Article ID Journal Published Year Pages File Type
4949570 Discrete Applied Mathematics 2017 14 Pages PDF
Abstract
Motivated by the elicitation or the learning of certain types of models for classifying objects in ordered categories based on several criteria, we categorize the positive Boolean functions up to 6 variables. We list all inequivalent positive Boolean functions and we determine the smallest degree k of the k-additive capacity that can be used for separating their true points from their false points. 1-additive Boolean functions are the well-studied threshold functions. Each function is described by its set of minimal true points. The latter correspond to the minimal winning coalitions of simple games. They also correspond to the minimal sufficient coalitions in the multiple criteria classification models we are interested in, namely, the MR-Sort and the noncompensatory sorting model.
Related Topics
Physical Sciences and Engineering Computer Science Computational Theory and Mathematics
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