Generalized dissemblance index as a difference of first moments of fuzzy numbers - A new perspective on the distance of fuzzy numbers

This paper investigates the formulation of the dissemblance index as a basis for the calculation of distances of fuzzy numbers and explores its potential linkages with standard and possibilistic moments of fuzzy numbers. Applying the LSC transformation introduced recently by Luukka, Stoklasa and Collan we transform the general formulation of the dissemblance index into its "probabilistic" analogy and show that the result can be interpreted as a difference of COGs of the respective fuzzy numbers (potentially with hedges applied to them). We also show that the difference of possibilistic means is a special case of the general dissemblance index, when w = 1. We also propose a generalized version of the possibilistic mean of a fuzzy number and prove its properties. We discuss the implications of this relationship on the practical use of the generalized dissemblance index and investigate its performance in the task of ranking of fuzzy numbers.