Geodesic
A criterion of consistency of information «quanta» on the preference relation of the decision maker
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 2 (2014), pp. 12-18

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A model of multicriteria decision problem is considered, where a decision maker has to choose one or several options from a set of possible choices based on estimates of the choices by several numerical criteria and his own preferences. It is well known that the choice must belong to the Pareto set, but in pratice this set is often too large to make a choice directly. Therefore a problem of reducing the Pareto set arises. An axiomatic approach to this problem is adopted. The decision maker is required to accept the so called axioms of rational choice. With these axioms, it is possible to perform the Pareto set reduction based on a certain kind of information «quanta» given by the decision maker. Each «quantum» represents a certain compromise, when the decision maker prefers to choose an option with higher estimates by one group of criteria even though by other criteria that option may have worse estimates. The decision maker can also specify a degree of certainty in such a compromise. An algorithm has been developed for accounting for these «quanta» and reducing the set of choices. In this paper consistency of the information provided by the decision maker is examined. A criterion of contradictoriness of the «quanta» is suggested that can be checked in the process of the algorithm for accounting the «quanta». Bibliogr. 7.
Keywords: Pareto set reduction, axiomatic approach, fuzzy sets.
Mots-clés : information «quanta» 
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     author = {O. V. Baskov},
     title = {A criterion of consistency of information {\guillemotleft}quanta{\guillemotright} on the preference relation of the decision maker},
     journal = {Vestnik Sankt-Peterburgskogo universiteta. Prikladna\^a matematika, informatika, processy upravleni\^a},
     pages = {12--18},
     publisher = {mathdoc},
     number = {2},
     year = {2014},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSPUI_2014_2_a1/}
}
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O. V. Baskov. A criterion of consistency of information «quanta» on the preference relation of the decision maker. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 2 (2014), pp. 12-18. http://geodesic.mathdoc.fr/item/VSPUI_2014_2_a1/