A First View on the Alternatives of Fuzzy Set Theory

Abstract

During many centuries probability theory and error calculus have been the only models to treat imprecision and uncertainty. In the past three decennia however a lot of new models have been introduced for handling incomplete information. Undoubtly fuzzy set theory initiated by Zadeh [1] in 1965 plays the central role. Besides this widely applied theory, many other models pretending to be competitive with fuzzy set theory have been launched: rough set theory, flou set theory, L-flou set theory, intuitionistic set theory ... Allthough we are convinced that freedom and openness in research has be be respected in a degree as large as possible we will warn for increasing the number of alternatives to a degree that introduces confusion and hence diminishes the trust in our models, especially for new practitioners. As I already mentioned in a previous paper [2], time has come to clean up the existing material, to summarize the relevant theoretical models and indicate their relevance by means of convicting concrete examples, by which I do not mean the stipulation in a superficial way of some possible areas of application but indeed the description of real situations and the solution of real problems. In this talk we will focuss on several alternative theories and try to indicate their mutual relationships and their relationships to earlier existing mathematical models.