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

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)].


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


Zbl 1114.03053
Full Text: DOI


[1] DOI: 10.1142/S021848850600428X · Zbl 1114.03053
[2] DOI: 10.1016/j.fss.2003.12.003 · Zbl 1064.03020
[3] DOI: 10.1016/0020-0255(75)90036-5 · Zbl 0397.68071
[4] DOI: 10.1016/S0019-9958(79)90730-7 · Zbl 0434.03020
[5] DOI: 10.1142/S021848859900026X · Zbl 1113.03317
[6] DOI: 10.1142/S0218488598000434 · Zbl 1087.68639
[7] DOI: 10.1016/S0165-0114(00)00079-8 · Zbl 1010.03047
[8] DOI: 10.1109/91.995115
[9] DOI: 10.1016/S0019-9958(76)80011-3 · Zbl 0331.02042
[10] DOI: 10.1016/0165-0114(81)90056-7 · Zbl 0457.04005
[11] DOI: 10.1007/3-540-58279-7_15
[12] Nieminen J., Kybernetika 13 pp 261–
[13] DOI: 10.1002/(SICI)1098-111X(199610)11:10<751::AID-INT3>3.0.CO;2-Y · Zbl 0865.04006
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.