Abstract

ACOSTA-FLORES, José Jesús. Interactive algorithm for decisions with several objectives, risk and uncertainty. Ing. invest. y tecnol. [online]. 2021, vol.22, n.2.  Epub July 30, 2021. ISSN 2594-0732.  https://doi.org/10.22201/fi.25940732e.2021.22.2.016.

The object of this article is to present a simple algorithm for multi-purpose decision analysis with risk and uncertainty, where we can contemplate in addition to the technical aspects other relevant: environmental, political or social. When the probability functions are unknown and are supposed to be uniform there is uncertainty and risk when these probability functions are known. In this article are known the functions of probability, triangular and normal, in addition to the uniforms. The algorithm, based on the concepts and methodology of Decision Theory, guides to the analyst so he can apply the principle of "divide and conquer". Initially he will have to make the decision maker aware that the analysis is based on his answers, so he should behave the same in real situations as in the conjecture. Afterwards, the random problem is transformed in one deterministic. Then the analyst performs dominance analysis to eliminate alternatives. If there were only one alternative, it would be the solution. If not, then we make compensatory swaps to eliminate a measure of effectiveness. Now the analyst returns to the dominance analysis. Both analyses continue to alternate dominance and compensatory swaps, until only remains an alternative. One of the limitations of this algorithm is the existence of a single decision maker. The formal development of the algorithm is original, as well as the determination of the equivalents under certainty in triangular and normal cases. Finally, we presented two hypothetical examples. The first with three investors where the best investments are found for each one; and the second, to determine the best location of an airport.

Keywords : Decisions; multiple objectives; uncertainty; risk; utility functions; certainty equivalents; criteria of dominance; compensatory swaps.

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