The unbearable richness of fuzzy relational calculus for knowledge processing

Summary form only given. The concept of a relation is one of the most fundamental notions in pure as well as in applied sciences. The fuzzification of this fundamental notion, i.e. instead of dealing with connected or unconnected objects one considers objects that are linked in some degree, has thoroughly enriched the applicability of this notion. Due to the notions of after and foreset introduced by Bandler and Kohout, some very important new ways of composing crisp and fuzzy relations and of imaging crisp and fuzzy sets under crisp and fuzzy relations have been introduced and substantially increased the expressiveness of the fizzy relational calculus, particularly for the representation and the processing of human knowledge. In this paper the author gives an overview of this new machinery and shows its expressive power to tackle incomplete information in several domains among them: information retrieval, medical diagnosis, expert systems, relational databases, preference structures, and ordering procedures.