Fuzzy rules and fuzzy functions: A combination of logic and arithmetic operations for fuzzy numbers. (English) Zbl 0938.03082
Summary: A general class of fuzzy numbers is introduced: triangular fuzzy numbers (TFNs) in extended representation. This representation allows the operations of fuzzy arithmetic as well as fuzzy logic to be defined within this class of extended TFN (at least approximately). This leads naturally to the definition of fuzzy functions, and it is shown that Sugeno-type fuzzy rules can be expressed by such functions. In this context the Sugeno controller is able to use fuzzy numbers as input variables, thus extending the original concept of using crisp values as input.
MSC:
| 03E72 | Theory of fuzzy sets, etc. |
| 26E50 | Fuzzy real analysis |
| 03B52 | Fuzzy logic; logic of vagueness |
| 93C42 | Fuzzy control/observation systems |
Keywords:
triangular fuzzy numbers; fuzzy arithmetic; fuzzy logic; fuzzy functions; Sugeno controllerReferences:
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