Approximation of Membership Functions and Aggregation Operators Using Splines
A good choice of membership functions and aggregation operators is crucial to the behavior fuzzy systems. In many cases there are no theoretical criteria that would justify the use of one or another function, and they are selected based on their goodness of fit to empirical data. This paper discusses a general non-parametric approach to construction of membership functions and aggregation operators based on empirical data. This method is computer oriented: it does not produce operators in closed algebraic form, but the quality of fit and flexibility are superior to other methods. The method is also general, since it can produce membership functions and operators from any class. Restrictions to a particular class can be easily introduced. Examples based on published empirical data are provided.
KeywordsMembership Function Aggregation Operator Algebraic Form Quadratic Spline Triangular Norm
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