The relationship between the maximum entropy and minimax ratio RIM quantifier problems
For knowledge aggregation often so-called ordered weighted averages (OWA) are used. A regular increasing monotone (RIM) quantifier introduced by Yager (2004) can be seen as a continuous form of OWA. The author considers two optimization problems, the maximum entropy RIM quantifier problem and the minimax ratio RIM quantifier problem. \textit{X. Liu} and \textit{H. Lou} [Fuzzy Sets Syst. 159, No. 13, 1673--1688 (2008; Zbl 1176.03037)] assert the equivalence of both problems if the RIM quantifier has a continuous generating function. The author shows by an example that this result is wrong and he proves the equivalence under the assumption that the generating function is absolutely continuous and Lebesgue integrable.
scientific article; zbMATH DE number 6117652
scientific article