Constructing confidence belief functions from one expert

It has become a noticeable topic on how to construct belief functions from the quantitative and qualitative opinions of one expert. The existing methods proposed in the literature addressing the topic, however, have paid little attention to the bounded rationality (BR) of the expert. This paper introduces a confidence belief function (BF) qualitatively and quantitatively under the assumption of BR, generated from a set of BFs sampled from the expert by interacting with a number of reliable information providers in a valid time interval. Besides, a procedure for quantitatively producing a confidence BF is presented, which is based on a statistical method mainly involving three steps, dividing the set of BFs into a number of non-conflicting or consistent subsets, forming the confidence interval-valued belief structures (IBSs) of the subsets, and integrating the IBSs into the confidence IBS of the set. A numerical example about a manager in a telecommunications company deciding whether to upgrade a business campaign or not is given to show the procedure for generating a confidence BF. Since the method of generating a confidence BF is on the power set of a frame of discernment, its scalability is also discussed.