Fuzzy Membership, Possibility, Probability and Negation in Biometrics

Abstract

This paper proposes a new formalization of the classical probability-possibility relation, which is further confirmed as a much complex, but natural provabilityreachability-possibility-probability-fuzzy membership-integrability interconnection. Searching for the right context in which this relation can be consistently expressed for the particular case of experimentally obtained iris recognition results brought us to a natural (canonic) and universal fuzzification procedure available for an entire class of continuous distributions, to a confluence point of statistics, classical logic, modal logic, fuzzy logic, system theory, measure theory and topology. The applications-initially intended for iris recognition scenarios-can be easily extrapolated anywhere else where there is a need of expressing the relation possibility-probability-fuzzy membership without weakening the σ-additivity condition within the definition of probability, condition that is considered here as the actual principle of possibility-probability consistency.