On cosine fuzzy sets and uncertainty quantification

This paper presents a definition of a generalized cosine-based fuzzy set, its application into simulation problems and uncertainty quantification in order to cover both aleatoric and epistemic uncertainties commonly seen in non-probabilistic models. The proposed cosine fuzzy set is able to represent different shapes via a parameter b which operates as the power of a cosine-type function adding flexibility to its behavior. Some special cases, some of its properties and a random variate generation method are described and applied into three examples: a random variate example and uncertainty quantification for two benchmark functions.