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Possibilistic networks constitute a promising framework for efficient treatment of uncertain and imprecise information in knowledge-based systems. In this paper, we propose a new method for induction of the structure (the qualitative part) and the attached possibility distributions (the quantitative part) of a possibilistic network from a database of sample cases that may contain imprecise or missing values. ; It turns out that a modified random-set approach to the semantics of possibility distributions is adequate to provide a possibilistic interpretation of the databases under consideration. Since constructing a possibilistic network can be viewed as a generalization of the structure identification problem in relational data, we have to overcome well-known complexity problems. ; Therefore we present an efficient Greedy search structure induction algorithm for possibilistic networks that has successfully been applied to construct a non-trivial network of practical interest from a given database.