Abstract
An algebra (S, +, *, ~, 0, 1) is called a de Morgan bisemilattice, if (S, +, *) is a bisemilattice, 1 and 0 are the unit and zero elements of S, and ~ is a unary operation that satisfies the involution law and de Morgan's laws. The author introduced multi-interval truth values; a multi-interval truth value is a collection of interval truth values. A set of multi-interval truth values is a de Morgan bisemilattices, if we introduce 3 operations that are given by applying Zadeh's extension principle to the conventional 3 operations min, max, and 1-x. This paper focuses on a de Morgan bisemilattice such that S is a set of 4 elements, and the two semilattices are associated with two linear orders. Then, the paper discusses some of the mathematical properties of functions over the S that are expressed by formulas composed of the de Morgan bisemilattices.
