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Equations in Type-2 Fuzzy Sets
Preview AbstractThe main concern of this paper is with the equations satisfied by the algebra of truth values of type-2 fuzzy sets. That algebra has elements all mappings from the unit interval into itself with operations given by certain convolutions of operations on the unit interval. There are a number of positive results. Among them is a decision procedure, similar to the method of truth tables, to determine when an equation holds in this algebra. One particular equation that holds in this algebra implies that every subalgebra of it that is a lattice is a distributive lattice. It is also shown that this algebra is locally finite. Many questions are left unanswered. For example, we do not know whether or not this algebra has a finite equational basis, that is, whether or not there is a finite set of equations from which all equations satisfied by this algebra follow. This and various other topics about the equations satisfied by this algebra will be discussed.