Comonotone lower probabilities for bivariate and discrete structures

Two random variables are called comonotone when there is an increasing relation between them, in the sense that when one of them increases (decreases), the other one also increases (decreases). This notion has been widely investigated in probability theory, and is related to the theory of copulas. This contribution studies the notion of comonotonicity in an imprecise setting. We define comonotone lower probabilities and investigate its characterizations. Also, we provide some sufficient conditions allowing to define a comonotone belief function with fixed marginals and characterize comonotone bivariate p-boxes.