Fuzzy Membership, Possibility, Probability and Negation in Biometrics

This paper proposes a new formalization of the classical probability-possibility relation, which is further confirmed as a much complex, but natural provability – reachability 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.