Automorphisms of the algebra of fuzzy truth values. II. (English) Zbl 1152.03331

Walker, Carol L.; Walker, Elbert A.

Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 16, No. 5, 627-643 (2008).

Summary: This paper continues an earlier investigation of automorphisms of the algebra of truth values of type-2 fuzzy sets. Several significant problems left unresolved are settled, the most basic being that the automorphism group of the algebra of fuzzy truth values is isomorphic in a natural way to the product of two copies of the automorphism group of the unit interval. This theorem has several corollaries concerning characteristic subalgebras.
For part I, cf. [Int. J. Uncertain. Fuzziness Knowl.-Based Syst. 14, No. 6, 711–732 (2006; Zbl 1114.03053)].

MSC:

03G25	Other algebras related to logic
03B52	Fuzzy logic; logic of vagueness
03E72	Theory of fuzzy sets, etc.

Citations:

Zbl 1114.03053

References:

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