Concluding Remarks

Decision-making under uncertainty accompanies all human activity, and so it is difficult to locate the beginnings of research in this field. At any rate, the consideration of problems in which nothing was known about the parameter but the set of its possible values—total uncertainty problems—can be found already in the work of Johann Bernoulli, Laplace, and Bayes alongside problems in which the unknown parameter was random with a given distribution. However, the “principle of insufficient foundation” (Bayes postulate) suggested therein, which in the case of total uncertainty recommended the consideration of all values of the unknown parameter as equiprobable, eventually proved to be logically inconsistent, and in 1854 it was subjected to serious criticism by J. Bull [29]. Attempts to save this principle by a formalization of conditions under which it does not lead to contradictions (see, for example, [10]) were undertaken later, but the overwhelming majority of researchers preferred to eschew the principle entirely, and as a result, quite a number of approaches to problems with uncertainty appeared.