C-sets of n-uninorms

The concept of n-uninorms was introduced in our earlier paper which is based on the existence of an n-neutral element for an associative, monotone non-decreasing in both variables and commutative (AMC) binary operator on [0,1]. There it was shown that the number of subclasses of n-uninorms is the (n+1)th Catalan number. An expression for the arbitrary member of each subclass was also given which is recursive in nature. In this paper we introduce a unique ordered set of distinct integers between 0 and n, called C-sets, for each subclass of n-uninorms. This enables us to(1)obtain an expression for arbitrary member of each subclass which is non-recursive in nature,(2)identify the minimum and the maximum members in general and of idempotent members in particular in each subclass,(3)relate C-sets of De Morgan pairs (for strict negation) of n-uninorms from different subclasses,(4)convert theoretical results into construction procedures which are algorithmic in nature.In process we generalize some of the existing results for uninorms in the literature.