The compability index G. Creating an index of closeness within weighted enviroment

Abstract

This article addresses the problem of measuring closeness in weighted environments (decision-making environments). The article belongs to the field of mathematical modelling based in order topology. The relevance of this article is related with having a dependable cardinal measure of distance in weighted environments (order topology). Weighted environments is a no isotropic structure where the different directions (axes) may have different importance (weight) hence, there exist privilege directions. In this kind of structure is very important to have a cardinal reliable index, able to say how close or compatible is the set of measures of one individual with respect to the group (or to anyone other). Or how close is one pattern of behavior to another or in some special cases to assess how good a rule of measurement or index, built with any cardinal MCDM method is.  Common examples of application of this is the interaction between actors in a decision making process (system values interaction), matching profiles, pattern recognition, and any situation where a process of measurement with qualitative variables is involved.