Title :
Partially Bipolar Choquet Integrals
Author :
Kojadinovic, Ivan ; Labreuche, Christophe
Author_Institution :
Dept. of Stat., Univ. of Auckland, Auckland, New Zealand
Abstract :
Grabisch and Labreuche have recently proposed an extension of the Choquet integral adapted to situations where the values to be aggregated lie on a bipolar scale. The resulting continuous piecewise linear aggregation function has the ability to represent decisional behaviors that depend on the ldquopositiverdquo or ldquonegativerdquo satisfaction of some of the criteria. Its main drawback is that it holds a huge number of parameters that makes its determination problematic in practice. From the observation that the decision maker usually adopts a bipolar reasoning only with respect to a (small) subset of criteria, we investigate Choquet-like aggregation models that are fully bipolar only with respect to certain criteria and whose number of parameters is much lower than that of the bipolar Choquet integral. The use of the proposed concepts is illustrated in an example.
Keywords :
decision making; decision theory; integral equations; operations research; piecewise linear techniques; set theory; bipolar reasoning; continuous piecewise linear aggregation function; decision making; multicriteria decision aiding; partial bipolar Choquet integral; subset; Aggregation operators; Choquet integral; bipolar scales; capacities; fuzzy measures; multicriteria decision aiding;
Journal_Title :
Fuzzy Systems, IEEE Transactions on
DOI :
10.1109/TFUZZ.2008.926587