Abstract
Many types of fuzzy truth values have been proposed, such as numerical truth values, interval truth values, triangular truth values and trapezoid truth values and so on. Recently, different type of fuzzy truth values (which we call multi-interval truth values) have been proposed and discussed. A characteristic feature of multi-interval truth values is that some of the truth values are not convex. This fact makes us difficult to understand algebraic properties on multi-interval truth values. This paper first shows that a set of multi-interval truth values is de Morgan bi-lattices when the conventional logical operations are introduced. Next, this paper focuses on functions over the set of the simplest multi-interval truth values, i.e., we define a multi-interval truth value as a non-empty subset of {0, 1, 2}. Then, this paper discusses mathematical properties of functions over multi-interval truth values.
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