Why Sugeno lambda-Measures

Authors

Hung T. Nguyen, New Mexico State University - Main CampusFollow
Vladik Kreinovich, The University of Texas at El PasoFollow
Joe Lorkowski, The University of Texas at El PasoFollow
Saiful Abu, The University of Texas at El PasoFollow

Publication Date

2-2015

Comments

Technical Report: UTEP-CS-15-17

Abstract

To describe expert uncertainty, it is often useful to go beyond additive probability measures and use non-additive (fuzzy) measures. One of the most widely and successfully used class of such measures is the class of Sugeno lambda-measures. Their success is somewhat paradoxical, since from the purely mathematical viewpoint, these measures are -- in some reasonable sense -- equivalent to probability measures. In this paper, we explain this success by showing that while mathematically, it is possible to reduce Sugeno measures to probability measures, from the computational viewpoint, using Sugeno measures is much more efficient. We also show that among all fuzzy measures equivalent to probability measures, Sugeno measures (and a slightly more general family of measures) are the only ones with this property.