A new type of fuzzy integrals for decision making based on bivariate symmetric means

We propose a new generalization of the discrete Choquet integral based on an arbitrary bivariate symmetric averaging function (mean). So far only the means with a natural multivariate extension were used for this purpose. In this paper, we use a general method based on a pruned binary tree to extend symmetric means with no obvious multivariate form, such as the logarithmic, identric, Heronian, Lagrangean, and Cauchy means. The generalized Choquet integral is built by computing the extensions of the bivariate means of the ordered inputs, and includes some existing extensions as special cases. Our construction is illustrated with multiple examples.