Fuzzy relation
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A Fuzzy relation is the cartesian product of mathematical fuzzy sets.[1] Two fuzzy sets are taken as input, and the fuzzy relation is equal to the cross product of the sets which is created by vector multiplication. Usually, a rule base is stored in a matrix notation which allows the fuzzy controller to update it's internal values.[2][3]
From a historical perspective, the first Fuzzy relation was mentioned in the year 1971 by the father of Fuzzy logic.[4]
A practical approach to describe a Fuzzy relation is based on a 2d table. At first, a table is created which contains of Fuzzy values from 0..1. The next step is to apply the if-then-rules to the values. The resulting numbers are stored in the table as an array.
Fuzzy relations can be utilized in Fuzzy databases.[5]
References
- ^ Timothy J. Ross (8 April 2005). Fuzzy Logic with Engineering Applications. John Wiley & Sons. pp. 59–. ISBN 978-0-470-86076-2.
- ^ Galindo, Jos (31 May 2008). Handbook of Research on Fuzzy Information Processing in Databases. IGI Global. pp. 17–. ISBN 978-1-59904-854-3.
- ^ Witold Pedrycz (31 March 1996). Fuzzy Modelling: Paradigms and Practice. Springer Science & Business Media. pp. 39–. ISBN 978-0-7923-9703-8.
- ^ Witold Pedrycz; Fernando Gomide (12 October 2007). Fuzzy Systems Engineering: Toward Human-Centric Computing. John Wiley & Sons. pp. 156–. ISBN 978-0-470-16895-0.
- ^ Zongmin Ma (30 March 2006). Fuzzy Database Modeling with XML. Springer Science & Business Media. p. 97–. ISBN 978-0-387-24249-1.
- category: Fuzzy logic