An Algebraic Structure of Multiple-Interval Truth Values

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, other type of fuzzy truth values (which are called multi-interval truth values) have been proposed and discussed. The characteristic feature of multi-interval truth values is that some of the truth values are not convex. This fact makes the algebraic structures of multi-interval truth values be complex. So, this paper clarifies some of the properties on functions over multi-interval truth values, when the number of variables and the number of non-convex multi-interval truth values are restricted.