We define a possibilistic disjunctive logic programming approach for modeling uncertain, incomplete and inconsistent information. This approach introduces the use of possibilistic disjunctive clauses which are able to capture incomplete information and incomplete states of a knowledge base at the same time. This approach is computable and moreover allows encoding uncertain information by using either numerical values or relative likelihoods. In order to define the semantics of the possibilistic disjunctive programs, three approaches are defined: 1.- The first is strictly close to the proof theory of possibilistic logic and answer set models; 2.- The second is based on partial evaluation, a fix-point operator and answer set models; and 3.- The last is also based on the proof theory of possibilistic logic and pstable semantics. In order to manage inconsistent possibilistic logic programs, a preference criterion between inconsistent possibilistic models is defined; in addition, the approach of cuts for restoring consistency of an inconsistent possibilistic knowledge base is adopted. The approach is illustrated by a medical scenario.