Preservation of the Exchange Principle under Lattice Operations on Fuzzy Implications
نویسندگان
چکیده
In this work, we solve an open problem related to the exchange principle of fuzzy implications [Problem 3.1, Fuzzy Sets and Systems 261(2015) 112-123]. We show that two important generalizations of the exchange principle, namely, the generalized exchange principle(GEP) and the mutual exchangeability(ME) are sufficient conditions for the solution of the problem. We also show that, under some conditions, these are necessary too. Finally, we investigate the pairs (I, J) from different families of fuzzy implications such that the exchange principle is preserved under the join and meet operations.
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