Theory of Opportunity

Opportunity theory is a mathematical theory dealing with a special type of uncertainty , alternative to probability theory . Professor Lotfi Zadeh first introduced the theory of possibilities in 1978 as an extension of his theories of fuzzy sets and fuzzy logic . D. Dubois and H. Prade later contributed to its development. Earlier, in the 1950s, economist J. Shackle proposed min / max algebra to describe the extent of potential surprises. In the late 1990s, Professor of Moscow State University Yu. P. Pytiev proposed a variant of the theory of possibilities, in which the possibility and necessity are determined by the values ​​of the linear countable-additive functional (integral).

The meaningful interpretation of probability-theoretical methods differs significantly from probability-theoretical methods. The possibility of an event, in contrast to the probability, which estimates the frequency of its occurrence in a regular stochastic experiment, is focused on a relative assessment of the truth of this event, its preference in comparison with any other. That is, only the relations “more”, “less” or “equal” can be meaningfully interpreted. At the same time, the possibility does not have an event-frequency interpretation (as opposed to probability), which connects it with experiment. Nevertheless, the theory of possibilities allows mathematically simulating reality on the basis of experimental facts, knowledge, hypotheses, and the opinions of researchers.