In this paper, the concept of intuitionistic fuzzy soft sets is applied to residuated lattices. The notion of intuitionistic fuzzy soft filters of a residuated lattice is introduced and some related properties are investigated. Then the representations of generated intuitionistic fuzzy soft filters are established. We prove that the lattice of all intuitionistic fuzzy soft filters of a residuat...

In this paper, we propose an extension of connected filters into the fuzzy set framework. We introduce a modeling of imprecision via the introduction of the fuzzy umbra image concept which allows us to express fuzzy connected operators for fuzzy gray scale images. Using this new tool, a set of filters families is proposed and their properties are discussed. The expression of classical filters i...

The logical foundations of processes handling uncertainty in information use some classes of algebras as algebraic semantics. The sets of provable formulas in corresponding inference systems from the point of view of uncertain information can be described by fuzzy filters of those algebraic semantics. Bounded residuated lattice ordered monoids (R`-monoids) are a common generalization of pseudo ...

The concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set is considered. In fact, this is a generalization of quasi-coincidence of a fuzzy point with a fuzzy set. By using this new idea, the notion of interval valued (∈,∈ ∨q)-fuzzy filters in BL-algebras which is a generalization of fuzzy filters of BL-algebras, is defined, and related properties are investiga...

Neutrosophic set is a new mathematical tool for handling problems involving imprecise, indeterminacy and inconsistent data. Pseudo-BCI algebra is a kind of non-classical logic algebra in close connection with various non-commutative fuzzy logics. Recently, we applied neutrosophic set theory to pseudo-BCI algebras. In this paper, we study neutrosophic filters in pseudo-BCI algebras. The concepts...

We give the simple general principle of studying the relations among fuzzy t-filters on residuated lattices. Using the general principle, we can easily determine the relations among fuzzy t-filters on different logical algebras.