Abstract

The problem of the choice of extreme multidimensional solutions of a given finite and admissible set and Pareto optimal, which is received by a person decision maker (PDM) in the dialogue process with the software expert system, was considered. Such a system increasing the level of both navigational safety and the safety of the fishery operates under the condition of "weak" assumptions about the type of structure preferences expressed through a utility function. It is shown that the "weak" assumptions about the form of the utility function in the software product of the expert system can be compensated, if the decision-maker is offered questions formulated on two levels as follows: "For what reduction by one criterion may you agree to receive a predetermined increment on other criteria, provided that other evaluation criteria remain unchanged?" or "What is to choose the reducing in the value of one criterion by a predetermined amount and the increasing the value of the other criterion by a predetermined value or leave the previous criteria values provided that the other evaluation criteria remain unchanged?". It offers the option of mathematical models of "man-machine" dialogues between a decision-maker and software expert system, while ensuring the safety of navigation and the safety of the fishery. As a result of using such dialogues either the only vector estimation, corresponding to the extreme decision of the person decision maker, in terms of its structure of preferences, or some subset of the extreme solutions, which will also contain this estimation, can be obtained.

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