Non-adaptability measures in the pseudo-questionnaires context

Authors:
C. Bertoluzza;V. Doldi;J. Jiménez;S. Montes
Affiliations:
Department of Computer Engineering and Systems Science, University of Pavia, Via Ferrata 1, 27100 Pavia, Italy;Department of Mathematics, University of Pavia, Via Ferrata 1, 27100 Pavia, Italy;Department of Mathematics, University of Oviedo, University Technical School of Industrial Engineers, Viesques Campus, 33203 Gijón, Spain;Department of Statistics and O.R., University of Oviedo, University Technical School of Industrial Engineers, Viesques Campus, 33203 Gijón, Spain
Venue:
International Journal of Approximate Reasoning
Year:
2008

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Abstract

Measuring the degree of non-adaptability of a partition to a criterion, represented by a reference partition, is an essential step in pseudo-questionnaires theory. In this work we characterize axiomatically the measure of non-adaptability in a general context. We base it on pre-orders on the set of all the possible experiences (complete or incomplete partitions). The construction of this measure is crucial for practical applications. It can be done in a natural way starting from the atoms of the partitions and constructing the non-adaptability measure by a process of successive aggregations made by suitable aggregation operators.