Abstract
Distributivity properties play an important role in fuzzy research. Based on the solution of the autodistributivity functional equations, we give a characterisation of two types of distributivity of fuzzy implication. Based on the mean disjunctive operator, the mean implication operator is introduced. Using the Pliant operators -where all operators have a common generator function- we show that some weakened properties of the fuzzy mean implications are valid. In the propositions we use the fixed point of the negation as a threshold. Finally, the generalized modus ponens is examined in this framework.
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Dombi, J. (2018). On Implication Operators. In: Torra, V., Mesiar, R., Baets, B. (eds) Aggregation Functions in Theory and in Practice. AGOP 2017. Advances in Intelligent Systems and Computing, vol 581. Springer, Cham. https://doi.org/10.1007/978-3-319-59306-7_25
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DOI: https://doi.org/10.1007/978-3-319-59306-7_25
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