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17-11-2017 | Foundations

Some results on fuzzy \(Z_{L}\)-continuous(algebraic) poset

Authors: Nana Ma, Bin Zhao

Published in: Soft Computing | Issue 14/2018

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Abstract

In this paper, based on complete residuated lattices, the properties of fuzzy \(Z_{L}\)-continuous posets and fuzzy \(Z_{L}\)-algebraic posets are investigated. Then we show that the set of fuzzy \(Z_{L}\)-ideals on the set of all compact elements of a fuzzy \(Z_{L}\)-algebraic poset is a fuzzy \(Z_{L}\)-closure system. Also, we prove that the image of a (strongly) fuzzy \(Z_{L}\)-continuous poset under a fuzzy \(Z_{L}\)-morphism is (strongly) fuzzy \(Z_{L}\)-continuous.

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Bandelt HJ, Erné M (1983) The category of \(Z\)-continuous posets. J Pure Appl Algebra 30:219–226MathSciNetCrossRefMATH

Baranga A (1996) \(Z\)-continuous posets. Discrete Math 152:33–45MathSciNetCrossRefMATH

Bělohlávek R (2002) Fuzzy relational systems, foundations and principles. Kluwer Academic Publishers, Plenum Publishers, New YorkCrossRefMATH

Bělohávek R (2003) Some properties of residuated lattices. Czechoslov Math J 53(1):161–171MathSciNetCrossRef

Davey BA, Priestley HA (2002) Introduction to lattices and order, 2nd edn. Cambridge University, CambridgeCrossRefMATH

Erné M (1999) \(Z\)-continuous posets and their topological manifestation. Appl Categ Struct 7:31–70MathSciNetCrossRefMATH

Erné M, Zhao DS (2001) \(Z\)-join spectra of \(Z\)-supercompactly generated lattices. Appl Categ Struct 9:41–63MathSciNetCrossRefMATH

Fan L (2001) A new approach to quantitative domain theory. Electron Notes Theor Comput Sci 45:77–87CrossRefMATH

Flagg B, Süderhauf P, Wagner K (1996) A logical approach to quantitative domain theory. Preprint, Elsevier, Amsterdam (submitted)

Flagg RC, Kopperman R (1997) Continuity spaces: reconciling domains and metric spaces. Theor Comput Sci 177:111–138MathSciNetCrossRefMATH

Gierz G et al (2003) Continuous lattices and domains. Cambridge University Press, CambridgeCrossRefMATH

Goguen JA (1966) \(L\)-fuzzy sets. J Math Anal Appl 18:145–174CrossRefMATH

Hofmann KH, Stralka AR (1973) Mapping clylinders compact monoids. Math Annalen 205:219–239MathSciNetCrossRefMATH

Hofmann KH, Stralka AR (1972) Push-outs and strict projective limits of semilattices. Semigroup Forum 5:243–261MathSciNetCrossRefMATH

Höhle U (1996) On the fundamentals of fuzzy set theory. J Math Anal Appl 201:786–826MathSciNetCrossRefMATH

Höhle U, Rodabaugh SE (eds) (1999) Mathematics of fuzzy sets: logic, topology, and measure theory. Kluwer Academic Publishers, BostonMATH

Rao SP (2014) Theoretical research into bases of fuzzy domains and its generalization. In: PhD Thesis, College of Mathematics and Econometrics, Hunan University, Changsha

Rutten JJMM (1995) Elements of generalized ultrametric domain theory. Theor Comput Sci 170:349–381MathSciNetCrossRefMATH

Scott DS (1971) Continuous lattices. Lect Notes Math 274:97–136MathSciNetCrossRef

Venugopalan P (1986) \(Z\)-continuous posets. Houst J Math 12:275–294MathSciNetMATH

Ward M, Dilworth RP (1939) Residuated lattices. Trans Am Math Soc 45:335–354MathSciNetCrossRefMATH

Wagner KR (1994) Solving recursive domain equations with enriched categories. In: PhD Thesis, School of Computer Science, Carnegie-Mellon University, Pittsburgh

Wright JB, Wagner EG, Thatcher JW (1978) A uniform approach to inductive posets and inductive closure. Theor Comput Sci 7:57–77MathSciNetCrossRefMATH

Yao W (2010) Quantitative domains via fuzzy sets: Part I: continuity of fuzzy directed complete posets. Fuzzy Sets Syst 161:973–987MathSciNetCrossRefMATH

Yao W, Lu LX (2009) Fuzzy Galois connections on fuzzy posets. Math Log Q 55:105–112MathSciNetCrossRefMATH

Zhang QY, Fan L (2005) Continuity in quantitative domains. Fuzzy Sets Syst 154:118–131MathSciNetCrossRefMATH

Zhang QY, Fan L (June 2006) A kind of \(L\)-fuzzy complete lattices and adjoint functor theorem for \(LF\)-Posets, In: Report on the Fourth International Symposium on Domain Theory, Hunan University, Changsha, China

Zhang QY, Xie WX, Fan L (2009) Fuzzy complete lattices. Fuzzy Sets Syst 160:2275–2291MathSciNetCrossRefMATH

Zhao NN (2011) Fuzzy \(Z\)-domain and some properties of relevant categories. In: MA Thesis, College of Mathematics and Information Science, Shaanxi Normal University, Xi’an

Title: Some results on fuzzy -continuous(algebraic) poset
Authors: Nana Ma
Bin Zhao
Publication date: 17-11-2017
Publisher: Springer Berlin Heidelberg
Published in: Soft Computing / Issue 14/2018
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-017-2924-9

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