This paper is aimed at proving the existence of a solution to the Volterra-Hamerstain integral equations in Partially-ordered spaces. To this end, some fixed point theorems are proved in this kind of spaces.

Let ℳ be a family of monomorphisms in the category A. To study mathematical notions in a category A, such as injectivity, tensor products, flatness, with respect to a class M of its (mono) morphisms , one should know some of the categorical properties of the pair (A, M). In this paper we take A to be the category Pos-S of S-Partially ordered sets and M=Mpo to be a particular class of monomorphisms, to be called Partially ordered regular pure (po-pure)} monomorphisms paper In this. we investigate some categorical properties such as limits and colimits for this class.

In this paper, we introduce a new class of (semi)hypergroup from a given (Partially) quasi-ordered (semi) hypergroup as a generaliza- tion of "El-hyperstructures". Then, we study some basic properties and important elements belong to this class.

In this paper, a concept of generalized weakly contraction map-pings in Partially ordered fuzzy metric spaces is introduced and coincidence point theorems on Partially ordered fuzzy metric spaces are proved. Also, as the corollary of these theorems, some common fixed point theorems on Partially ordered fuzzy metric spaces are presented.

We introduce a new method for ranked set sampling with multiple criteria. The method relaxes the restriction of selecting just one individual variable from each ranked set. Under the new method for ranking, units are ranked in sets based on linear extensions in Partially order set theory with considering all variables simultaneously. Results willbe evaluated by a relatively extensive simulation studies on Bivariate normal distribution and two real case studies on commercial and medicinal use of flowers, and the pollution of herb-layer by Lead, Cadmium, Zinc and Sulfur in some regions of the southwest of Germany.

In this paper, pretopological and topological operators are introduced based on Partially continuous linear transformations of the membership and non-membership functions for intuitionistic fuzzy sets. They turn out to be a generalization of the topological operators for intuitionistic fuzzy sets. On the other hand it is a generalization of the fuzzy set pretopological operators introduced by Wenzhong and Kimfung.

The starting point of this paper is given by Priestley’s papers, where a theory of representation of distributive lattices is presented. The purpose of this paper is to develop a representation theory of fuzzy distributive lattices in the finite case. In this way, some results of Priestley’s papers are extended. In the main theorem, we show that the category of finite fuzzy Priestley spaces is equivalent to the dual of the category of finite fuzzy distributive lattices. Several examples are also presented.