On the Relationship Between the Quantifier Threshold and OWA Operators

The OWA weighting vector and the fuzzy quantifiers are strictly related. An intuitive way for shaping a monotonic quantifier, is by means of the threshold that makes a separation between the regions of what is satisfactory and what is not. Therefore, the characteristics of a threshold can be directly related to the OWA weighting vector and to its metrics: the attitudinal character and the entropy (or dispersion). Generally these two metrics are supposed to be independent, although some limitations in their value come when they are considered jointly. In this paper we argue that these two metrics are strongly related by the definition of quantifier threshold, and we show how they can be used jointly to verify and validate a quantifier and its threshold.