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A new proof of Nguyen's compatibility theorem in a more general context

✍ Scribed by Carlo Bertoluzza; Antonella Bodini

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 234 KB
Volume: 95
Category: Article
ISSN: 0165-0114
DOI: 10.1016/s0165-0114(96)00332-6

No coin nor oath required. For personal study only.

✦ Synopsis

Let f(R,S) 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 or-cuts of f(R, S) to be equal to the crisp images of the or-cuts of R, S. Here we give a simplified proof of this theorem which also holds in a more general context: particularly for second-order fuzzy subsets. (~) 1998 Elsevier Science B.V.

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