Abstract
The traditional way for fuzzifying the real-valued functions is based on the extension principle. In this paper, we shall propose a new methodology to fuzzify the real-valued function based on the form of decomposition theorem. We shall also claim that this new methodology prefers to be used in real situations when the fuzziness is taken into account. An interesting application of this new methodology is to define the new types of arithmetics of fuzzy numbers. The differentiations and integrals of fuzzy-number-valued functions can also be defined by this new methodology.
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