Comparing Intervals Using Type Reduction

Many decision making processes are based on choosing options with maximum utility. Often utility assessments are associated with uncertainty, which may be mathematically modeled by intervals of utilities. Intervals of utilities may be mapped to single utility values by so-called type reduction methods which have been originally developed in the context of interval type-2 defuzzification: the method by Nie and Tan (NT), consistent linear type reduction (CLTR), consistent quadratic type reduction (CQTR), and the uncertainty weight method (UW). This paper considers the problem of comparing pairs of utility intervals using type reduction methods. Three different possible relations between pairs of intervals (disjoint, overlapping, and inclusive) are distinguished in an extensive experimental study, which yields recommendations for the choice of type reduction methods with respect to the level of risk that the decision maker is willing to take. If the focus is on mean utility, then we recommend the Nie-Tan method. For more cautious decision making, when very low utilities should be avoided, we recommend consistent linear type reduction with a high value of the cautiousness parameter or consistent quadratic type reduction. For more risky decision making with a strong focus on very high utilities we recommend consistent linear type reduction with a low value of the cautiousness parameter.