On aggregation functions based on linguistically quantified propositions and finitely additive set functions

摘要

We study aggregation functions defined as convex combinations of the linguistically quantified propositions "at least kcriteria are satisfied". Our approach is similar to the TOWA function in spirit but instead of using a maxitive measure we propose to rely on a real-valued finitely additive set function. This assumption leads to a new framework. However, it is combinatorial by nature and, in general, it produces functions with high computational costs. Therefore, we analyze some particular settings and introduce new aggregation functions which can alleviate the combinatorial burden thanks to several combinatorial identities. These methods have interesting features and in particular, some of them make it possible to set different types of relationships between criteria by allowing the use of different t-norms. The interest of our proposals is illustrated witha famous example which cannot be modeled by classical aggregation functions such as the Choquet integral. (C) 2015 Elsevier B.V. All rights reserved.