Comparing poly-interval alternatives: “mean-risk” method

For poly-interval objects, such as generalized interval estimations and fuzzy values, are proposed methods to calculate numerical characteristics, which are similar to characteristics of distribution functions of probability theory (mathematical expectation, variance, average semideviation). The methods are based on the defuzzification of interval estimates of the indicated numerical characteristics in the case of fuzzy poly-interval objects and on the representation of generalized interval estimations as a probability mixture of distributions forming such generalized estimations. These results allow extend the well-known “mean-risk” method, which is usually used for comparing mono-interval values on their preference and risk, to the case of poly-interval estimations.