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Extremal values-based aggregation functions
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DOI：10.1016/j.fss.2024.109097.png)
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Abstract
En 中文
We introduce and study aggregation functions based on extremal values, namely extended (l, u)-aggregation functions whose outputs only depend on a fixed number l of extremal lower input values and a fixed number u of extremal upper input values, independently of the arity of the input n-tuples (n >= l + u). We discuss several general properties of (l, u)-aggregation functions and we study special (l, u)-aggregation functions with neutral element, including t-conorms, t-norms and uninorms. We also study (l, u)-aggregation functions defined by means of integrals with respect to discrete fuzzy measures, as well as (l, u)-ordered weighted quasi-arithmetic means based on appropriate weighting vectors. We also stress some generalizations based on recently introduced new types of monotonicity. Some possible applications are sketched, too.
Keywords:
Aggregation function
Choquet integral
Classification
Extended aggregation function
Ordered weighted quasi-arithmetic mean
Sugeno integral
t-conorm
t-norm
Symmetric discrete fuzzy measure
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