Filter theory in MTL-algebras based on Uni-soft property

Document Type : Research Paper


1 Department of Mathematics‎, ‎University of Tabuk‎, ‎Tabuk 71491‎, ‎Saudi Arabia.

2 Department of Mathematics‎, ‎King Abdulaziz University‎, ‎P.O‎. ‎Box 80203 Jeddah 21589‎, ‎Saudi Arabia.

3 Department of Mathematics‎, ‎College of basic education‎, ‎Public authority for applied education and training‎, ‎Kuwait.


‎The notion of (Boolean) uni-soft filters‎ ‎in MTL-algebras is introduced‎, ‎and several properties of them are‎ ‎investigated‎. ‎Characterizations of (Boolean) uni-soft filters are discussed‎, ‎and some (necessary and sufficient) conditions‎ ‎for a uni-soft filter to be Boolean are provided‎.
‎The condensational property for a Boolean uni-soft filter is established.


Main Subjects

N. Cagman, F. Citak and S. Enginoglu, Soft set theory and uni-int decision making, Eur. J. Oper. Res. 207 (2010) 848--855.
D. Chen, E.C.C. Tsang, D.S. Yeung and X. Wang, The parametrization reduction of soft sets and its applications, Comput. Math. Appl. 49 (2005) 757--763.
F. Esteva and L. Godo, Monoidal t-norm based logic: towards a logic for left-continuous t-norms, Fuzzy Sets and Systems 124 (2001) 271--288.
P. Hajek, Metamathematics of Fuzzy Logic, Kluwer Academic Press, Dordrecht, 1998.
P.K. Maji, R. Biswas and A.R. Roy, Soft set theory, Comput. Math. Appl. 45 (2003) 555--562.
P.K. Maji, A.R. Roy and R. Biswas, An application of soft sets in a decision making problem, Comput. Math. Appl. 44 (2002) 1077--1083.
D. Molodtsov, Soft set theory-first results, Comput. Math. Appl. 37 (1999) 19--31.
E. Turunen, BL-algebras of basic fuzzy logic, Mathware Soft Comput. 6 (1999) 49--61.