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The Threshold Decision Making Effectuated By The Enumerating Preference Function

Author

Listed:
  • FUAD T. ALESKEROV

    (Department of Mathematics for Economics, National Research University Higher School of Economics, 20 Myasnitskaya Street, Moscow 101000, Russian Federation;
    Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russian Federation)

  • 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;
    Laboratory of Algorithms and Technologies for Network Analysis, National Research University, Higher School of Economics, 136 Rodionova Street, Nizhny Novgorod 603093, Russian Federation)

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.

Suggested Citation

  • Fuad T. Aleskerov & Vyacheslav V. Chistyakov, 2013. "The Threshold Decision Making Effectuated By The Enumerating Preference Function," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 12(06), pages 1201-1222.
    • Handle: RePEc:wsi:ijitdm:v:12:y:2013:i:06:n:s021962201350034x
    DOI: 10.1142/S021962201350034X
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    Cited by:

    1. F. Aleskerov & E. Victorova, 2016. "An analysis of potential conflict zones in the arctic region," Papers 1701.07321, arXiv.org.
    2. Chistyakov, V. & Chumakova, K., 2018. "Restoring Indifference Classes via Ordinal Numbers under the Discrete Leximin and Leximax Preference Orderings," Journal of the New Economic Association, New Economic Association, vol. 39(3), pages 12-31.
    3. Fuad T. Aleskerov & Vladimir V. Pislyakov & Timur V. Vitkup, 2014. "Ranking Journals In Economics, Management And Political Sciences By The Threshold Aggregation Procedure," HSE Working papers WP BRP 73/EC/2014, National Research University Higher School of Economics.

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