# FILTERS OF RESIDUATED LATTICES BASED ON SOFT SET THEORY

• JUN, YOUNG BAE (Department of Mathematics Education Gyeongsang National University) ;
• LEE, KYOUNG JA (Department of Mathematics Education Hannam University) ;
• PARK, CHUL HWAN (Faculty of Mechanical Engineering Ulsan College) ;
• ROH, EUN HWAN (Department of Mathematics Education Chinju National University of Education)
• Published : 2015.06.30
• 73 7

#### Abstract

Strong uni-soft filters and divisible uni-soft filters in residuated lattices are introduced, and several properties are investigated. Characterizations of a strong and divisible uni-soft filter are discussed. Conditions for a uni-soft filter to be divisible are established. Relations between a divisible uni-soft filter and a strong uni-soft filter are considered.

#### Keywords

residuated lattice;(divisible, strong) filter;uni-soft filter;divisible uni-soft filter;strong uni-soft filter

#### References

1. R. Belohlavek, Some properties of residuated lattices, Czechoslovak Math. J. 53(123) (2003), no. 1, 161-171. https://doi.org/10.1023/A:1022935811257
2. N. Cagman and S. Enginoglu, Soft set theory and uni-int decision making, European J. Oper. Res. 207 (2010), no. 2, 848-855. https://doi.org/10.1016/j.ejor.2010.05.004
3. F. Esteva and L. Godo, Monoidal t-norm based logic: towards a logic for left-continuous t-norms, Fuzzy Sets and Systems 124 (2001), no. 3, 271-288. https://doi.org/10.1016/S0165-0114(01)00098-7
4. P. Hajek, Metamathematics of Fuzzy Logic, Kluwer Academic Press, Dordrecht, 1998.
5. Y. B. Jun, S. S. Ahn, and K. J. Lee, Classes of int-soft filters in residuated lattices, The Scientific World J. 2014 (2014), Article ID 595160, 12 pages.
6. Y. B. Jun and S. Z. Song, Uni-soft filters and uni-soft G-filters in residuated lattices, J. Comput. Anal. Appl. (in press).
7. Z. M. Ma and B. Q. Hu, Characterizations and new subclasses of I-filters in residuated lattices, Fuzzy Sets and Systems 247 (2014), 92-107. https://doi.org/10.1016/j.fss.2013.11.009
8. P. K. Maji, R. Biswas, and A. R. Roy, Soft set theory, Comput. Math. Appl. 45 (2003), no. 4-5, 555-562. https://doi.org/10.1016/S0898-1221(03)00016-6
9. D. Molodtsov, Soft set theory - First results, Comput. Math. Appl. 37 (1999), no. 4-5, 19-31.
10. J. G. Shen and X. H. Zhang, On filters of residuated lattice, Chinese Quart. J. Math. 21 (2006), no. 3, 443-447.
11. E. Turunen, BL-algebras of basic fuzzy logic, Mathware Soft Comput. 6 (1999), no. 1, 49-61.
12. E. Turunen, Boolean deductive systems of BL-algebras, Arch. Math. Logic 40 (2001), no. 6, 467-473. https://doi.org/10.1007/s001530100088
13. X. H. Zhang, H. Zhou, and X. Mao, IMTL(MV)-filters and fuzzy IMTL(MV)-filters of residuated lattices, J. Intell. Fuzzy Systems 26 (2014), no. 2, 589-596.
14. Y. Q. Zhu and Y. Xu, On filter theory of residuated lattices, Inform. Sci. 180 (2010), no. 19, 3614-3632. https://doi.org/10.1016/j.ins.2010.05.034