TY - JOUR T1 - Soft Lattice Implication Algebras Based on Fuzzy Sets TT - Soft Lattice Implication Algebras Based on Fuzzy Sets AU - Zhan, Jianming AU - Xu, Yang PY - 2011 DA - April JF - Hacettepe Journal of Mathematics and Statistics PB - Hacettepe University WT - DergiPark SN - 2651-477X SP - 483 EP - 492 VL - 40 IS - 4 LA - en AB - In this paper, we deal with soft lattice implication algebras based on fuzzy sets. Using the concepts of fuzzy (implicative) filters, (∈,∈ ∨q)- fuzzy (implicative) filters and (∈,∈∨q)-fuzzy (implicative) filters, some characterizations for ∈-soft sets and q-soft sets to be (implicative) filteristic soft lattice implication algebras are established. KW - (Implicative) filter KW - (Implicative) filteristic soft lattice implication algebra KW - 2000 AMS Classification: 03 B 05 CR - Aktas, H. and Cagman, N. Soft sets and soft groups, Inform. Sci. 177, 2726–2735, 2007. CR - Bhakat, S. K. and Das, P. (∈, ∈ ∨ q)-fuzzy subgroup, Fuzzy Sets and Systems 80, 359–368, Jun, Y. B. Soft BCK/BCI-algebras, Comput. Math. Appl. 56, 1408–1413, 2008. CR - Jun, Y. B. and Park, C. H. Applications of soft sets in ideal theory of BCK/BCI-algebras, Inform. Sci. 178, 2466–2475, 2008. CR - Jun, Y. B., Xu, Y. and Ma, J. Redefined fuzzy implicative filters, Inform. Sci. 177, 1422– , 2007. CR - Jun, Y. B., Xu, Y. and Qin, K. Fuzzy filters redefined in lattice implication algebras, J. Fuzzy Math. 14, 345–353, 2006. CR - Maji, P. J., Roy, A. R. and Biswas, R. An application of soft sets in a decision making problem, Comput. Math. Appl. 44, 1077–1083, 2002. CR - Maji, P. K., Biswas, R. and Roy, A. R. Soft set theory, Comput. Math. Appl. 45, 555–562, Molodtsov, D. Soft set theory - First results, Comput. Math. Appl. 37, 19–31, 1999. CR - Pu, P. M. and Liu, Y. M. Fuzzy topology I, Neighborhood structure of a fuzzy point and Moore-Smith convergence, J. Math. Anal. Appl. 76, 571–599, 1980. CR - Xu, Y. Lattice implication algebras, J. Southeast Jiaotong Univ. (in Chinese) 1, 20–27, 1993. CR - Xu, Y. and Qin, K. Y. On fuzzy filters of lattice implication algebras, J. Fuzzy Math. 1, –260, 1993. CR - Xu, Y., Ruan, D., Qin, K. and Liu, J. Lattice-valued Logic (Springer, Berlin, 2003). CR - Zadeh, L. A. From circuit theory to system theory, Proc. Inst. Radio Eng. 50, 856–865, 1962. CR - Zadeh, L. A. Toward a generalized theory of uncertainty (GTU)-an outine, Inform. Sci. 172, –40, 2005. CR - Zhan, J., Chen, Y. and Tan, Z. Fuzzy fantastic filters of lattice implication algebras, Sci. Math. Japon 59, 159–161, 2004. CR - Zhan, J. and Jun, Y. B. Notes on redefined fuzzy implicative filters of lattice implication algebras, Inform. Sci. 179, 3182–3186, 2009. CR - Zhan, J. and Tan, Z. On n-fold fuzzy implicative filters of lattice implication algebras, J. Fuzzy Math. 14, 103–123, 2006. CR - Zhan, J. and Xu, Y. Generalized fuzzy filters of lattice implication algebras, FSKD, IEEE Computer Society 6, 281–283, 2009. UR - https://dergipark.org.tr/en/pub/hujms/issue//101416 L1 - https://dergipark.org.tr/en/download/article-file/86541 ER -