Some Generalizations of Possibility and Necessity Measures

摘要

Possibility measures were introduced by L. A. Zadeh [8] as an auxiliary tool for numerical characterization and processing of uncertainty involved in real life situations. Since then the original very simple notion of these measures viewed as functions defined on the powerset of a given universal set X to the unit interval [0,1] has been subjected to various modifications and generalizations. In this paper, some generalizations of possibility measures and their dual-necessity measures are considered and studied their properties. The domains of these measures are generalised to Boolean algebras, atomic Bollean algebras and L-fuzzy sets and co-domains to complete lattices and lattice intervals. Particular functions induced by generalized possibility distributions and satisfying the axiomatic requirements of lattice interval valued possibility and necessity measures are generated with the aid of extended fuzzy connectives and the conditions under which the measures will satisfy the natural relations are analysed.