Modeling flexibility, vagueness and uncertainty in Operations Research

During the last four decases a large number of primarily mathematical methods have been developed and applied in Operations Research. These methods normally require that a problem has been formally modelled adequately. This modelling-even though recognized as an important task of Operations Research-is still not supported well by efficient modelling aids. The lack of modelling tools is particularly regrettable if the problems to be solved are ill-structured, and often leads to a rejection of the use of Operational Research OR methods for that type of problem, i.e. the restriction of the use of Operational Research OR approaches to well-structured problems only. In the recent past the emergence of Expert Systems as one possibly interesting potential tool for Operations Researchers has directed the attention of scientists as well as practitioners to ill-structured problems. Here the modelling of vagueness and uncertainty is of particular importance. Therefore it seems to be advisable for the Operations Researchers to study ways which are suited for modelling appropriately uncertainty. This paper sketches some of the most promising approaches in this direction such as the theory of evidence, possibility theory, and fuzzy set theory. It also describes the most promising application of these methods to problems in Operational Research OR.