A theory of possibility distributions
Abstract Possibility distributions form a widely accepted method for representing a certain type of uncertain knowledge. As yet, most mechanisms for processing possibility distributions have been founded on intuitive argumentation only. As a solution a comprehensive, mathematically sound theory of possibility distributions is proposed that is based on three simple axioms and the Principle of Minimal Specificity. Possibilistic knowledge-bases are represented by sets of possibility distributions. Inferring information from a knowledge-base is interpreted as combining its possibility distributions into the most specific one we are allowed to infer. On these assumptions it is shown in particular that the max—min-composition is an unambiguous mechanism for the aggregation of possibility distributions that are defined on different and freely chosen subspaces of a given Cartesian product of universes. A special type of possibility distribution ( Possibilistic Relation of Dependence or PROD ) is postulated as a description of dependencies between variables. They play an important role in a theory of possibilistic fuzzy systems that is presented as a general framework for fuzzy modeling of real-world problems.