Gaussian Successive Fuzzy Integral for Sequential Multi-decision Making

Fuzzy integral provides a powerful tool for fusing multiple sources of information or evidence to give an evaluation that expresses the level of confidence (or preference) in a particular hypothesis (or decision). However, the computational framework of the fuzzy integral is not suitable for sequential decision making tasks, since it assumes that the sources of information have been readily available prior to information fusion. In a sequential decision making task, information is progressively accumulated, while decisions are made at various time instants. In this paper, we reformulate the computational framework of the fuzzy integral in order to translate its framework into a successive one. To this end, three issues have been encountered: (i) how to collect the richest information for sequential decision making, (ii) how to efficiently preserve the constantly increasing amount of incoming information, and (iii) how to build up an effective computational scheme in order to gratify the requirement of real-time decision making. The derived scheme, called the Gaussian successive fuzzy integral scheme, was closely examined to validate its feasibility in real-time sequential multi-decision making on the basis of incremental information gathering.