Type-2 fuzzy sets and bichains

Abstract

This paper is a continuation of the study of the variety generated by the truth value algebra of type-2 fuzzy sets. That variety and some of its reducts were shown to be generated by finite algebras, and in particular to be locally finite. A basic question remaining is whether or not these algebras have finite equational bases, and that is our principal concern in this paper. The variety generated by the truth value algebra of type-2 fuzzy sets with only its two semilattice operations in its type is generated by a four element algebra that is a bichain. Our initial goal is to understand the equational properties of this particular bichain, and in particular whether or not it has a finite equational basis.