A note on the tau-additive measures

Abstract

In this note, we point out that some results shown in Jónás et al. (2022) [2] are not valid. In that paper, a class of unary functions called tau function was introduced. By using the tau functions, the authors introduced a class of monotone measures called tau-additive measure and asserted that a tau function is either concave or convex and, as a consequence, a tau-additive measure is either submodular or supermodular. We present two examples to show that all these assertions are false.