Czasopismo
Tytuł artykułu
Autorzy
Warianty tytułu
Języki publikacji
Abstrakty
Bounded integral residuated lattices form a large class of algebras containing some classes of algebras behind many valued and fuzzy logics. In the paper we introduce and investigate multiplicative interior and additive closure operators (mi- and ac-operators) generalizing topological interior and closure operators on such algebras. We describe connections between mi- and ac-operators, and for residuated lattices with Glivenko property we give connections between operators on them and on the residuated lattices of their regular elements.
Kategorie tematyczne
Wydawca
Czasopismo
Rocznik
Tom
Numer
Strony
534-544
Opis fizyczny
Daty
wydano
2014-03-01
online
2013-12-21
Twórcy
Bibliografia
- [1] Balbes R., Dwinger P., Distributive Lattices, University of Missouri Press, Columbia, 1974
- [2] Cignoli R.L.O., D’Ottaviano I.M.L., Mundici D., Algebraic Foundations of Many-Valued Reasoning, Trends Log. Stud. Log. Libr., 7, Kluwer, Dordrecht, 2000 http://dx.doi.org/10.1007/978-94-015-9480-6[Crossref]
- [3] Cignoli, R., Torrens Torrell A., Glivenko like theorems in natural expansions of BCK-logic, MLQ Math. Log. Q., 2004, 50(2), 111–125 http://dx.doi.org/10.1002/malq.200310082[Crossref]
- [4] Ciungu L.C., Classes of residuated lattices, An. Univ. Craiova Ser. Mat. Inform., 2006, 33, 189–207
- [5] Dvurečenskij A., Every linear pseudo BL-algebra admits a state, Soft Computing, 2007, 11(6), 495–501 http://dx.doi.org/10.1007/s00500-006-0078-2[Crossref][WoS]
- [6] Dvurečenskij A., Rachůnek J., On Riečan and Bosbach states for bounded non-commutative Rℓ-monoids, Math. Slovaca, 2006, 56(5), 487–500
- [7] Dvurečenskij A., Rachůnek J., Probabilistic averaging in bounded commutative residuated ℓ-monoids, Discrete Math., 2006, 306(13), 1317–1326 http://dx.doi.org/10.1016/j.disc.2005.12.024[Crossref]
- [8] Dvurečenskij A., Rachůnek J., Probabilistic averaging in bounded Rℓ-monoids, Semigroup Forum, 2006, 72(2), 190–206
- [9] Esteva F., Godo L., Monoidal t-norm based logic: towards a logic for left-continuous t-norms, Fuzzy Sets and Systems, 2001, 124(3), 271–288 http://dx.doi.org/10.1016/S0165-0114(01)00098-7[Crossref]
- [10] Flondor P., Georgescu G., Iorgulescu A., Pseudo-t-norms and pseudo-BL algebras, Soft Computing, 2001, 5(5), 355–371 http://dx.doi.org/10.1007/s005000100137[Crossref][WoS]
- [11] Galatos N., Jipsen P., Kowalski T., Ono H., Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Stud. Logic Found. Math., 151, Elsevier, Amsterdam, 2007
- [12] Georgescu G., Iorgulescu A., Pseudo-MV algebras, Mult.-Valued Logic, 2001, 6(1–2), 95–135
- [13] Hájek P., Metamathematics of Fuzzy Logic, Trends Log. Stud. Log. Libr., 4, Kluwer, Dordrecht, 1998 http://dx.doi.org/10.1007/978-94-011-5300-3[Crossref]
- [14] Jipsen P., Tsinakis C., A Survey of Residuated Lattices, In: Ordered Algebraic Structures, Gainesville, February 28–March 3, 2001, Dev. Math., 7, Kluwer, Dordrecht, 2006, 19–56
- [15] di Nola A., Georgescu G., Iorgulescu A., Pseudo-BL algebras I, Mult.-Valued Log., 2002, 8(5–6), 673–714
- [16] Rachůnek J., A non-commutative generalization of MV-algebras, Czechoslovak Math. J., 2002, 52(2), 255–273 http://dx.doi.org/10.1023/A:1021766309509[Crossref]
- [17] Rachůnek J., Šalounová D., A generalization of local fuzzy structures, Soft Computing, 2007, 11(6), 565–571 http://dx.doi.org/10.1007/s00500-006-0101-7[WoS][Crossref]
- [18] Rachůnek J., Šalounová D., States on Generalizations of Fuzzy Structures, Palacký University Press, Olomouc, 2011
- [19] Rachůnek J., Slezák V., Negation in bounded commutative DRℓ-monoids, Czechoslovak Math. J., 2007, 56(131)(2), 755–763
- [20] Rachůnek J., Švrček F., MV-algebras with additive closure operators, Acta Univ. Palack. Olomouc. Fac. Rerum Natur. Math., 2000, 39, 183–189
- [21] Rachůnek J., Švrček F., Interior and closure operators on bounded commutative residuated ℓ-monoids, Discuss. Math. Gen. Algebra Appl., 2008, 28(1), 11–27 http://dx.doi.org/10.7151/dmgaa.1132[Crossref]
- [22] Sikorski R., Boolean Algebras, 2nd ed., Ergeb. Math. Grenzgeb., 25, Academic Press, New York/Springer, Berlin-New York, 1964
- [23] Švrček F., Interior and closure operators on bounded residuated lattice ordered monoids, Czechoslovak Math. J., 2008, 58(133) (2), 345–357 [WoS]
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_2478_s11533-013-0349-y