Statistical and fuzzy optimal decisions: I. Statistical decisions

In the proposed series of two articles, the methods of optimal statistical and fuzzy (possibility-theoretical) decisions are described from a unified point of view. In the second article [22], we consider the possibility-theoretical methods for optimal decisions (to be more precise, optimal identification methods or, in other words, methods for optimal choice of one of a number of alternative hypotheses concerning the affiliation of the object of investigation to one of a finite number of classes), as well as the methods for optimal estimation of fuzzy elements. The quality of the decision is determined in terms of the risk of losses accompanying the decision and is characterized by the values of possibility and/or inevitability of losses. The presentation follows the scheme adopted in the theory of statistical decisions [16, 17]. In the present work, which is the first in the series, elements of statistical decision theory, whose analogs were obtained in [22] and which make it possible to reconstruct the possibility empirically, are presented for the convenience of the readers who want to trace the analogy between the probability-theoretical methods and the possibility-theoretical methods for decision optimization [22]. © Pleiades Publishing, Inc., 2006.