Weighted Entropy: Evaluating Feasible Weights with an Inversion Procedure and Eliciting a New Probability-Possibility Transformation

In this article, after an extended literature survey on the topics of weighted entropy and possibility theory, including probability-possibility transformations, we present some new results regarding the analytical study of the maximum point of weighted entropy. Then, we build an inversion procedure which allows for computing feasible weights given an optimal point solution, which shows to be insensitive to a positive linear scaling. From there, we associate the calculated feasible weights with a possibility distribution and show that the inversion procedure can be interpreted to elicit a new probability-possibility transformation, which is studied from the perspective of a set of axioms including consistency and preference order preservation. Numeric examples are outlined and some related criteria are evaluated while the new probability-possibility transformation is compared with other standard possibility distributions mentioned in the literature, with the results showing an admissible performance. However, there is an intrinsic limitation regarding a least upper bound of the optimal point of weighted entropy and another restriction concerning a threshold for consistency, but an alternative is still mentioned that can be considered for future work related to this subject.