Soft Rings Related to Fuzzy Set Theory ABSTRACT | FULL TEXT

Xianping Liu, Dajing Xiang, K. P. Shum, Jianming Zhan
1.221 526


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.

Anahtar kelimeler

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


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.