Optimal weights and feasible orness of ordered weighted averaging functions in the framework of Tsallis entropy

Abstract

We discuss the application of the maximum entropy principle to the strict weighting vectors of ordered weighted averaging functions with a given orness. The problem has been thoroughly investigated by O'Hagan, Filev and Yager, and Fullér and Majlender in the context of the classical Shannon entropy. In this paper we extend the analysis to the more general context of Tsallis entropy for positive parameter values, which reduces to Shannon entropy in the unit parameter case. In our approach, whose key element is the convenient choice of a composite Lagrange multiplier, the existence of an optimal and monotonic strict weighting vector is proven for a feasible orness interval $({\Omega }_{min}^{\gamma },{\Omega }_{max}^{\gamma })$ which depends on the Tsallis entropy parameter. In the small parameter domain (under unit) the feasible orness interval remains the full unit interval, as in the standard Shannon entropy case. On the other hand, in the large parameter domain (over unit) the feasible orness interval reduces to a symmetric interval around the neutral orness $\Omega =1/2$, which gradually reduces for increasing values of the Tsallis entropy parameter.