Type-2 Intervals of Constant Height

Abstract

The algebra of truth values for fuzzy sets of type-2, with operations due to Zadeh, contains as subalgebras those of type-1 and of interval-valued fuzzy sets. It also contains many other interesting sub algebras, some of which could possibly serve as a basis of a useful fuzzy set theory. This paper is about such a sub algebra, one which generalizes the truth value algebra of interval-valued fuzzy sets. We investigate it as an algebra, and determine its automorphism group. In particular, we show that it is a characteristic subalgebra of the containing truth value algebra of fuzzy sets of type-2, and that its automorphisms are exactly those induced by automorphisms of that algebra.