Handling uncertainties of membership functions with Shadowed Fuzzy Sets

Type-2 fuzzy set, as an extension to ordinary fuzzy set, is defined as a fuzzy set with fuzzy membership function. Type-2 fuzzy set enables capturing the uncertainty of membership functions. However due to the three dimensional nature of type-2 fuzzy sets and the high computational complexity of their operations, in real applications, interval type-2 fuzzy sets are used. In interval type-2 fuzzy sets the distribution sitting on the top of the Footprint of Uncertainty that constitutes the third dimension of type-2 fuzzy set is ignored and hence the membership grades are intervals. This results in simpler operations and easier concept but causes loss of information. Shadowed fuzzy set discussed in this paper, provides a framework whose simplicity is comparable with interval type-2 fuzzy set but on the other hand preserves the fuzziness of the third dimension of type-2 fuzzy sets.