r-Bounded Fuzzy Measures are Equivalent to epsilon-Possibility Measures

Authors

Karen A. Richart-Ruiz, The University of Texas at El PasoFollow
Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

6-2014

Comments

Technical Report: UTEP-CS-14-32a

Published in Proceedings of IEEE International Conference on Systems, Man, and Cybernetics SMC'2014, San Diego, California, October 5-8, 2014, pp. 1229-1234.

Abstract

Traditional probabilistic description of uncertainty is based on additive probability measures. To describe non-probabilistic uncertainty, it is therefore reasonable to consider non-additive measures. An important class of non-additive measures are possibility measures, for which m(A union B) = max(m(A), m(B)). In this paper, we show that possibility measures are, in some sense, universal approximators: for every epsilon > 0, every non-additive measure which satisfies a certain reasonable boundedness property is equivalent to a measure which is epsilon-close to a possibility measure.