Possibility and necessity measures and integral equivalence

Integral equivalence of couples (μ,x) and (μ,y), where μ is a possibility (necessity) measure on [n]={1,…,n} and x,y∈[0,1]n is discussed and studied. We characterize the sets H(μ,x) of all y such that the couples (μ,x) and (μ,y) are integral equivalent and we add an illustrative example. Subsequently, a new characterization of possibility (necessity) measures is obtained and the coincidence of universal integrals for possibility (necessity) measures and particular vectors from [0,1]n is shown, thus generalizing these results introduced by Dubois and Rico for the Choquet and the Sugeno integrals.