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Algebraic structures of soft sets associated with new operations. (English) Zbl 1221.03056
Summary: Recently, new operations have been defined for soft sets. We study some important properties associated with these new operations. A collection of all soft sets with respect to new operations give rise to four idempotent monoids. Then with the help of these monoids we can study semiring (hemiring) structures of soft sets. Some of these semirings (hemirings) are actually lattices. Finally, we show that soft sets with a fixed set of parameters are MV-algebras and BCK-algebras.
03E72Fuzzy set theory
06F35BCK-algebras, BCI-algebras
[1]Chen, D.: The parameterization reduction of soft sets and its application, Computers and mathematics with applications 49, 757-763 (2005)
[2]Kong, Z.; Gao, L.; Wong, L.; Li, S.: The normal parameter reduction of soft sets and its algorithm, Computers and mathematics with applications 56, 3029-3037 (2008) · Zbl 1165.90699 · doi:10.1016/j.camwa.2008.07.013
[3]Maji, P. K.; Biswas, R.; Roy, R.: An application of soft sets in decision making problems, Computers and mathematics with applications 44, 1077-1083 (2002) · Zbl 1044.90042 · doi:10.1016/S0898-1221(02)00216-X
[4]Maji, P. K.; Roy, R.: A fuzzy set theoretic approach to decision making problems, Journal of computational and applied mathematics with applications 203, 412-418 (2007) · Zbl 1128.90536 · doi:10.1016/j.cam.2006.04.008
[5]Maji, P. K.; Biswas, R.; Roy, R.: Fuzzy soft sets, The journal of fuzzy mathematics 9, No. 3, 589-602 (2001) · Zbl 0995.03040
[6]Meng, J.; Jun, Y. B.: BCK-algebras, (1994)
[7]D. Pei, D. Miao, From soft sets to information systems, in: Granular Computing, 2005 IEEE Inter. Conf., vol 2, pp. 617–621.
[8]Shabir, M.; Ali, M. I.: Comments on de morgan’s law in fuzzy soft sets, The journal of fuzzy mathematics 18, No. 3, 679-686 (2010) · Zbl 1227.03069
[9]Feng, F.; Li, C.; Davvaz, B.; Ali, M. I.: Soft sets combined with fuzzy sets and rough sets: a tentative approach, Soft computing 14, 899-911 (2010) · Zbl 1201.03046 · doi:10.1007/s00500-009-0465-6
[10]Ali, M. I.; Feng, F.; Liu, X. Y.; Min, W. K.; Shabir, M.: On some new operations in soft set theory, Computers and mathematics with applications 57, 1547-1553 (2009) · Zbl 1186.03068 · doi:10.1016/j.camwa.2008.11.009
[11]Aktas, H.; Cagman, Naim: Soft sets and soft groups, Information sciences 177, 2726-2735 (2007) · Zbl 1119.03050 · doi:10.1016/j.ins.2006.12.008
[12]Jun, Y. B.; Park, C. H.: Applications of soft sets in ideal theory of BCK/BCI-algebras, Information sciences 178, 2466-2475 (2008) · Zbl 1184.06014 · doi:10.1016/j.ins.2008.01.017
[13]Jun, Y. B.: Soft BCK/BCI-algebras, Computers and mathematics with applications 56, 1408-1413 (2008)
[14]Shabir, M.; Ali, M. I.: Soft ideals and generalized fuzzy ideals in semigroups, New mathematics and natural computation 5, No. 3, 599-615 (2009) · Zbl 1178.20061 · doi:10.1142/S1793005709001544
[15]Feng, F.; Jun, Y. B.; Zhao, X. Z.: Soft semirings, Computers and mathematics with applications 56, 2621-2628 (2008)
[16]Qin, K.; Hong, Z.: On soft equality, Journal of computational and applied mathematics 234, 1347-1355 (2010) · Zbl 1188.08001 · doi:10.1016/j.cam.2010.02.028
[17]Molodtsov, D.: Soft set theory-first results, Computers and mathematics with applications 37, 19-31 (1999) · Zbl 0936.03049 · doi:10.1016/S0898-1221(99)00056-5
[18]Maji, P. K.; Biswas, R.; Roy, R.: Soft set theory, Computers and mathematics with applications 45, 555-562 (2003)
[19]Chang, C. C.: A new proof of the completeness of the łukasiewicz axioms, Transactions of the American mathematical society 93, 460-490 (1958)
[20]Imai, Y.; Iseki, K.: On axiom systems of proposition calculi, Proceedings of the Japan Academy 42, 19-22 (1966) · Zbl 0156.24812 · doi:10.3792/pja/1195522169