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Aggregation operators with annihilator. (English) Zbl 1081.68107

The authors study commutative aggregation operators which have an annihilator, i.e. an element which is the outcome of the aggregation as soon as it is one of the aggregated data. And they restrict their considerations to binary aggregation operators.
They prove that each such (associative) operator \(A\) is the median of the annihilator \(a\) and two general binary (and associative) aggregation operators \(F,G\) always satisfying the inequalities \(F(a,x)\leq a\leq G(a,x)\). Furthermore they discuss in detail the consequences of the assumption that one or both of the sections \(A(1,x)\) and \(A(0,x)\) are continuous as functions of \(x\).

MSC:

68T37 Reasoning under uncertainty in the context of artificial intelligence
26B99 Functions of several variables
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