Abstract
Abstract The known problem of intransitivity of preferences arising in decision making is revised in view of risks of invalid decisions based on formal methods. The cognitive approach to analysis is applied considering transitivity of preferences as heuristics with a limited domain of validity. A conception of rational intransitivity of expert's preferences is advanced. With this in view, the adaptive approach to develop mathematical means of problem solving traditionally using the axiom of transitivity is proposed. The original implementation of the adaptive approach is presented for the general problem of the best element selection with diversity of similar problems within the general one.
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