Abstract
Representation of the binary relations and choice functions by the utility functions was considered. The results of utility maximization were presented for the classical case of no comparison threshold and with a threshold depending on one alternative. Models were constructed where the threshold depends on two compared alternatives and/or admissible set of alternatives. A model of choice describing H.A. Simon's concept of choice was proposed and considered. The class of binary relations of partial order and its subclasses were studied. Some new classes of binary relations such as weak biorders and simple and simplest semiorders were constructed, and their representations by the threshold utility function were determined.
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