Extending the Fuzzy Rule Interpolation "FIVE" by Fuzzy Observation

Some difficulties emerging during the construction of fuzzy rule bases are inherited from the type of the applied fuzzy reasoning. In fuzzy systems, when classical methods (e.g. the Compositional Rule of Inference) are applied, the completeness of the fuzzy rule base is required to generate meaningful output. This means, that the fuzzy rule base has to cover all possible inputs. The way of building a complete rule base is not always straightforward. One simple solution to handle sparse fuzzy rule bases and to make infer reasonable output is the application of fuzzy rule interpolation (FRI) methods. On the other hand most of the FRI methods share the burden of high computational demand. However there is a method “FIVE” (Fuzzy Interpolation based on Vague Environment, originally introduced in [8], [11] and [12]) which is simple and quick enough to fit even the requirements of direct control, where the conclusions are applied as real-time control actions, too. Beyond the simplicity and therefore the high reasoning speed, “FIVE” has two obvious drawbacks, the lack of the fuzziness on the observation and conclusion side. The main contribution of this paper is the introduction of a way for handling fuzzy observations by extending the original “FIVE” concept with the ability of merging vague environments.