A Note on the Distributivity of Fuzzy Implications over Representable Uninorms

Recently, many works have appeared dealing with the distributivity of fuzzy implications over t-norms, tconorms and uninorms (see [2, 3, 4, 5, 12, 13, 14]). These equations have a very important role to play in efficient inferencing in approximate reasoning, especially fuzzy control systems (see [6]). In this work we present some results connected with two functional equations describing the distributivity of fuzzy implications over representable uninorms. Toward this end, some new solutions of the additive Cauchy functional equation on the set [−∞,∞] has been obtained.