In this paper, we introduce the notion of fuzzy n-fold integral lter in BL-algebras and we state and prove several properties of fuzzy n-fold integral lters. Using a level subset of a fuzzy set in a

In this paper, some fundamental properties of maximal µ-open sets such as decomposition theorem for a maximal µ-open set, are given in a generalized topological space. Some basic properties of intersection of maximal µ-open sets are established, cohere the law of µ-radical µ-closure in a quasi topological space is obtained, among the other things.

In this paper we characterize both the Cliord and left Cliord ordered semigroups by their bi-ideals and quasi-ideals. Also we characterize principal bi-ideal generated by an ordered idempotent in a completely regular ordered semigroup.

Four-part semigroups form a new class of semigroups which became important when sets of Boolean operations which are closed under the binary superposition operation f + g := f(g;:::;g), were studied. In this paper we describe the lattice of all subsemigroups of an arbitrary four-part semigroup, determine regular and idempotent elements, regular and idempotent subsemigroups, homomorphic images, Green’s relations, and prove a representation theorem for four-part semigroups.

Let pn/qn = [a0;a1,…,an] be the n‐th convergent of the continued fraction expansion of [a0;a1,a2,…]. Leaping convergents are those of every r‐th convergent prn+i/qrn+i(n = 0,1,2,…) for fixed integers r and i with r⩾2 and i = 0,1,…,r−1. The leaping convergents for the e‐type Hurwitz continued fractions have been studied. In special, recurrence relations and explicit forms of such leaping convergents have been treated. In this paper, we consider recurrence relations and explicit forms of the leaping convergents for some different types of Hurwitz continued fractions.

The paper considers an algebraic notion of automorphic equivalence of models and of multi-models. It is applied to the solution of the problem of informational equivalence of knowledge bases. We show that in the case of linear subjects of knowledge the problem can be reduced to the well-known in computational group theory problems about isomorphism and conjugacy of subgroups of a general linear group.

We show that for an arbitrary Set-endofunctor T the generalized membership function given by a sub-cartesian transformation μ from T to the filter functor F can be alternatively defined by the collection of subcoalgebras of constant T -coalgebras. Sub-natural transformations e between any two functors S and T are shown to be sub-cartesian if and only if they respect μ. The class of T -coalgebras whose structure map factors through e is shown to be a covariety if e is a natural and sub-cartesian mono-transformation.