Multi-interval truth valued logic

Many types of fuzzy truth values have been proposed, for example, numerical truth values, interval truth values, triangular truth values and trapezoid truth values and so on. This paper will discuss on algebraic structures on a new type of fuzzy truth values called multi-interval truth values. A multi-interval truth value is defined by the union of some of interval truth values. The operations on multi-interval truth values will be defined by applying the extension principle to the operations AND, OR, and NOT on numerical truth values. Then, the paper will show that an algebraic structure of multi-interval truth values with the operations defined is a de Morgan bisemilattice, which is a bisemilattice with the unit and zero, and with a unary operation that satisfies the involution and de Morgan's laws.