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A general model of parameterized OWA aggregation with given orness level. (English) Zbl 1194.90124

The main part of this review is the author’s abstract. The reviewer adds only that this article can be used also as a good subject introduction: the suitable subject survey, 60 references, and the section “Another view of the problems solutions and some discussions” are present.
“The paper proposes a general optimization model with separable strictly convex objective function to obtain the consistent OWA (ordered weighted averaging) operator family. The consistency means that the aggregation value of the operator monotonically changes with the given orness level. Some properties of the problem are discussed with its analytical solution. The model includes the two most commonly used maximum entropy OWA operator and minimum variance OWA operator determination methods as its special cases. The solution equivalence to the general minimax problem is proved. Then, with the conclusion that the RIM (regular increasing monotone quantifier) can be seen as the continuous case of OWA operator with infinite dimension, the paper further proposes a general RIM quantifier determination model, and analytically solves it with the optimal control technique. Some properties of the optimal solution and the solution equivalence to the minimax problem for RIM quantifier are also proved. Comparing with that of the OWA operator problem, the RIM quantifier solutions are usually more simple, intuitive, dimension free and can be connected to the linguistic terms in natural language. With the solutions of these general problems, we not only can use the OWA operator or RIM quantifier to obtain aggregation value that monotonically changes with the orness level for any aggregated set, but also can obtain the parametrized OWA or RIM quantifier families in some specific function forms, which can incorporate the background knowledge or the required characteristic of the aggregation problems.”

MSC:

90C70 Fuzzy and other nonstochastic uncertainty mathematical programming
68T37 Reasoning under uncertainty in the context of artificial intelligence
90C47 Minimax problems in mathematical programming
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