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A New Approach to Interval-Valued Choquet Integrals and the Problem of Ordering in Interval-Valued Fuzzy Set Applications

Journal Article

Bustince H., Galar M., Bedregal B., Kolesárová A., Mesiar Radko

serial: IEEE Transactions on Fuzzy Systems vol.21, 6 (2013), p. 1150-1162

project(s): GAP402/11/0378, GA ČR

keywords: Interval-valued Choquet integral, Shapley value, interval-valued ordered weighted aggregation (OWA) operators, interval-valued decision making

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abstract (eng):

We consider the problem of choosing a total order between intervals in multiexpert decision making problems. To do so, we first start researching the additivity of interval-valued aggregation functions. Next, we briefly treat the problem of preserving admissible orders by linear transformations.We study the construction of interval-valued ordered weighted aggregation operators by means of admissible orders and discuss their properties. In this setting, we present the definition of an interval-valued Choquet integral with respect to an admissible order based on an admissible pair of aggregation functions. The importance of the definition of the Choquet integral, which is introduced by us here, lies in the fact that if the considered data are pointwise (i.e., if they are not proper intervals), then it recovers the classical concept of this aggregation. Next, we show that if we make use of intervals in multiexpert decision making problems, then the solution at which we arrive may depend on the total order between intervals that has been chosen.


bocek: 2012-12-21 16:10