The pairwise comparisons method is a powerful tool used for establishing the relative order between different concepts in situations in which it is difficult (or sometimes even impossible) to provide explicit rating. Appropriate ratings are determined by solving eigenvalue problem for the pairwise comparisons matrix. This study presents a new iterative heuristic rating estimation algorithm that tries to deal with the situation when exact estimations for some concepts (stimulus) C K are a priori known and fixed, whilst the estimates for the others (unknown concepts C U ) need to be computed. The relationship between the local estimation error, understood as the average absolute error E(c) over all direct estimates for the concept c ∈ C U and the pairwise comparisons matrix inconsistency index is shown. The problem of convergence of subsequent intermediate results is discussed and the convergence conditions are given.

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The Heuristic Ratio Estimation (HRE) approach proposes a new way of using the pairwise comparisons matrix. It allows the assumption that the weights of some alternatives (herein referred to as concepts) are known and fixed, hence the weight vector needs to be estimated only for the other unknown values. The main purpose of this paper is to extend the previously proposed iterative HRE algorithm and present all the heuristics that create a generalized approach. Theoretical considerations are accompanied by a few numerical examples demonstrating how the selected heuristics can be used in practice.

SUMMARYIncreasing demand for computationally efficient algorithms and processors has turned the attention of researchers toward parallel and concurrent solutions. Because the frequency of contemporary processors cannot be tweaked infinitely, the only hopes for squeezing more performance from computers are parallel processing and parallel computation. The important part of every parallel solution is concurrent data structures, which allow multithread programming environments to be taken advantage of. In this article, a new concurrent dynamic set structure is proposed. It is based on the van Emde Boas trees concept, where on every node of a tree, an array of the node's children is stored. The structure is equipped with a simple but effective locking algorithm, which allows it to be used concurrently by any number of threads. The presented algorithm idea is accompanied by an experimental implementation written in JAVA 6. Preliminary tests prove that, especially for moderately larger data sets with a predominance of read operations, the concurrent van Emde Boas array proposed in this article may be a viable alternative for other structures providing a similar functionality.