Fuzzy Relations and Cognitive Representations

Abstract

Fuzzy set theory and fuzzy logics were able to demonstrate impressive achievements in control theory and in technical applications already in the 1970s; but Lotfi Zadeh’s great concern was - and still is - to demonstrate the power of his radically different approach to representing human concepts as a representational foundation in Artificial Intelligence. With his approach of introducing graded compatibility values to describe relations between concepts and real-world entities, formal systems can characterize states of affairs in terms of a manageable number of concepts - much like humans who describe the world by concepts that are qualified through linguistic hedges, prosodic emphasis or attenuation, and many other subtle ways of describing situations in a differentiated way to capture their essential significance in a concise manner.

Such mechanisms enable humans to summarize complex events in a meaningful way. Without the ability to drastically eliminate details of events, people would be incapable of dealing with the complexity of the world. With this insight, Lotfi Zadeh described in the 1970s [7] his personal grand challenge for Artificial Intelligence: the ability to automatically summarize the content of a paper or a book as capable humans can do it. Zadeh realized that this would be extremely difficult to achieve by the dominating approaches in AI, at the time; the Fuzzy Set approach, in contrast, has a built-in approach to generalize from specific instances and to ignore insignificant details.