Sugeno-Like Operators in Preference and Uncertain Environments

Sugeno-like operators are binary operations-based generalization of Sugeno integral and are still defined on real valued fuzzy measures. This article discusses the aggregation methods in the situation where both inputs and fuzzy measures are attached with numerical uncertainties. That is, when an input vector and a fuzzy measure are given, each of the entries of the vector and the measure value on each subset can be attached with numerical uncertainty degrees. To fulfill this meaningful aim of performing Sugeno-like aggregation with numerical uncertainties, it needs two parts of work. We first formally define basic uncertain vector and basic uncertain fuzzy measure. Then, we discuss the methods to construct or adjust basic uncertain vector and basic uncertain fuzzy measure in two situations, the general fuzzy measure situation and the probability measure only situation, respectively. With uncertain input and uncertain fuzzy measure, we then accordingly propose the corresponding restricted Sugeno-like operator, for which some different logic restrictions are analyzed. All the proposals also have full consistency for they can immediately degenerates into Sugeno-like operator when the attached uncertainties disappear.