Possibility distribution calculus and the arithmetic of fuzzy numbers

Abstract

Based on possibility theory and multi-valued logic and taking inspiration from the seminal work in probability theory by A. N. Kolmogorov, we aim at laying a hopefully equally sound foundation for fuzzy arithmetic. A possibilistic interpretation of fuzzy arithmetic has long been known even without taking it to its full consequences: to achieve this aim, in this paper we stress the basic role of the two limit-cases of possibilistic interactivity, namely deterministic equality versus non-interactivity, thus getting rid of weak points which have ridden more traditional approaches to fuzzy arithmetic. Both complete and incomplete arithmetic are covered.