Abstract: Main features of a new method of expert knowledge elicitation – method of generalized interval estimations – and peculiarities of its using in decision making are presented. Expert estimation of an analyzed quantitative parameter is defined in the framework of the method by a set of intervals. This set may be shown on a plane (X, Y) by a curvilinear trapezoid. If densities of probability distributions were defined on Y-axis (“weights” of different interval estimations at their set) and on X-axis (for all interval estimations at the set) we received generalized interval estimation (GIE) of the parameter. GIE method may be used at different directions. Firstly, we may reduce GIE to mono-interval estimation averaging distributions on X-axis, taking into account their weights, and use then famous probabilistic methods to analyze problem. The average distribution is in fact a probability mixture of distributions on intervals of their set. Secondly, we may study complete structure of interval estimations that reflects expert knowledge in details. Here we automatically receive for resulting diagrams (X -parameter value, Y - level of probability) such probability distributions that are boundaries of all distributions of GIE (probability tube, or box). Besides we may receive probability distributions for different sections of p-tube both for parameter values and for probability levels and use these curves in the process of decision-making. At last, we may use GIE method as an instrument of scenario analysis in decision-making. Illustrative examples are given in the paper to demonstrate the decision-making, expert knowledge and scenario analysis aspects of the proposed approach.

Keywords: Generalized interval estimations, scenario analysis, generalized probability distributions, probability tubes.

ACM Classification Keywords: H.4.2 Types of Systems – Decision support; G.3 Probability and Statistics – Distribution functions.

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GENERALIZED INTERVAL ESTIMATIONS IN DECISION MAKING AND SCENARIO ANALYSIS

Gennady Shepelyov, Michael Sternin