On generating uninorms on some special classes of bounded lattices

Some Conclusions on the Direct Product of Uninorms on Bounded Lattices

“…Definition 6 [1,10,13] Let L be a bounded lattice. An operation U : L 2 → L is called a uninorm on L, if it is commutative, associative, monotone and has a neutral element e ∈ L.…”

“…Here is an example illustrating such a case. Example 9 Consider the uninorm U 1 : [0, 1] 2 → [0, 1] with neutral element 1 2 defined as follows:…”

“…and consider the uninorm U := U min(T nM ,S M , 1 2 ) : [0, 1] 2 → [0, 1] with neutral element 1 2 defined in Example 5. We know that K U = (0, 1 2 ) by Aşıcı (see [3]). Similarly, it can be shown that K U 1 = (0, 1 2 ).…”

“…We know that K U = (0, 1 2 ) by Aşıcı (see [3]). Similarly, it can be shown that K U 1 = (0, 1 2 ). Also, it is clear that K U×U 1 = (0, 1 2 ) × (0, 1 2 ) = K U × K U 1 .…”