A Method for Ranking Non-Linear Qualitative Decision Preferences using Copulas

Biljana Mileva-Boshkoska and Marko Bohanec
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Biljana Mileva-Boshkoska: Jožef Stefan International Postgraduate School, Slovenia
Marko Bohanec: Jožef Stefan Institute and University of Nova Gorica, Slovenia

International Journal of Decision Support System Technology (IJDSST), 2012, vol. 4, issue 2, 42-58

Abstract: This paper addresses the problem of option ranking in qualitative evaluation models. Current approaches make the assumptions that when qualitative data are suitably mapped into discrete quantitative ones, they form monotone or closely linear tabular value functions. Although the power of using monotone and linear functions to model decision maker’s preferences is impressive, there are many cases when they fail to successfully model non-linear decision preferences. Therefore, the authors propose a new method for ranking discrete non-linear decision maker preferences based on copula functions. Copulas are functions that capture the non-linear dependences among random variables. Hence each attribute is considered as a random variable. The variables are nested into hierarchical copula structures to determine the non-linear dependences among all attributes at hand. The obtained copula structure is used for obtaining regression function and consequently for option ranking. The application of the method is presented on two examples.

Date: 2012
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