Fuzzy control

By the expression Fuzzy logic one denotes several topics which are related with the notion of fuzzy subset defined in 1965 by Lotfi Zadeh. Mainly, we have to distinguish two interpretations of the word "fuzzy logic". The first one is related with an informal utilization of the notion of fuzzy set and it is devoted to the applications. In such a case should be better expressions as "fuzzy set theory" or "fuzzy logic in board sense".

Another interpretation is given in considering fuzzy logic as a chapter of formal logic, more precisely of multi-valued logic. In such a case one uses the expression "fuzzy logic in narrow sense" or "formal fuzzy logic".

See also

• Multi-valued logic
• Soft-computing
• Neuro-fuzzy
• Fuzzy subalgebra
• Fuzzy associative matrix
• FuzzyCLIPS expert system
• Fuzzy control system
• Fuzzy set
• Paradox of the heap
• Pattern recognition
• Rough set

Bibliography

• Chang C. C.,Keisler H. J., Continuous Model Theory, Princeton University Press, Princeton, 1996.
• Cignoli R., D’Ottaviano I. M. L. , Mundici D. , ‘’Algebraic Foundations of Many-Valued Reasoning’’. Kluwer, Dordrecht, 1999.
• Cox E., The Fuzzy Systems Handbook (1994), ISBN 0-12-194270-8
• Elkan C.. The Paradoxical Success of Fuzzy Logic. November 1993. Available from Elkan's home page.
• Gerla G., Fuzzy logic: Mathematical Tools for Approximate Reasoning, Kluwer, 2001.
• Hájek P., Metamathematics of fuzzy logic. Kluwer 1998.
• Hájek P., Fuzzy logic and arithmetical hierarchy, Fuzzy Sets and Systems, 3, (1995), 359-363.
• Höppner F., Klawonn F., Kruse R. and Runkler T., Fuzzy Cluster Analysis (1999), ISBN 0-471-98864-2.
• Klir G. and Folger T., Fuzzy Sets, Uncertainty, and Information (1988), ISBN 0-13-345984-5.
• Klir G. , UTE H. St. Clair and Bo Yuan Fuzzy Set Theory Foundations and Applications,1997.
• Klir G. and Bo Yuan, Fuzzy Sets and Fuzzy Logic (1995) ISBN 0-13-101171-5
• Bart Kosko, Fuzzy Thinking: The New Science of Fuzzy Logic (1993), Hyperion. ISBN 0-7868-8021-X
• Montagna F., Three complexity problems in quantified fuzzy logic. Studia Logica, 68,(2001), 143-152.
• Novák V., Perfilieva I, Mockor J., Mathematical Principles of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht, (1999).
• Yager R. and Filev D., Essentials of Fuzzy Modeling and Control (1994), ISBN 0-471-01761-2
• Zimmermann H., Fuzzy Set Theory and its Applications (2001), ISBN 0-7923-7435-5.
• Kevin M. Passino and Stephen Yurkovich, Fuzzy Control, Addison Wesley Longman, Menlo Park, CA, 1998.
• Wiedermann J. , Characterizing the super-Turing computing power and efficiency of classical fuzzy Turing machines, Theor. Comput. Sci. 317, (2004), 61-69.
• Zadeh L.A., Fuzzy algorithms, Information and Control, 5,(1968), 94-102.
• Zadeh L.A., Fuzzy Sets, ‘’Information and Control’’, 8 (1965) 338­353.
• Zemankova-Leech, M., Fuzzy Relational Data Bases (1983), Ph. D. Dissertation, Florida State University.