On Continuity of Ordered Aggregation Operators

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Abstract

Many aggregation operators involve sorting operations. People usually call them ordered aggregation operators, such as the ordered weighted averaging operators. The stability of these operators depends on the continuity of sorting operations. In this paper, we will show that the sorting operations have a very good continuity and thus the ordered aggregation operators are robust. However, the analysis of the continuity of sorting operations involving intuitionist fuzzy values is difficult. In this case, we may need to introduce a new topology and the results turn out to be rather complicated.

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