Fuzzy prime ideals of pseudo-MV algebras. (English) Zbl 1132.06006

Pseudo-MV algebras, as a non-commutative generalization of MV-algebras, are an algebraic counterpart of the non-commutative Łukasiewicz infinite-valued propositional logic. The paper deals with fuzzy ideals of pseudo-MV algebras. The author gives a new construction of the fuzzy ideal generated by a fuzzy set of a pseudo-MV algebra. Further, fuzzy prime ideals are introduced and connections between them and prime ideals of pseudo-MV algebras are described.


06D35 MV-algebras
Full Text: DOI


[1] Balbes R, Dwinger P (1974) Distributive lattices. University of Missouri Press, Columbia · Zbl 0321.06012
[2] Birkhoff G (1967) Lattice theory, 3rd edn, vol 25. Coll Publ, American Math Society · Zbl 0153.02501
[3] Boicescu V, Filipoiu A, Georgescu G, Rudeanu S (1991) Łukasiewicz-Moisil algebras, Annals of Discrete Math, vol 49. North-Holland, Amsterdam · Zbl 0726.06007
[4] Chang CC (1958) Algebraic analysis of many valued logics. Trans Am Math Soc 88:467–490 · Zbl 0084.00704
[5] Dvurečenskij A (2001) States on pseudo MV-algebras. Studia Logica 68:301–327 · Zbl 0999.06011
[6] Georgescu G, Iorgulescu A (1999) Pseudo-MV algebras: a non-commutative extension of MV-algebras. The proceedings of the fourth international symposium on economic informatics, Bucharest, Romania, May 1999, pp 961–968 · Zbl 0985.06007
[7] Georgescu G, Iorgulescu A (2001) Pseudo-MV algebras. Multi Val Logic 6:95–135 · Zbl 1014.06008
[8] Hoo CS (1994) Fuzzy ideals of BCI and MV-algebras. Fuzzy Sets Syst 62:111–114 · Zbl 0826.06011
[9] Hoo CS (1994) Fuzzy implicative and Boolean ideals of MV-algebras. Fuzzy Sets Syst 66:315–327 · Zbl 0844.06007
[10] Jun YB, Walendziak A (2006) Fuzzy ideals of pseudo MV-algebras. Inter Rev Fuzzy Math 1:21–31 · Zbl 1128.06005
[11] Rachunek J (2002) A non-commutative generalization of MV-algebras. Czechoslovak Math J 52:255–273 · Zbl 1012.06012
[12] Rachunek J (2002) Prime spectra of a non-commutative generalizations of MV-algebras. Algebra Univ 48:151–169 · Zbl 1058.06015
[13] Swamy UM, Viswanadha Raju D (1991) Algebraic fuzzy systems. Fuzzy Sets Syst 41:187–194 · Zbl 0732.08002
[14] Walendziak A (2005) On implicative ideals of pseudo MV-algebras. Sci Math Jpn 62:281–287, e-2005, 363–369 · Zbl 1086.06011
[15] Zadeh LA (1965) Fuzzy sets. Inform Control 8:338–353 · Zbl 0139.24606
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