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.

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