Order-Compatible Topologies on a Partially Ordered Set

Order-compatible Topologies on a Partially Ordered Set

On Partially Ordered Sets Possessing a Unique Order-compatible Topology

1. Introduction. Let A" be a partially ordered set (poset) with respect to a relation ^, and possessing least and greatest elements O and / respectively. Let us call a subset S of A" up-directed (down-directed) if and only if for all xES and y ES there exists zGS such that 3^x, z^y (z^x, z^y). Following McShane [2], we call a subset K of X Dedekind-closed if and only if whenever S is an up-dire...

Sampling of Multiple Variables Based on Partially Ordered Set Theory

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...

On the Structure of Indiscernibility Relations Compatible with a Partially Ordered Set

In a recently published work the author investigates indiscernibility relations on information systems with a partially ordered universe. Specifically, he introduces a notion of compatibility between the (partially ordered) universe and an indiscernibility relation on its support, and establishes a criterion for compatibility. In this paper we make a first step in the direction of investigating...

Searching On Division Partially Ordered Set

Let P = {pi|i = 1, 2, . . . , n} be a set of n elements with partial order defined as follows: pi ≤ pj if and only if i divides j. Assume real numbers are assigned to all members of P in an order preserving manner, this results in a set A of n real numbers. Given an unknown x ∈ R, we want to determine whether x is belong to A or not, by comparing x with as few elements of A as possible. We pres...