On the relationship between symmetric maxitive, minitive, and modular aggregation operators
Information Sciences: an International Journal
The ordered multiplicative modular geometric operator
Knowledge-Based Systems
MDAI'12 Proceedings of the 9th international conference on Modeling Decisions for Artificial Intelligence
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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.