Possibilistic Aggregations in the Discrete Covering Problem: Application in the Problem of Optimal Choice of Alternatives

In this paper a new criterion is introduced for the discrete covering problem. In this criterion the a priori information represented by a possibility measure and a misbelief distribution on alternatives are condensed by aggregation instruments. Using the Dempster-Shafer belief structure and representations of a possibility measure through associated probabilities, a new criterion for discrete covering problem is constructed based on aggregation by the Most Typical Value (MTV), namely, Monotone Expectation (ME) (or Choquet integral). A bicriterial problem is obtained using a new criterion and the criterion of average price minimization. The example on the application of a new criterion is presented, where the possibility distribution on the optimal choice of the candidates (alternatives) is represented by expert valuations. Key–Words: Minimal fuzzy covering, possibility measure, associated probabilities, average misbelief criterion, MTV, ME, Dempster–Shafer belief structure