Uncertainty measures of complex preference relations for decision making

Varied extensions of preference relations have been developed to cope with uncertain scenes. However, the introduced uncertainty, which might decrease the reliability of a final decision, has not been paid sufficient attention. In this study, a new concept, referred to as complex preference relation (CPR), is proposed to formalize most of the existing types of preference relations under uncertainty. Two distinct uncertainty measures are proposed to restrict the uncertainty degree of a CPR. The preference-oriented measure, which looks into the uncertainty of each piece of preference, gives limits to a CPR by its maximum variance. The rank-oriented measure, which focuses on the resultant ranks, restricts uncertainty by the probability of rank reversal. Stochastic uncertainty degrees are defined as a reference to enable the determination of uncertainty thresholds by risk appetites directly. A series of simulation experiments are conducted to demonstrate the features and connections of the two measures.