Yang XU, Jianming ZHAN

Soft Lattice Implication Algebras Based on Fuzzy Sets

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.

Keywords:

(Implicative) filter (Implicative) filteristic soft lattice implication algebra, 2000 AMS Classification: 03 B 05,

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Aktas, H. and Cagman, N. Soft sets and soft groups, Inform. Sci. 177, 2726–2735, 2007.
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.
Jun, Y. B. and Park, C. H. Applications of soft sets in ideal theory of BCK/BCI-algebras, Inform. Sci. 178, 2466–2475, 2008.
Jun, Y. B., Xu, Y. and Ma, J. Redefined fuzzy implicative filters, Inform. Sci. 177, 1422– , 2007.
Jun, Y. B., Xu, Y. and Qin, K. Fuzzy filters redefined in lattice implication algebras, J. Fuzzy Math. 14, 345–353, 2006.
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.
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.
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.
Xu, Y. Lattice implication algebras, J. Southeast Jiaotong Univ. (in Chinese) 1, 20–27, 1993.
Xu, Y. and Qin, K. Y. On fuzzy filters of lattice implication algebras, J. Fuzzy Math. 1, –260, 1993.
Xu, Y., Ruan, D., Qin, K. and Liu, J. Lattice-valued Logic (Springer, Berlin, 2003).
Zadeh, L. A. From circuit theory to system theory, Proc. Inst. Radio Eng. 50, 856–865, 1962.
Zadeh, L. A. Toward a generalized theory of uncertainty (GTU)-an outine, Inform. Sci. 172, –40, 2005.
Zhan, J., Chen, Y. and Tan, Z. Fuzzy fantastic filters of lattice implication algebras, Sci. Math. Japon 59, 159–161, 2004.
Zhan, J. and Jun, Y. B. Notes on redefined fuzzy implicative filters of lattice implication algebras, Inform. Sci. 179, 3182–3186, 2009.
Zhan, J. and Tan, Z. On n-fold fuzzy implicative filters of lattice implication algebras, J. Fuzzy Math. 14, 103–123, 2006.
Zhan, J. and Xu, Y. Generalized fuzzy filters of lattice implication algebras, FSKD, IEEE Computer Society 6, 281–283, 2009.