Quantification of uncertainty and training of fuzzy logic systems

The theory of fuzzy sets is an important tool in the design of many systems in a variety of disciplines, because of its ability to effectively handle uncertainty. Being able to quantify the amount of uncertainty associated with a fuzzy set is therefore an important issue. Firstly a quantitative measure of fuzziness is proposed, then it is used to find defuzzification methods that have the least amount of uncertainty associated with the produced defuzzified value, and finally, using the proposed measure, an adaptive algorithm that updates the centers of the consequent membership functions, to reduce uncertainty at the system output is derived. The effectiveness of the algorithm is illustrated with an application in nonlinear system identification.