JOURNAL BROWSE
Search
Advanced SearchSearch Tips
UNION-SOFT SETS WITH APPLICATIONS IN BCK/BCI-ALGEBRAS
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
UNION-SOFT SETS WITH APPLICATIONS IN BCK/BCI-ALGEBRAS
Jun, Young Bae;
  PDF(new window)
 Abstract
The aim of this article is to lay a foundation for providing a soft algebraic tool in considering many problems that contain uncertainties. In order to provide these soft algebraic structures, the notion of union-soft sets is introduced, and its application to BCK/BCI-algebras is considered. The notions of union-soft algebras, union-soft (commutative) ideals and closed union-soft ideals are introduced, and related properties and relations are investigated. Conditions for a union-soft ideal to be closed are provided. Conditions for a union-soft ideal to be a union-soft commutative ideal are also provided. Characterizations of (closed) union-soft ideals and union-soft commutative ideals are established. Extension property for a union-soft commutative ideal is established.
 Keywords
exclusive set;union-soft algebra;(closed) union-soft ideal;union-soft commutative ideal;
 Language
English
 Cited by
 References
1.
U. Acar, F. Koyuncu, and B. Tanay, Soft sets and soft rings, Comput. Math. Appl. 59 (2010), no. 11, 3458-3463. crossref(new window)

2.
H. Aktas and N. Cagman, Soft sets and soft groups, Inform. Sci. 177 (2007), no. 13, 2726-2735. crossref(new window)

3.
A. O. Atagun and A. Sezgin, Soft substructures of rings, fields and modules, Comput. Math. Appl. 61 (2011), no. 3, 592-601. crossref(new window)

4.
N. Cagman, F. Citak, and S. Enginoglu, Soft set theory and uni-int decision making, European J. Oper. Res. 207 (2010), no. 2, 848-855. crossref(new window)

5.
N. Cagman and S. Enginoglu, Soft matrix theory and its decision making, Comput. Math. Appl. 59 (2010), no. 10, 3308-3314. crossref(new window)

6.
N. Cagman and S. Enginoglu, FP-soft set theory and its applications, Ann. Fuzzy Math. Inform. 2 (2011), no. 2, 219-226.

7.
D. Chen, E. C. C. Tsang, D. S. Yeung, and X. Wang, The parameterization reduction of soft sets and its applications, Comput. Math. Appl. 49 (2005), no. 5-6, 757-763. crossref(new window)

8.
F. Feng, Soft rough sets applied to multicriteria group decision making, Ann. Fuzzy Math. Inform. 2 (2011), no. 1, 69-80.

9.
F. Feng, Y. B. Jun, and X. Zhao, Soft semirings, Comput. Math. Appl. 56 (2008), no. 10, 2621-2628. crossref(new window)

10.
F. Feng, X. Liu, V. Leoreanu-Fotea, and Y. B. Jun, Soft sets and soft rough sets, Inform. Sci. 181 (2011), no. 6, 1125-1137 crossref(new window)

11.
Y. Huang, BCI-algebra, Science Press, Beijing, 2006.

12.
Y. B. Jun, Soft BCK/BCI-algebras, Comput. Math. Appl. 56 (2008), no. 5, 1408-1413. crossref(new window)

13.
Y. B. Jun, H. S. Kim, and J. Neggers, Pseudo d-algebras, Inform. Sci. 179 (2009), no. 11, 1751-1759. crossref(new window)

14.
Y. B. Jun, K. J. Lee, and A. Khan, Soft ordered semigroups, Math. Log. Q. 56 (2010), no. 1, 42-50. crossref(new window)

15.
Y. B. Jun, K. J. Lee, and C. H. Park, Soft set theory applied to ideals in d-algebras, Comput. Math. Appl. 57 (2009), no. 3, 367-378. crossref(new window)

16.
Y. B. Jun, K. J. Lee, and J. Zhan, Soft p-ideals of soft BCI-algebras, Comput. Math. Appl. 58 (2009), no. 10, 2060-2068. crossref(new window)

17.
Y. B. Jun and C. H. Park, Applications of soft sets in ideal theory of BCK/BCI-algebras, Inform. Sci. 178 (2008), no. 11, 2466-2475.

18.
P. K. Maji, R. Biswas, and A. R. Roy, Soft set theory, Comput. Math. Appl. 45 (2003), no. 4-5, 555-562. crossref(new window)

19.
P. K. Maji, A. R. Roy, and R. Biswas, An application of soft sets in a decision making problem, Comput. Math. Appl. 44 (2002), no. 8-9, 1077-1083. crossref(new window)

20.
J. Meng and Y. B. Jun, BCK-algebras, Kyungmoon Sa Co., Seoul, 1994.

21.
J. Meng and S. M. Wei, Periods of elements in BCI-algebras, Math. Japon. 38 (1993), no. 3, 427-431.

22.
D. Molodtsov, Soft set theory - First results, Comput. Math. Appl. 37 (1999), no. 4-5, 19-31.

23.
C. H. Park, Y. B. Jun, and M. A. Ozturk, Soft WS-algebras, Commun. Korean Math. Soc. 23 (2008), no. 3, 313-324. crossref(new window)

24.
L. A. Zadeh, From circuit theory to system theory, Proc. Inst. Radio Eng. 50 (1962), 856-865.

25.
L. A. Zadeh, Fuzzy sets, Inform. Control 8 (1965), 338-353. crossref(new window)

26.
L. A. Zadeh, Toward a generalized theory of uncertainty (GTU)-an outline, Inform. Sci. 172 (2005), no. 1-2, 1-40. crossref(new window)

27.
J. Zhan and Y. B. Jun, Soft BL-algebras based on fuzzy sets, Comput. Math. Appl. 59 (2010), no. 6, 2037-2046. crossref(new window)