Fuzzy Decision Theory

In real decision situations a decision maker (DM) is often confronted with the problem that the information which is necessary for constructing a classical decision model is not available, or the cost for getting this information seems too high. Subsequently, the DM abstains from constructing a decision model; the DM fears that this model is not an authentic image of the real problem. Fuzzy set theory offers the possibility to construct decision models with vague data. Many decision models with fuzzy components are proposed in literature, but only fuzzy consequences and fuzzy probabilities are important for practical applications. Therefore, the focus of this paper is concentrated on these subjects. It is shown that the principle of Bernoulli can easily be extended to decision models with fuzzy utilities. Furthermore it is possible to use additional information in order to improve the prior probabilities. Moreover, fuzzy probabilities can be used combined with crisp utilities, described by real numbers, or fuzzy utilities. Apart from the fact that fuzzy models offer a more realistic modeling of decision situations, the proposed interactive solution process leads to a reduction of information costs. That circumstance is caused by the fact that additional information is gathered in correspondence with the requirements and under consideration of cost–benefit relations.