Modeling risk attitudes by gain at confidence: a case study of transportation problem

Abstract

Risks arise when decisions are made in a state of indeterminacy (e.g., randomness, fuzziness and uncertainty). Confronted with risks, different decision-makers have different attitudes (risk-seeking, risk-neutral and risk-averse) that are traditionally modeled by the expected utility function. In order to provide a more natural and direct approach to model the risk attitudes, this paper proposes a concept of gain at confidence, where the confidence level indicates the risk attitude, and the gain is its corresponding outcome. To illustrate the performance of modeling risk attitude, in both stochastic and uncertain environments with a transportation problem background, we compare gain at confidence method with expected utility method by analyzing the optimality order relation of the same set of feasible solutions. Three main conclusions are drawn from the analysis. (1) In stochastic environments, we get the same order relation by the gain at confidence method and the expected utility method. Meanwhile, the gain at confidence values represent realistic objective values rather than relative utilities. (2) In uncertain environments, we get the similar conclusion, and find that gain at confidence is easier to calculate than expected utility. (3) Under the same structure and parameter settings, these stochastic models and uncertain models draw the same order relation, which implies uncertain gain at confidence model is an efficient method to model risk attitude.