THE THRESHOLD DECISION MAKING EFFECTUATED BY THE ENUMERATING PREFERENCE FUNCTION

Fuad Aleskerov and Vyacheslav V. Chistyakov ()
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Vyacheslav V. Chistyakov: Department of Applied Mathematics, National Research University, Higher School of Economics, 25/12 Bol'shaya Pechërskaya Street, Nizhny Novgorod 603155, Russian Federation;

International Journal of Information Technology & Decision Making (IJITDM), 2013, vol. 12, issue 06, 1201-1222

Abstract: Based on the leximin and leximax preferences, we consider two threshold preference relations on the setXof alternatives, each of which is characterized by ann-dimensional vector(n ≥ 2)with integer components varying between 1 andm(m ≥ 2). We determine explicitly in terms of binomial coefficients the unique utility function for each of the two relations, which in addition mapsXonto the natural 'interval'$\{1,2, \ldots, \vert \tilde{X}\vert\}$, where$\tilde{X} = X/I$is the quotient set ofXwith respect to the indifference relationIonXinduced by the threshold preference. This permits us to evaluate all equivalence classes and indifference classes of the threshold order onX, present an algorithm of ordering the monotone representatives of indifference classes, and restore the indifference class of an alternative via its ordinal number with respect to the threshold preference order.

Keywords: Weak order; surjective utility function; indifference class; ordinal number; ordering algorithm; dual preference (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (3)

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Persistent link: https://EconPapers.repec.org/RePEc:wsi:ijitdm:v:12:y:2013:i:06:n:s021962201350034x

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DOI: 10.1142/S021962201350034X

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