Abstract of Meeting Paper

Society for Risk Analysis - Europe 1998 Annual Meeting

Project Analysis in Conditions of Risk and Uncertainty. R. N. Bakhtizin, O. G. Kantor, and L. N. Rodionova, Department of Mathematical Models in Economics, Ufa State Petroleum Technological University, 1, Kosmonavtov St. Ufa, Russia 450062, telephone +7.34.72.43.14.38, e-mail info@oil.ru

In practice it is necessary to make decision, taking into account several parameters, contradicting with each other very often. So it would not be an exaggeration to say, that every problem of the project analysis is multi-criteria problem. But one must always remember, that it is impossible to come to the right conclusion without taking into opinion the factors of risk and uncertainty, because they can influence greatly the final results.

It is well known, that the mathematical description of these factors is the most difficult part of the constructing of mathematical model during the project analysis. In our work the technique of fuzzy sets and logic is used to formulize these factors. So we received an opportunity to begin the decision of new multi-criteria problem without the factors of risk and uncertainty, which is equal to the first problem. As a rule, in practice the approximate methods are used for the decision of multi-criteria problems.

Usually such methods permit to find only a local decision. But when it is necessary to find a global decision, the number of available methods is less. We suggest a method, which consist of next steps:

• to consider the great number of trial points from the sphere of available elements (for the construction of the trial points we used - consequences, which have been known as the consequences with the best parameters of distribution);
• to calculate the values of all criterions;
• to solve the problem of choice the best point, using the technique of fuzzy sets and logic (after we have constructed the membership functions for each criterion in each trial point, we realize an aggregation of the values of the membership functions for each trial point) .

In this case the process of decision making becomes very simple, because we have a chance to compare the trial points with each other by only one parameter.