Possibility: Fundamental Numerical Characteristics, Distributions and Measures

Abstract

In automatic, and especially automatized, control, indiscriminability of the outcomes in the multioutcome situations (for example, states of the controlled plants or values of the quantitative characteristics) often is the stumbling block. Some of the indiscriminable outcomes can lead to grave consequences, and the space of all outcomes cannot be probabilistic because of the lack of statistical regularity. Under these conditions, the models of possibility that are developed mostly at the abstract level within the framework of the fuzzy set theory are more adequate than the existing ones. The paper introduced the empirically motivated fundamental numerical characteristics allowing one to render a natural quantitative sense to the models of possibility. The distributions of the possibilities of outcome occurrences and the event measures that are of practical interest were constructed.