Applications of Fuzzy Set Theory and Fuzzy Logic

Fuzzy set theory provides a major newer paradigm in modeling and reasoning with uncertainty. Though there were several forerunners in science and philosophy, in particular in the areas of multivalued logic and vague concepts. Zadeh, a professor at Berkeley was the first to propose a theory of fuzzy sets and an associated logic, namely fuzzy logic. Essentially, a fuzzy set is a set whose members of the set may have degrees of membership between 0 and 1, as opposed to classical sets where each element must have either 0 or 1 as the membership degree—if 0, the element is completely outside the set; if 1, the element is completely in the set. As classical logic is based on classical set theory, fuzzy logic is based on fuzzy set theory.

Major industrial application areas

The first wave: Process control

The first industrial application of fuzzy logic was in the area of fuzzy controllers for cement kilns. Their usage then found popularity in Japan. The Japanese caught the idea, and applied it in an automatic-drive fuzzy control system for subway trains in Sendai City. The final product was extremely successful, and was generally praised as superior to other comparable systems based on classical control. This success encouraged a rapid increase in the Japanese’s interest in fuzzy controller during the late 1980s. This led to applications in other areas, like elevator control systems and air conditioning systems. In the early 1990s, the Japanese began to apply fuzzy controller in consumer products, like camcorders, washing machines, vacuum cleaners, and cars. The Japanese success led to increased interest in Europe and the US in fuzzy controller techniques.

The second wave: information systems

The second wave of fuzzy logic systems started in Europe in the early 1990s, namely in the area of information systems, in particular in databases and information retrieval. The first fuzzy logic based search engine was developed by Yager, Machine Intelligence Institute, US. It was aimed for application netbased commerce systems, namely, at that time the only in the world, the French Minitel. It was first demonstrated to the public at the Joint International Conference of Artificial Intelligence in 1992 in Chambery, France. In 1999, the technique was adopted by the Danish search engine Jubii. Internet and the Web gave new interest to application of fuzzy logic technology. In the net based society we have an enormous amount of information and knowledge electronic accessible for decision makers and human in general. Much of this information is inherently uncertain—lack of precision, vague concepts, more or less reliable information, etc. On the other hand, to be useful, users must be able to utilize it, despite the uncertainties. 

Today, this technique has found huge applications in the area of decision sciences in business intelligence and decision making, and is being thought of as one of the biggest change creating mathematical tool.

By fuzzy set theory we can provide exact representations of concepts and relations that are vague, that is, with no sharp yes-no borderline between cases covered, and cases not covered, by the concept or relation. This allows us to represent, for instance, that a document deals with a topic T1 to some degree (between 0 and 1), that a user is interested in a topic T2 to some degree, and that a topic T3 implies a topic T4 to some degree. By fuzzy set theory and fuzzy logic, we can not only represent such knowledge, but also utilize it to its full extent, taking the kind and the form of the uncertainties into account. This does not mean than fuzzy logic renders classical logic and probability theory obsolete. On the contrary, though fuzzy sets and fuzzy logic extend membership degrees and truth values from 0 and 1 to the real interval from 0 to 1, the definition of the fuzzy logic formalism still rely on the classical logic. Further more, we apply statistics based on probability theory in fuzzy data mining of knowledge — the main difference being that probabilities now are associated to fuzzy sets. Another advantage of fuzzy logic is that it allows fast processing of large bodies of complex knowledge, since processing is performed by numerical computations and not symbolic unification as in, e.g., logic programming formalisms. As opposed to neural nets, fuzzy logic has the advantage that it supports explicit representation of knowledge, like in symbolic formalisms, allowing us to combine knowledge in a controlled way.
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Arpan Kar

Professor at Indian Institute of Management
Dr. Kar is a Professor in Information Systems Management in Indian Institute of Management (IIM), one of the top institutions in Business Management education globally. He has extensive experience in teaching, training, consultancy and research. He has over 35 high impact publications. Prior to joining academia, he has rich experience in Cognizant Business Consulting and IBM Research Laboratory. He is the Editor of Business Fundas.
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