A new approach to uncertainty description through accomplishment membership functions

Abstract

Human linguistic reasoning and statement logic are able to solve uncertain propositions. Similar capabilities are expected to be found on intelligent systems so they are provided with some sort of artificial logic evaluation. Many approaches to uncertainty measurement have been developed before, mainly referring to probability or possibility theories. Some conceptual restrictions are imposed by forcing a distribution function to be conceptually consistent. In this work, conditions imposed to possibility theory are relaxed and the theoretical perspective is oriented to degrees of accomplishment. Conceptual implications and their relation to numerical calculations with respect to a specific class of membership functions are presented. Relation to possibility theory and certainty measurement are discussed to show logical consistency, together with a synthetic numerical example which helps to elaborate conclusions about data dispersion and its relation to the accomplishment proposal.