Distance and similarity measures between uncertain variables

Abstract

Uncertainty theory is a branch of mathematics based on normality, monotonicity, self-duality, countable subadditivity, and product measure axioms. Different from randomness and fuzziness, uncertainty theory provides a new mathematical model for uncertain phenomena. Distance and similarity measure have played an important role in uncertainty theory as well as many other disciplines. This paper first proposes some new distances between uncertain variables. Then the definition of the degree of similarity between uncertain variables is introduced and several similarity measures between uncertain variables are generated from distance measures. Finally, the distance and similarity measures proposed are applied to pattern recognition.