Eliciting dual interval probabilities from interval comparison matrices

In recent years, dealing with uncertainty using interval probabilities, such as combination, marginalization, condition, Bayesian inferences, has received considerable attention. However, how to elicit interval probabilities from subjective judgment is still a fundamental problem in applications of interval probabilities. In this paper, interval-valued pairwise comparisons of events are used to characterize the judgment of a person about which one is more likely to occur between each pair of events. From the interval comparison matrix, we elicit the dual interval probabilities by linear programming problems. The ratios of the estimated interval probabilities are used to approximate the interval comparison values from the outside and the inside of them. In other words, the inclusion relations between the interval comparison values and the ratios of the obtained interval probabilities hold. A numerical example concerning a new product development is presented to illustrate how to estimate dual interval probabilities and use interval probabilities to make a decision.