{"title":"Filteristic Soft Lattice Implication Algebras","authors":"Yi Liu, Yang Xu","volume":60,"journal":"International Journal of Mathematical and Computational Sciences","pagesStart":1977,"pagesEnd":1984,"ISSN":"1307-6892","URL":"https:\/\/publications.waset.org\/pdf\/9679","abstract":"
Applying the idea of soft set theory to lattice implication algebras, the novel concept of (implicative) filteristic soft lattice implication algebras which related to (implicative) filter(for short, (IF-)F-soft lattice implication algebras) are introduced. Basic properties of (IF-)F-soft lattice implication algebras are derived. Two kinds of fuzzy filters (i.e.(2, 2 _qk)((2, 2 _ qk))-fuzzy (implicative) filter) of L are introduced, which are generalizations of fuzzy (implicative) filters. Some characterizations for a soft set to be a (IF-)F-soft lattice implication algebra are provided. Analogously, this idea can be used in other types of filteristic lattice implication algebras (such as fantastic (positive implicative) filteristic soft lattice implication algebras).<\/p>\r\n","references":"[1] Y. Xu, Lattice implication algebra, J. Southwest Jiaotong Univ.,\r\n28(1993), 20-27.\r\n[2] Y. Xu and K.Y. Qin, Fuzzy lattice implication algebras, J.Southwest\r\nJiaotong Univ., 2(1995), 121-27.\r\n[3] Y. Xu and K.Y.Qin, On filters of lattice implication algebras, J.Fuzzy\r\nMath., 2(1993), 251-260.\r\n[4] Y. Xu, D. Ruan, K. Y.Qin, J. Liu, Lattice-valued logic-an alternative\r\napproach to treat fuzziness and incomparability, Berlin: Springer-Verlag,\r\n2003.\r\n[5] L. A. Zadeh, Fuzzy set, Inform. Sci., 8(1965), 338-353.\r\n[6] P. M. Pu and Y.M.Liu, Fuzzy topology I, Neighborhood structure of\r\na fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl.,\r\n76(1980), 571-599.\r\n[7] Y. Liu and Y. Xu, Inter-valued (\u00ae, \u252c\u00bb)-fuzzy implication subalgebras,\r\nComput. Sci., 38(4)(2011),263-266.\r\n[8] Y. Liu and Y. Xu, New types of fuzzy filters on lattice implication\r\nalgebras, J. Math. Research., 3(2011),57-63.\r\n[9] S. K. Bhakat and P. Das, (2, 2 _q)-fuzzy subgroups, Fuzzy Sets Syst.,\r\n80(1996), 359-368.\r\n[10] B. Davvaz, (2, 2 _q)-fuzzy subnear-rings and ideals, Soft Comput.,\r\n10(2006), 206-211.\r\n[11] W. A. Dudek, M. Shabir, M. Irfan Ali, (\u00ae, \u252c\u00bb)-fuzzy ideals of hemirings,\r\nComput. Math. Appl., 58 (2009), 310-321.\r\n[12] D. Molodtsov, Soft set-first results, Comput. Math. Appl., 37(1999),\r\n19-31.\r\n[13] H. Aktas and N. Cagman, soft sets and soft groups, Inform. Sci.,\r\n177(2009), 2726-2735.\r\n[14] P. K. Maji, R. Biswas, A. R. Roy, soft set theory, Comput. Math.\r\nAppl., 45 (2003), 555-562.\r\n[15] P. K. Maji, R. Biswas, A. R. Roy, fuzzy soft set, J. fuzzy Math. Appl.,\r\n9(3)(2001), 589-602.\r\n[16] P. K. Maji, A. R. Roy, R. Biswas, An application of soft sets in a\r\ndecision making problem, Comput. Math. Appl., 44 (2002), 1077-1083.\r\n[17] F. Feng, Y. B.Jun, X. Z. Zhang, Soft semiring, Comput. Math. Appl.,\r\n56 (2008), 2621-2628.\r\n[18] Y. B.Jun and S. Z.Song, Soft subalgebras and soft ideals of BCK\/BCIalgebras\r\nrelated to fuzzy set theory, Math. Commun., 14(2009), 271-281.\r\n[19] Y. B. Jun and C. H. Park, Applications of soft sets in ideal theory of\r\nBCK\/BCI-algebras, Inform. Sci., 178(2008), 2446-2475.\r\n[20] Y.B.Jun, Y.Xu, J.Ma, Redefined fuzzy implication filters, Inform. Sci.,\r\n177(2007), 422-1429.\r\n[21] J.M.Zhan and Y.B.Jun, Notes on redefined fuzzy implication filters of\r\nlattice implication algebras, Inform. Sci., 179(2009), 3182-3186.\r\n[22] J. M. Zhan and Y. B. Jun, Soft BL-algebras based on fuzzy sets,\r\nComput. Math. Appl., 59(2010), 2037-2046.\r\n[23] Y.Q. Yin and J. M. Zhan, New types of fuzzy filters in BL-algebras,\r\nComput. Math. Appl., 59(2010), 2115-2125.\r\n[24] D. Pei and D. Miao, From soft sets to information systems, Granular\r\ncomput., 2005 IEEE Inter. Conf., 2(2005), 419-430.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 60, 2011"}