New transformations of aggregation functions based on monotone systems of functions. (English) Zbl 1476.68258
Summary: The paper introduces a Generalized-Convex-Sum-Transformation of aggregation functions. It has the form of a transformation of aggregation functions by monotone systems of functions. A special case of the proposed Generalized-Convex-Sum-Transformation is the well-known \(\ast \)-product, also called the Darsow product of copulas. Similarly, our approach covers Choquet integrals with respect to capacities induced by the considered aggregation function. The paper offers basic definitions and some properties of the mentioned transformation. Various examples illustrating the transformation are presented. The paper also gives two alternative transformations of aggregation functions under which the dimension of the transformed aggregation functions is higher than that of the original one. Interestingly, if a copula is transformed, under some conditions put on the monotone systems of functions, the transformed aggregation function is again a copula.
MSC:
| 68T37 | Reasoning under uncertainty in the context of artificial intelligence |
| 28E10 | Fuzzy measure theory |
| 62H05 | Characterization and structure theory for multivariate probability distributions; copulas |
Keywords:
aggregation function; convex sum; copula; \( \ast \)-product; GCS-transform; weighted arithmetic meanReferences:
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