∨-distributive n-ary semicopulas on lattices.

In the present paper, definitions of an n -ary semicopula on a bounded lattice L , a ∨-distributive n -ary semicopula on L and an infinite ∨-distributive n -ary semicopula on L are introduced. A relation between the set of all bounded lattices L with a ∨-distributive n -ary semicopula on L and the set of all bounded lattices L with a ∨-distributive m -ary semicopula on L , where 2 ≤ n , 2 ≤ m , n ≠ m , is obtained. The method is given for investigation of the following questions: a description of all bounded lattices L such that every n -ary semicopula on L is ∨-distributive and a description of all complete lattices L such that every n -ary semicopula on L is infinite ∨-distributive. [ABSTRACT FROM AUTHOR]