Decision making; dispersion; entropy; evaluation; OWA operator; probability distribution; scatter

This study proposes a novel concept of Scatter for probability distribution (on [0,1]). The proposed measurement is different from famous Shannon Entropy since it considers [0,1] as a chain instead of a normal set. The measurement works easily and reasonably in practice and conforms to human intuition. Some interesting properties like symmetricity, translation invariance, weak convergence and concavity of this new measurement are also obtained. The measurement also has good potential in more theoretical studies and applications. The novel concept can also be suitably adapted for discrete OWA operators and RIM quantifiers. We then propose a new measurement, the Preference Scatter, with its normalized form, the Normalized Preference Scatter, for OWA weights collections. We analyze its reasonability as a new measurement for OWA weights collections with comparisons to some other measurements like Orness, Normalized Dispersion and Hurwicz Degree of OWA operators. In addition, the corresponding Preference Scatter for RIM quantifiers is defined.