Bipolar distributions in fuzzy sets theory

In this paper we consider the problem of measuring latent variables with ordinal scales and we put forward an original approach to this issue, which combines the use of Intuitionistic Fuzzy Sets with the calculation of bipolar means and bipolar distributions. Intuitionistic Fuzzy theory allows a researcher to model the degree of membership and non-membership to a certain fuzzy set, as well as the residual uncertainty. It is fundamental, for decision making, to properly model such source of variability. We focus on the definition of uncertainty, using bipolar distributions and introducing Intuitionistic Bipolar Fuzzy Sets. This allows us to distinguish between a negative and a positive component of uncertainty, which represents a novelty in Intuitionistic Fuzzy analysis. We apply this method to a national evaluation survey (The Magellano Project) proposed by the Italian Ministry of Public Administration, aimed at involving employees in management decision.