This paper is mainly devoted to solving the distributivity equations for 2-uninorms over semi-uninorms. Our investigations are motivated by the couple of distributive logical connectives and their generalizations, such as t-norms, t-conorms, uninorms, nullnorms, and fuzzy implications, which are often used in fuzzy set theory. Recently, there are their two generalizations. One is a 2-uninorm covering both a uninorm and a nullnorm, which forms a class of commutative, associative and increasing operators on the unit interval with an absorbing element separating two subintervals having their own neutral elements. The other is a semi-uninorm, which generalizes a uninorm by omitting commutativity and associativity. In this work, all possible solutions of the distributivity equation for the three defined subclasses of 2-uninorms over semi-uninorms are characterized.
['Ya-Ming Wang', 'Feng Qin']
Distributivity for 2-Uninorms over Semi-uninorms