On practical problems with the explanation of the difference between possibility and probability

Abstract: In his famous paper “Fuzzy Sets as a Basis for a Theory of Possibility” (Zadeh, 1978) Professor Lofti Zadeh introduced the notion of possibility distribution πX and the concept of possibility measure. He defined in the paper the possibility distribution function to be numerically equal to the membership function (πX = μF ). In this paper Professor Zadeh draws the special attention of the reader to the fact that: “ . . . there is a fundamental difference between probability and possibility”. To explain this difference he had given a special example illustrating the difference, which then was cited by many authors of books on Fuzzy Set Theory and gained great importance for understanding the notion of possibility. In the paper the author presents his doubts as to this important example, explains why it is incorrect and gives a correct version of the example based on the notion of possibility distribution of Dubois and Prade.