The distributivity property of increasing binary operations

This paper is mainly devoted to solving the functional equations of distributivity and conditional distributivity of increasing binary operations with the unit. Our investigations are motivated by distributive logical connectives and their generalizations used in fuzzy set theory. In particular, some assumptions (namely associativity and commutativity) and results about conditional distributivity of uninorms and triangular norms and triangular conorms were simplified. Moreover, some other properties e.g. componentwise convexity (concavity) for special operations from the class of quasi-copulas is considered.