PIU: risk-sensitive decision making using Pareto optimization of interval utilities induced by fuzzy preference relations

Decision making is a process that ranks or chooses subsets from given sets of options, for example, project proposals or machine tools, with high relevance in industry and economics. Each decision option may be associated with a degree of utility with respect to a specific criterion. Often experts are not willing or able to quantify utilities but rather compare individual pairs of options, which leads to fuzzy pairwise preference matrices. Conventionally, decision making on preference matrices uses scoring indices that exhibit different characteristics. Selecting the most appropriate scoring index is often difficult. Scoring indices are associated with different levels of risk, and none of these indices alone can be considered superior. We show that any fuzzy preference matrix induces interval utilities which can be interpreted as memberships of interval type-2 fuzzy sets, so preference-based decision making has to take into account uncertainty and therefore has to be risk sensitive. We propose a risk-sensitive preference-based decision making method called Pareto optimization of interval utilities (PIU) that chooses a subset of options ranked by degrees of risk. This allows the decision maker to choose an option that represents an appropriate trade-off between opportunity and risk for the given decision problem. Experiments with the YouTube Comedy Slam data set show that PIU compared with conventional scoring methods allows to trade a slight decrease in the best-case utility for a strong increase in the worst-case utility, and vice versa.