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Title: Interior and closure operators on bounded residuated lattice ordered monoids (English)
Author: Švrček, Filip
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 58
Issue: 2
Year: 2008
Pages: 345-357
Summary lang: English
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Category: math
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Summary: $GMV$-algebras endowed with additive closure operators or with its duals-multiplicative interior operators (closure or interior $GMV$-algebras) were introduced as a non-commutative generalization of topological Boolean algebras. In the paper, the multiplicative interior and additive closure operators on $DRl$-monoids are introduced as natural generalizations of the multiplicative interior and additive closure operators on $GMV$-algebras. (English)
Keyword: $GMV$-algebra
Keyword: $DRl$-monoid
Keyword: filter
MSC: 03G25
MSC: 06D35
MSC: 06F05
idZBL: Zbl 1174.06323
idMR: MR2411094
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Date available: 2009-09-24T11:55:14Z
Last updated: 2020-07-03
Stable URL: http://hdl.handle.net/10338.dmlcz/128262
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Reference: [1] P. Bahls, J. Cole, N. Galatos, P. Jipsen and C. Tsinakis: Cancellative residuated lattices.Alg. Univ. 50 (2003), 83–106. MR 2026830, 10.1007/s00012-003-1822-4
Reference: [2] K. Blount and C. Tsinakis: The structure of residuated lattices.Intern. J. Alg. Comp. 13 (2003), 437–461. MR 2022118, 10.1142/S0218196703001511
Reference: [3] R. O. L. Cignoli, I. M. L. D’Ottaviano and D. Mundici: Algebraic Foundations of Many-Valued Reasoning.Kluwer Acad. Publ., Dordrecht-Boston-London, 2000. MR 1786097
Reference: [4] A. Dvurečenskij: States on pseudo $MV$-algebras.Studia Logica 68 (2001), 301–327. MR 1865858, 10.1023/A:1012490620450
Reference: [5] A. Dvurečenskij: Every linear pseudo $BL$-algebra admits a state.Soft Computing (2006).
Reference: [6] A. Dvurečenskij and M. Hyčko: On the existence of states for linear pseudo $BL$-algebras.Atti Sem. Mat. Fis. Univ. Modena e Reggio Emilia 53 (2005), 93–110. MR 2199034
Reference: [7] A. Dvurečenskij and S. Pulmannová: New Trends in Quantum Structures.Kluwer Acad. Publ., Dordrecht-Boston-London, 2000. MR 1861369
Reference: [8] A. Dvurečenskij and J. Rachůnek: On Riečan and Bosbach states for bounded $Rl$-monoids.(to appear).
Reference: [9] A. Dvurečenskij and J. Rachůnek: Probabilistic averaging in bounded $Rl$-monoids.Semigroup Forum 72 (2006), 190–206. MR 2216089
Reference: [10] G. Georgescu and A. Iorgulescu: Pseudo-$MV$-algebras.Multiple Valued Logic 6 (2001), 95–135. MR 1817439
Reference: [11] A. di Nola, G. Georgescu and A. Iorgulescu: Pseudo-$BL$-algebras I.Multiple Valued Logic 8 (2002), 673–714. MR 1948853
Reference: [12] A. di Nola, G. Georgescu and A. Iorgulescu: Pseudo-$BL$-algebras II.Multiple Valued Logic 8 (2002), 715–750. MR 1948854
Reference: [13] P. Hájek: Metamathematics of Fuzzy Logic.Kluwer, Amsterdam, 1998. MR 1900263
Reference: [14] P. Jipsen and C. Tsinakis: A survey of residuated lattices.Ordered algebraic structures (ed. J. Martinez), Kluwer Acad. Publ. Dordrecht, 2002, pp. 19–56. MR 2083033
Reference: [15] T. Kovář: A General Theory of Dually Residuated Lattice Ordered Monoids.Ph.D. Thesis Palacký University, Olomouc, 1996.
Reference: [16] J. Kühr: Dually Residuated Lattice Ordered Monoids.Ph.D. Thesis, Palacký Univ., Olomouc, 2003. MR 2070377
Reference: [17] J. Kühr: Remarks on ideals in lower-bounded dually residuated lattice-ordered monoids.Acta Univ. Palacki. Olomouc, Mathematica 43 (2004), 105–112. MR 2124607
Reference: [18] J. Kühr: Ideals of noncommutative ${\mathcal{D}}Rl$-monoids.Czech. Math. J. 55 (2002), 97–111. MR 2121658
Reference: [19] J. Rachůnek: $DRl$-semigroups and $MV$-algebras.Czech. Math. J. 48 (1998), 365–372. 10.1023/A:1022801907138
Reference: [20] J. Rachůnek: $MV$-algebras are categorically equivalent to a class of $DRl_{1(i)}$-semigroups.Math. Bohem. 123 (1998), 437–441. MR 1667115
Reference: [21] J. Rachůnek: A duality between algebras of basic logic and bounded representable $DRl$-monoids.Math. Bohem. 126 (2001), 561–569. MR 1970259
Reference: [22] J. Rachůnek: A non-commutative generalization of $MV$-algebras.Czech. Math. J. 52 (2002), 255–273. MR 1905434, 10.1023/A:1021766309509
Reference: [23] J. Rachůnek and V. Slezák: Bounded dually residuated lattice ordered monoids as a generalization of fuzzy structures.Math. Slovaca 56 (2006), 223–233. MR 2229343
Reference: [24] J. Rachůnek and D. Šalounová: Local bounded commutative residuated $l$-monoids.(to appear). MR 2309973
Reference: [25] J. Rachůnek and F. Švrček: $MV$-algebras with additive closure operators.Acta Univ. Palacki., Mathematica 39 (2000), 183–189.
Reference: [26] F. Švrček: Operators on $GMV$-algebras.Math. Bohem. 129 (2004), 337–347. MR 2102608
Reference: [27] H. Rasiowa and R. Sikorski: The Mathematics of Metamathematics.Panstw. Wyd. Nauk., Warszawa, 1963. MR 0163850
Reference: [28] K. L. N. Swamy: Dually residuated lattice ordered semigroups.Math. Ann. 159 (1965), 105–114. Zbl 0138.02104, MR 0183797, 10.1007/BF01360284
Reference: [29] E. Turunen: Mathematics Behind Fuzzy Logic.Physica-Verlag, Heidelberg-New York, 1999. Zbl 0940.03029, MR 1716958
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