On aggregation functions based on linguistically quantified propositions and finitely additive set functions
We study aggregation functions defined as convex combinations of the linguistically quantified propositions "at least k criteria 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 with a famous example which cannot be modeled by classical aggregation functions such as the Choquet integral.
We consider some routing criterions for connections with QoS requirements in the Internet, which support QoS guarantees for both the services and networks. First we investigate the path consumption, and give the definition of the path consumption function (PCF). Then we observe the path selection's influence on the link residual bandwidth, we find that letting the narrowband connection choose those links with small residual bandwidth can increase the admission probability of the broadband ones. We define the bandwidth fragmentation function (BFF) for connections which reflects this influence. After that we give the definition of the network efficiency function (NEF) for the network performance measure. A QoS routing scheme and some simulation results are given. We conclude with a summary and with directions for future work.