Intervals Pairs of Fuzzy Values Triples etc Can We Thus Get an Arbitrary Ordering

Traditional fuzzy logic uses real numbers as truth values This description is not always adequate so in interval valued fuzzy logic we use pairs t t of real numbers t t to describe a truth value To make this description even more adequate instead of using real numbers to described each value t and t we can use intervals and thus get fuzzy values which can be described by real numbers each We can iterate this procedure again and again The question is can we get an arbitrary partially ordered set in this manner An arbitrary lattice In this paper we show that although we cannot thus generate arbitrary lattices we can actually generate an arbitrary partially ordered set in this manner In this sense the intervalization operation is indeed universal