The choice of a measure of comparison in granular learning methods

Maria Rifqi (1) , Vincent Berger (2) , Bernadette Bouchon-Meunier (1)

1 APA - Apprentissage et Acquisition des connaissances
2 MPQ (UMR_7162) - Laboratoire Matériaux et Phénomènes Quantiques

This paper gives an explicit method to choose a measure of comparison. The proposed solution lies in a new representation of measures of comparison obtained by normalization of arguments. This normalization leads to a desirable property: measures of comparison do not depend on the scale of the system. Another consequence of this normalization is the fact that measures of satisfiability can be described by a unique argument and measures of resemblance by two arguments. The analysis of behaviours of measures of comparison is easy thanks to a geometrical interpretation and to a natural definition of the power of discrimination of a given measure of comparison. We focus on two families of measures of similitude: measures of satisfiability and measures of resemblance. For each family, we discuss the role of the new parameter we point out and we propose new measures satisfying particular properties. For measures of satisfiability, the parameter $\phi$ controls the severity towards difference between sets whereas the parameter $\rho$ penalizes the differences between two sets for a measure of resemblance.

Domaines: Informatique [cs]; Intelligence artificielle [cs.AI]

Maria Rifqi, Vincent Berger, Bernadette Bouchon-Meunier. The choice of a measure of comparison in granular learning methods. North American Fuzzy Information Processing Society Annual Meeting, NAFIPS 1999, Jun 1999, New York, United States. pp.218-222, ⟨10.1109/NAFIPS.1999.781686⟩. ⟨hal-01075371⟩