Exhaustive zero-convergence structures on Boolean algebras
Let be a periodic time scale. The purpose of this paper is to use a modification of Krasnoselskii’s fixed point theorem due to Burton to prove the existence of periodic solutions on time scale of the nonlinear dynamic equation with variable delay , , where is the -derivative on and is the -derivative on . We invert the given equation to obtain an equivalent integral equation from which we define a fixed point mapping written as a sum of a large contraction and a compact map. We show...
Two categories and of fuzzy sets over an -algebra are investigated. Full subcategories of these categories are introduced consisting of objects , , where is a subset of all extensional subobjects of an object . It is proved that all these subcategories are quasi-reflective subcategories in the corresponding categories.
The main goal of this paper is to construct fuzzy connectives on algebraic completely distributive lattice(ACDL) by means of extending fuzzy connectives on the set of completely join-prime elements or on the set of completely meet-prime elements, and discuss some properties of the new fuzzy connectives. Firstly, we present the methods to construct t-norms, t-conorms, fuzzy negations valued on ACDL and discuss whether De Morgan triple will be kept. Then we put forward two ways to extend fuzzy implications...