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The Ordered Modular Averages

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2 Author(s)
Mesiar, R. ; Inst. for Res. & Applic. of Fuzzy Modelling, Univ. of Ostrava, Ostrava, Czech Republic ; Mesiarova-Zemánková, A.

Ordered modular averages (OMAs) generalize ordered weighted averages operators, with the replacement of the additivity property by the modularity. OMAs can be seen as a symmetrized idempotent modular aggregation functions, characterized by comonotone modularity. Each OMA can be seen also as a copula-based integral with respect to a symmetric capacity. Special OMAs are characterized, such as associative operators, operators with neutral element, or operators with an annihilator. Some construction methods for OMAs are also discussed.

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Fuzzy Systems, IEEE Transactions on  (Volume:19 ,  Issue: 1 )