Abstract
•Determine decision using observation of variables describing state of system.•Use of belief structures to model uncertain information.•Include fuzzy sets in belief structure.•Makes use of the Choquet integral.•Comparison of interval-valued satisfactions.
On multiple occasions, suitability of actions depends on uncertain estimation of current situation. In general, we are not certain about a current state of a system, as well as not sure about suitability of a specific action. Observations of a system depends on reliability of obtained measurement, our confidence in them, or simply on availability of all measurements that are required to determine the system's status. At the same time, we are not sure about conditions that should be satisfied for a given actions. In many cases, this is still related to confidence in measurements.
In the paper, we focus on a problem of determining a decision action based on the observation of multiple variables describing the state of a system. In particular, we address the case where we have some uncertainty in the observed values of the variables. Initially, we consider the situation where our uncertain observations are in a form of granules associated with probabilities. Further, we consider a generalization of the problem in which our random aspect of the uncertainty is replaced by a more general measure-based formulation of uncertainty that requires the use of the Choquet integral.