Betweenness,Łukasiewicz Rough Inclusions,Euclidean Representations in Information Systems,Hyper–granules and Conflict Resolution *

Abstract

In this work, we approach the problem of data analysis from a new angle: we investigate a relational method of separation of data into disjoint sub–data employing a modified betweenness relation, successfully applied by us in the area of behavioral robotics, and, we set a scheme for applications to be studied. The effect of the action by that relation on data is selection of a sub–data, say, ‘kernel’ with the property that each thing in it is a convex combination, in a sense explained below, of some other things in the kernel. One can say that kernel thus exhibited is ‘self–closed’. Algorithmically, this is achieved by means of a new construct, called by us a ‘dual indiscernibility matrix’. On the other hand, the complement to kernel consists of things in the data, which have some attribute values not met in any other thing. It is proper to call this complement to kernel the residuum. We examine both the kernel and the residuum from the point of view of quality of classification into decision classes for a few standard data sets from the UC Irvine Repository finding the results very satisfactory. Conceptually, our work is set in the framework of rough set theory and rough mereology and the main tool in inducing of the betweenness relation is the Łukasiewicz rough inclusion. Apart from the classification problem, we propose some strategies for conflict resolution based on concepts introduced in this work, and in this way we continue conflict analysis in rough set framework initiated by Zdzisław Pawlak.