An introduction to applications of possibility theory (+ commentaries by L.A. Zadeh, W. Bandler, T. Saaty, A. Kandel, D. Dubois & H. Prade, R.M. Tong and M. Kochen)

Abstract

A new form of uncertainty called possibilistic uncertainty is introduced. As opposed to probabilistic uncertainty, which is based upon an additive measure and is applicable in cases of repeated experiments, possibilistic uncertainty is based upon a non-additive measure and is a generalization of the idea of ease of attainment in a situation. We discuss the properties of possibilistic uncertainty and describe some prototypical examples. We also discuss the idea of language as being a generator of possibilistic variables. We introduce fuzzy subsets as a means of translating linguistic values into possibility distributions and the idea of approximate reasoning as a means of simulating a large class of human reasoning operations. We introduce a measure of specificity of a possibility distribution and discuss applications of fuzzy set theory to intelligent quering of data bases and multiple criteria decision making. Finally, we introduce some ideas from fuzzy arithmetic.