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General forms of lower triangular ordinal sums of fuzzy implications. (Chinese. English summary) Zbl 1463.03006

Summary: By using the method of ordinal sum, we investigated the necessary and sufficient conditions for a general fuzzy implication to be a proper complement to linear transformations of a given family of fuzzy implications on a given family of lower triangular parts of subsquares in the unit square. We put all kinds of lower triangular ordinal sum implications into a unified framework, and then gave the general form of construction of lower triangular ordinal sums of fuzzy implications.

MSC:

03B52 Fuzzy logic; logic of vagueness
03E72 Theory of fuzzy sets, etc.
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