On a new class of uninorms on bounded lattices

Construction of uninorms on bounded lattices

“…Such uninorms are interesting not only from a theoretical point of view (because of their structure, namely combination of a t-norm and a t-conorm), but also for their applications, since they have proved to be useful in several fields like expert systems, neural networks, fuzzy quantifiers. The uninorms were also studied by many authors in other papers [5,6,7,9,10,11,12,13,18,20,21].…”

An extension of the ordering based on nullnorms

“…Since S * is ∧-distributive, we have that Consider the unique idempotent nullnorm F with zero element a ∈ L \ {0, 1} defined as follows [13]:…”

Some methods to obtain t-norms and t-conorms on bounded lattices

“…Definition 2.4. (Ç aylı et al [7], Ç aylı [9,11]) Let (L, ≤, 0, 1) be a bounded lattice. An operation T : L 2 → L is called a t-norm on L if it is commutative, associative, increasing with respect to both variables and has the neutral element 1 such that T (x, 1) = x, for all x ∈ L. Definition 2.5.…”