In this paper we consider some fundamental properties of generalized rough sets induced by binary relations on algebras and show that 1. Any reflexive binary relation determines a topology. 2. If h… (More)

In this paper we consider fundamental properties of some types of filters (Boolean, positive implicative, implicative and fantastic filters) of BL algebras defined in Haveshki et al. (Soft Comput… (More)

We show in this paper that almost all results proved in many papers about fuzzy algebras can be proved uniformly and immediately by using so-called “Transfer Principle”.

In this work, four modal-like operators on Boolean lattices are introduced and their theory is presented from lattice-theoretical, topological an d lgebraic point of view. It is also shown how rough… (More)

In this short paper we give an affirmative answer to the problem left open in [3], that is, for any residuated lattice, if prime filters and prime filters of the second kind coincide, then must be an… (More)

We give a characterization theorem of extended filters on residuated lattices, from which many results are immediately obtained. We show that, for a bounded integral commutative residuated lattice X,… (More)

We consider the relationship between ideals of a BCI-algebra and order ideals of its adjoint semigroup. We show that (1) if I is an ideal, then I =M−1(M(I)), (2)M(M−1(J)) is the order ideal generated… (More)