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
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.
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
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.