Fuzzy Integral Equations

Abstract We introduce a definition of the integral of a fuzzy-valued function that is only slightly different from the usual one, yet that is more intuitive and that can be applied to a larger class of functions. We show that our definition is equivalent to the extension principle for functions of this class. We then apply integration theory of fuzzy-valued functions to integral equations. We define a “measure” of the fuzziness of a fuzzy-valued function and show that, using this measure, we can view the integration of fuzzy functions as a fuzzy linear transformation 'from a certain subspace of fuzzy-valued functions to the space of fuzzy numbers. We then show how this can be used to study Fredholm integral equations of the second kind.