A Parametrized Model for Optimization with Mixed Fuzzy and Possibilistic Uncertainty

Abstract

Fuzzy and possibilistic uncertainty are very closely related, and sometimes coexist in optimization under uncertainty problems. Fuzzy uncertainty in mathematical programming problems typically represents flexibility on the part of the decision maker. On the other hand, possibilistic uncertainty generally expresses a lack of information about the values the parameters will assume.

Several models for mixed fuzzy and possibilistic programming problems have previously been published. The semantic interpretation of these models, however, is of questionable value. The mixed models in the literature find solutions in which the fuzzy uncertainty (or flexibility) and the possibilistic uncertainty (or lack of confidence in the outcome) are held to the same levels.

This chapter proposes a new mixed model which allows a trade-off between fuzzy and possibilistic uncertainty. This trade-off corresponds to a semantic interpretations consistent with human decision-making. The new model shares characteristics with multi-objective programming and Markowitz models. Model structure, semantic justification, and solution approaches are covered.