Union-soft sets with applications in BCK/BCI-algebras
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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) unionsoft ideals and union-soft commutative ideals are established. Extension property for a union-soft commutative ideal is established.
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) unionsoft ideals and union-soft commutative ideals are established. Extension property for a union-soft commutative ideal is established.
참고문헌 (27)
- U. Acar, "Soft sets and soft rings", Comput. Math. Appl, 59(11), pp.3458~3463 (2010)
- H. Aktas, "Soft sets and soft groups", Inform. Sci, 13, pp.2726~2735 (2007)
- A. O. Atagun, "Soft substructures of rings, fields and modules", Comput. Math. Appl, 61(3), pp.592~601 (2011)
- N. Cagman, "Soft set theory and uni-int decision making", European J. Oper. Res, 207(2), pp.848~855 (2010)
- N. Cagman, "Soft matrix theory and its decision making", Comput. Math. Appl, 59(10), pp.3308~3314 (2010)
- N. Cagman, "FP-soft set theory and its applications", Ann. Fuzzy Math. Inform, 2(2), pp.219~226 (2011)
- D. Chen, "The parameterization reduction of soft sets and its applications", Comput. Math. Appl, 49(5), pp.757~763 (2005)
- F. Feng, "Soft rough sets applied to multicriteria group decision making", Ann. Fuzzy Math. Inform, 2(1), pp.69~80 (2011)
- F. Feng, "Soft semirings", Comput. Math. Appl, 56(10), pp.2621~2628 (2008)
- F. Feng, "Soft sets and soft rough sets", Inform. Sci, 181(6), pp.1125~1137 (2011)
- Y. Huang, "BCI-algebra" (2006), Science Press
- Y. B. Jun, "Soft BCK", BCI-algebras, 2008, pp.56(5), 1408~1413
- Y. B. Jun, "Pseudo d-algebras", Inform. Sci, 179(11), pp.1751~1759 (2009)
- Y. B. Jun, "Soft ordered semigroups", Math. Log. Q, 56(1), pp.42~50 (2010)
- Y. B. Jun, "Soft set theory applied to ideals in d-algebras", Comput. Math. Appl, 57(3), pp.367~378 (2009)
- Y. B. Jun, "Soft p-ideals of soft BCI-algebras", Comput. Math. Appl, 58(10), pp.2060~2068 (2009)
- Y. B. Jun, "Applications of soft sets in ideal theory of BCK", BCI-algebras, 2008, pp.178(11), 2466~2475
- P. K. Maji, "Soft set theory", Comput. Math. Appl, 45(4), pp.555~562 (2003)
- P. K. Maji, "An application of soft sets in a decision making problem", Comput. Math. Appl, 44(8), pp.1077~1083 (2002)
- J. Meng, "BCK-algebras" (1994), Kyungmoon Sa Co.
- J. Meng, "Periods of elements in BCI-algebras", Math. Japon, 38(3), pp.427~431 (1993)
- D. Molodtsov, "Soft set theory - First results", Comput. Math. Appl, 37(4), pp.19~31 (1999)
- 박철환, "Soft WS-algebras", 대한수학회논문집, 23(3), pp.313~324 (2008), 대한수학회
- L. A. Zadeh, "From circuit theory to system theory", Proc. Inst. Radio Eng, 50, pp.856~865 (1962)
- L. A. Zadeh, "Fuzzy sets", Inform. Control, 8, pp.338~353 (1965)
- L. A. Zadeh, "FToward a generalized theory of uncertainty (GTU)–an outline", Inform. Sci, 172(1), pp.1~40 (2005)
- J. Zhan, "Soft BL-algebras based on fuzzy sets", Comput. Math. Appl, 59(6), pp.2037~2046 (2010)