Majorization on a Partially Ordered Set

Majorization for partially ordered sets

We generalize the classical notion of majorization in Rn to a majorization order for functions defined on a partially ordered set P . In this generalization we use inequalities for partial sums associated with ideals in P . Basic properties are established, including connections to classical majorization. Moreover, we investigate transfers (given by doubly stochastic matrices), complexity issue...

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...

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...

Partitions of a Finite Partially Ordered Set

In this paper, we investigate the notion of partition of a finite partially ordered set (poset, for short). We will define three different notions of partition of a poset, namely, monotone, regular, and open partition. For each of these notions we will find three equivalent definitions, that will be shown to be equivalent. We start by defining partitions of a poset in terms of fibres of some su...

The Imbedding Operators on a Partially Ordered Set