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On Some Properties and Comparative Analysis for Different OWA Monoids

We study the properties of OWA multiplication monoid. By introducing and‐accumulation vectors of OWA operators, we consider the set of all n‐dimensional OWA operators as a lattice. Then, we analyze some monotonicity properties of OWA operators based on an ordering induced by and‐accumulation vectors. We also show that the lattice‐theoretical operations are a kind of counterpart of the OWA multiplication monoid (and its dual, additive monoid). An example of using the OWA multiplication monoid and the lattice‐theoretical structure in decision making problem is provided.