S. YAMAK, Ş. YILMAZ, O. KAZANCI

SOFT SETS AND SOFT BCH-ALGEBRAS

In this paper, the concept of soft BCH-algebra is introduced and in the meantime, some of their properties and structural characteristics are discussed and studied. The bi-intersection, extended intersection, restricted union, ∨-union, ∧-intersection and cartesian product of the family of soft BCH-algebras and soft BCH-subalgebras are established. Also, the theorems of homomorphic image and homomorphic pre-image of soft sets are given. Moreover, the notion of soft BCHhomomorphism is introduced and its basic properties are studied.

Keywords:

Soft sets, BCH-algebras Soft BCH-algebras, 2000 AMS Classification: 06 F 35, Soft BCH-subalgebras,

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Ahmad, B. On classification of BCH-algebras, Math. Japon. 35, 801–804, 1990.
Irfan Ali, M., Feng, F., Liu, X., Minc, W. K. and Shabir, M. On some new operations in soft set theory, Computers and Mathematics with Applications 57, 1547–1553, 2009.
Akta¸s, H. and C¸ a˘gman, N. Soft sets and soft groups, Information Sciences 177, 2726–2735, 2007. [4] Chaudhry, M. A. and Fakhar-Ud-Din, H. Ideals and filters in BCH-algebras, Math. Japon. 44, 101–111, 1996.
Chaudhry, M. A. On BCH-algebras, Math. Japon. 36, 665–676, 1991.
Chaudhary, M. A. and Fakhar-Ud-Din, H. On some classes of BCH-algebras, Int. J. Math. Math. Sci. 27, 1739–1750, 2003.
Chen, D., Tsang, E. C. C., Yeung, D. S. and Wang, X. The parameterization reduction of soft sets and its applications, Computers and Mathematics with Applications 49, 757–763, 2005. [8] Dudek, W. A. and Thomys, J. On decompositions of BCH-algebras, Math. Japon. 35, 1131– 1138, 1990.
Feng, F., Jun, Y. B. and Zhao, X. Soft semirings, Computers and Mathematics with Appli- cations 56, 2621–2628, 2008.
Hu, Q. P. and Li, X. On BCH-algebras, Math. Seminar Notes 11, 313–320, 1983.
Hu, Q. P. and Li, X. On proper BCH-algebras, Math. Japonica 30, 659–661, 1985.
Imai, Y. and Is´eki, K. On axiom systems of propositional calculi, XIV, Proc. Japan Acad. 42, 19–22, 1966.
Is´eki, K. An algebra related with a propositional calculus, Proc. Japan Acad. 42, 26–29, 1966. [14] Jun, Y. B., Roh, E. H. and Kim, H. S. On fuzzy B-algebras, Czechoslovak Math. J. 52 (127), 375–384, 2002.
Jun, Y. B. Soft BCK/BCI-algebras, Computers and Mathematics with Applications 56, 1408–1413, 2008.
Jun, Y. B. and Park, C. H. Applications of soft sets in ideal theory of BCK/BCI-algebras, Information Sciences178, 2466–2475, 2008.
Maji, P. K., Biswas, R. and Roy, A. R. Soft set theory, Computers and Mathematics with Applications 45, 555–562, 2003.
Maji, P. K., Roy, A. R. and Biswas, R. An application of soft sets in a decision making problem, Comput. Math. Appl. 44, 1077–1083, 2002.
Molodtsov, D. Soft set theory - first results, Computers and Mathematics with Applications 37, 19–31, 1999.
Roh, E. H., Jun, Y. B. and Zhang, Q. Special subset in BCH-algebras, Far East J. Math. Sci. (FJMS) 3, 723–729, 2001.
Roh, E. H., Kim, S. Y. and Jun, Y. B. On a problem in BCH-algebras, Math. Japon. 52 279–283, 2000.
Roy, A. R. and Maji, P. K. A fuzzy soft set theoretic approach to decision making problems, Journal of Computational and Applied Mathematics 203, 412–418, 2007.