A thorough study of interrelationship in fuzzy implication axioms

A fuzzy implication is an extension of the classical binary implication in fuzzy logic that plays an important role in the approximate reasoning process and in decision making applications. It should satisfy different potential axioms, among which 8 axioms are most important. Different authors have investigated the dependence and independence of the 8 axioms but the investigation is yet not complete. We study a complete interrelationship of all the 8 axioms, and give for each independence case a counter-example.

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