pp. 51-66, https://izlik.org/JA88UC26BH.
Vancouver 1.Xianping Liu, Dajing Xiang, K. P. Shum, Jianming Zhan. Soft Rings Related to Fuzzy Set Theory ABSTRACT | FULL TEXT. Hacettepe Journal of Mathematics and Statistics [Internet]. 2013 Jan. 1;42(1):51-66. Available from: https://izlik.org/JA88UC26BH

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