Probabilistic Indices of Quality of Approximation

Abstract

A new index of quality of approximation, called the index of mutual information, is proposed in this chapter. It measures the mutual information between the relations respectively determined by condition and decision attributes. Its computation is based on the comparison of two graphs, each one representing a set of attributes. Applications in the context of indiscernibility as well as in the context of dominance relations are considered. The combination of the new measurement approach with the transformation into probabilities of being the preferred option is also explored. A procedure to select the most important attributes is outlined. Illustrative examples are provided.