Type-2 fuzzy sets, an elaboration over type-1 fuzzy sets, are an interesting method for handling uncertainty in rules and parameters in fuzzy systems. However, their adoption has not been as wide as one could have expected. In this paper we provide a simple introduction to type-2 fuzzy sets; then we propose a novel method for calculating operations on type-2 fuzzy sets with normal type-1 membership values, for which we redefine set ordering. Finally, based on the max ordering of fuzzy set and highest degree of separation, we propose an approximation for performing the operations, which ensures that the calculation is accurate for the most important parts of the membership values.

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Abstract-The notion of distributed interval, as a formal framework for information granulation, represented by the collection of finite number of general-intervals is introduced. Operations on distributed intervals are defined based on the corresponding general-intervals'. Distributed intervals provide a bi-criteria framework for information granulation that can be used as a conceptually rich structure in granular computing.