Multi-valued Choquet integral based on a couple of set functions with an application in multi-attribute decision-making

As a generalization of Choquet integrals, the generalized Choquet type set-valued integral of functions w.r.t. set multifunctions and ????-additive measures have been performed in our previous paper [66]. The present paper is its continuation and it brings a novel set-valued type Choquet integral, named double set function multi-valued Choquet integral (DSMVCI), where the ????additive measure is replaced by a fuzzy measure. Various kinds of its properties and convergence theorems are obtained, and set-valued type Jensen’s and Markov’s type inequalities are proved. Its application in multi-attribute decision-making with hesitant fuzzy information is given.