Fifty Years of Fuzzy Sets: Contributions to Fuzzy Theory (Preface to the Special Issue)

Abstract

The Special Issue of International Journal of Intelligent Systems lists all the achievements and challenges of fuzzy sets. On the first stage, the main challenge is to provide theoretical classification analysis of numerous semiheuristic techniques for transforming imprecise expert knowledge into numbers. This analysis should enable us to better understand why different techniques are successful and help us select a technique that is the most appropriate for a given situation. With regard to the second stage, researchers have performed a thorough analysis of different ways to combine and process different relations. The main remaining theoretical challenges, in our opinion, are related not so much to the mathematics of these operations, but rather to their meaning. On the third defuzzification stage, the main theoretical challenge is to explain why some defuzzification procedures are empirically successful.