Conceptual differences between possibility theory and fuzzy sets in modeling uncertainty

Abstract

Many engineering applications, in the field of fuzzy sets theory and the possibility theory, have been developed without taking account much attention to the semantics involved in its use. As a result, there is a very friendly and robust mathematical structure to combine fuzzy sets, but often this is presented without assigning any interpretative structures. In doing so, it is taken a risk on the one hand, confuse their use, and also, deny the users of this technique of guidelines on how and in which situations is adequate to apply this rule. Inevitably, this situation leads to the development of simple operations, which are semantically meaningless. Then, this paper presents both explanations and examples that seek to explain and highlight the underlying differences, in order to make better use of fuzzy sets in decision making