Description: Theoretical-probabilistic methods are widely and successfully used in research for modeling aspects of uncertainty and fuzziness reflecting the incompleteness of knowledge or their unreliability. But theoretical-probabilistic methods proved to be ineffective in the simulation of a wide class of processes and phenomena in which the crucial role is played by uncertainty and obscurity. It is a question of modeling complex physical, social and economic systems, subjective judgments for modeling and research which can not be performed by statistical tests. In this paper, the goal is to construct a generalized model of the theory of possibility by using, in addition to the measure of possibilities the measure necessity and the mathematical justification of such a model of space of possibilities. The construction of a theory clearly follows the scheme of probability theory. This allows us to follow the formal analogies and differences between the concepts and methods of probability theory and the theory of possibilities. The most significant difference between this theories is the interpretation of the physical content of an event, which is described in terms of possibilities. This is significantly different from frequency interpretation in terms of probabilities. This allows you to simulate and explore a much wide class of tasks than would be possible to do with probability theory methods.
Keywords: space model, measure of necessarily, measure of possibility, continuation of measures