# A Reminder on Fuzzy Logic

• Dimiter Driankov
Chapter
Part of the Studies in Fuzziness and Soft Computing book series (STUDFUZZ, volume 61)

## Abstract

Fuzzy logic was primarily designed to represent and reason with knowledge expressed in a linguistic or verbal form. However, when using a languageoriented approach for representing knowledge about a certain system of interest, one is bound to encounter a number of non-trivial problems. Suppose, for example [10], that you are asked how strongly you agree that a given distance, [0m, 40m] which an indoor robot has to travel is a large distance. One way to answer this question is to say that if x ≥ d then you agree it is a large distance and if x < d then you disagree. Thus, if you place a mark on an agree-disagree scale, it might be distributed uniformly over the right half of the scale whenever x ≥ d and uniformly over the left half if x < d.

## Keywords

Membership Function Fuzzy Logic Fuzzy Rule Fuzzy Controller Linguistic Variable
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## References

1. 1.
Black, M., “Vagueness: An Exercise in Logical Analysis,” Philos. Sci., 4(1937)427–455.
2. 2.
Bonissone, P.P., A Pattern Recognition Approach to the Problem of Linguistic Approximation in Systems Analysis, Memo UCB/ERL M78/57, Electronics Research Lab., Univ. of California, Berkeley.Google Scholar
3. 3.
Cheeseman, P.C., “An Inquiry into Computer Understanding,” Computational Intelligence, 4(1)(1988)58–66.
4. 4.
Cox, R.T., “On Inference and Inquiry—An Essay in Inductive Logic.” In: L. Levine, and M. Tribus (eds.), The Maximum Entropy Formalism, Cambridge, MA, MIT Press, 1979.Google Scholar
5. 5.
Dombi, J., “A General Class of Fuzzy Operators and Fuzziness Measures Induced by Fuzzy Operators,” Fuzzy Sets and Systems, 8(1982)149–163.
6. 6.
Driankov, D., Hellendoorn, H., and Reinfrank, M., An Introduction to Fuzzy Control, 2nd rev. ed., Springer Verlag, 1996.
7. 7.
Hellendoorn, H., and Driankov, D. Fuzzy Model Identification - Selected Apvroaches. Springer Verlag, 1997.
8. 8.
Dubois, D., and Prade, H., “Comments on ‘An Inquiry into Computer Understanding’,” Computational Intelligence, 4(1)(1988)73–76.
9. 9.
10. 10.
Kochen, M., “Applications of Fuzzy Sets in Psychology.” In: L.A. Zadeh, K.S. Fu, K. Tanaka, and M. Shimura, (eds), Fuzzy Sets and their Applications to Cognitive and Decision Processes, New York, Academic Press, 1975, pp. 395–408.Google Scholar
11. 11.
Pedrycz, W., Fuzzy Control and Fuzzy Systems, 2nd revised edition, Research Studies Publ., 1992.Google Scholar
12. 12.
Schweitzer, B., and Sklar, A., “Associative Functions and Statistical Triangle Inequalities,” Publicationes Mathematicae Debrecen, 8(1961)169–186.
13. 13.
Schweitzer, B., and Sklar, A., “Associative Functions and Abstract Semigroups,” Publicationes Mathematicae Debrecen, 10(1963)69–81.
14. 14.
Weber, S., “A General Concept of Fuzzy Connectives, Negations and Implications Based on t-norms and t-co-norms,” Fuzzy Sets and Systems, 11(1983)115–134.
15. 15.
Zadeh, L.A., “Probability Measures of Fuzzy Events,” J. of Mathematical Analysis and Applications, 23(1968) 421–427.

## Authors and Affiliations

• Dimiter Driankov

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