Summary
A common approach in the multiple criteria decision making is to obtain the overall evaluation by aggregating the partial evaluations. For this, a member of a large family of aggregation operators is used. Many of these operators commonly employed in decision making (weighted average, ordered weighted average, minimum, maximum, . . .) can be used only when criteria are independent. On the other hand, the Choquet integral, a generalization of the aforementioned operators, can be used even when some interactions between criteria occur. We present a fuzzified Choquet integral capable of dealing not only with fuzzy partial evaluations (first level fuzzification), but also with fuzzy weights (second level fuzzification). We also provide an effective way to evaluate the fully fuzzified integral, which allows its straightforward application to decision making problems with inherent uncertainty.
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Fuzzification of Choquet Integral and Its Application in Multiple Criteria Decision Making
(ProQuest: ... denotes formulae omitted.)
1. Multiple Criteria Decision Making and the Choquet IntegralIn a multiple criteria decision making (MCDM) problem a decision maker is expected to choose the best out of a set of alternatives X = [X^sub 1^,X^sub 2^ .. .,x^sub m^}. Each alternative X^sub 1^, i = 1,2,.. .,m is described by a vector of values (xn, #¿2, . . . , Xin), which represents the consequences of the alternative with respect to n given criteria. Usually the original values X^sub ij^ are evaluated with respect to particular j-th goals, j = 1,2,..., n, and replaced by partial evaluations h^sub j^(x^sub ij^). To each alternative X^sub 1^ is then assigned an n-tuple of partial evaluations (h^sub 1^(x^sub i1^),h^sub 2^(2^sub i2^), . . . , h^sub n^(x^sub in^)), for which we will use the shorthand notation of (h^sub i1^,h^sub i2^,.. .,h^sub in^). The overall evaluation h(xi) will be analogically denoted by h^sub i^.To solve the MCDM problem the decision maker can employ, for example, multiple criteria utility function [14], Saaty AHP [13], ELEKTRE methods [15], partial goals method [7] , etc. The choice of the method depends ...See the full content of this document
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