Abstract

Let f(R̃,S̃) be the image of a pair of fuzzy subsets constructed by applying Zadeh's (1975) extension principle to a function of two variables. Nguyen (1978) gave a necessary and sufficient condition for the a-cuts of f( R ̃ , S ̃ ) to be equal to t he crisp images of the a-cuts of Here we give a simplified proof of this theorem which also holds in a more general context: particularly for second-order fuzzy subsets.

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