Fuzzy relation
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Before it make sense to explain what a fuzzy relation is, there is a need to introduce the term cartesian product. A cartesian product combines existing mathematical sets into a new set. This is realized by vector multiplication which is equal to the cross product.
Fuzzy relation are working the same way, except the case that the original sets are containing fuzzy values.[1] Two fuzzy sets are taken as input, and the fuzzy relation is equal to the cross product of the sets. 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.
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.
- category: Fuzzy logic