A Restriction Level Approach to the Representation of Imprecise Properties

D. Sánchez, M. Delgado, M.A. Vila.

In this paper we introduce an alternative representation of imprecise properties that verify all the logical equivalencies of the crisp case. An imprecise property (or proposition) on the objects of an universe X is represented by a collection of crisp realizations, each one corresponding to a Restriction Level (RL). A fuzzy subset of X can be seen as a summary of a RL-representation, both representations being equivalent only for the combination of atomic properties via maximum and minimum. Our approach allows us to extend crisp operations to the imprecise case, keeping all the properties of the crisp case, notably those involving negation.

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