Different families of functions have been proposed in the literature with the purpose of simultaneously generalizing weighted means and OWA operators (see, for instance, WOWA and SUOWA operators). Recently, Jin, Mesiar, and Yager [L. Jin, R. Mesiar, and R. R. Yager, Melting probability measure with OWA operator to generate fuzzy measure: the Crescent Method, IEEE Transactions on Fuzzy Systems, in press] have introduced in the literature a new procedure called The Crescent Method to melt additive capacities with those of OWA operators. The main aim of this paper is to establish a relationship between the Crescent Method and SUOWA operators. From this relationship we give closed-form expressions for some well-known indices such
as the Shapley values, the veto and favor indices, and the k-conjunctiveness and k-disjunctiveness indices.
