SUOWA operators are a new family of aggregation functions that simultaneously generalize weighted means and OWA oper-ators. Semi-uninorms, which are an extension of uninorms by dispensing with the symmetry and associativity properties, play a fundamental role in their definition. In this paper we show several procedures to construct semi-uninorms. The first one allows us to obtain continuous semi-uninorms by using ordinal sums of aggregation operators while the second one is based on a combination of several given semi-uninorms. We also pay special attention to the smallest and the largest idempotent semi-uninorms and we point out some advantages of SUOWA operators over WOWA operators
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