Generated aggregation operators
نویسنده
چکیده
Two basic aggregation methods of reals are idempotent ones (min, max, arithmetic mean) and Archimedean ones (sum, bounded sum). Under some additional requirements, these methods can be shown to be the only possible up to isomorphic transformation and composition of operators (e. g. ordinal sum), see for example Isemigroups of Mostert and Shields [15], compare also [9], or quasi-arithmetic means [3]. Because of simplicity, we restrict our considerations to the unit interval inputs and outputs. However, a general real valued scale case is then a matter of rescaling only.
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