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International Journal of General Systems Volume 32, 2003 - Issue 4: Issue Fuzzy Logic in Systems Modelling
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Original Articles

Openings and closures of fuzzy preorderings: theoretical basics and applications to fuzzy rule-based systems

Ulrich Bodenhofer Software Competence Center Hagenberg, A-4232, Hagenberg, AustriaCorrespondence[email protected]
,
Martine De Cock‡ Department of Applied Mathematics and Computer Science, Ghent University, B-9000, Gent, Belgium
&
Etienne E. Kerre Department of Applied Mathematics and Computer Science, Ghent University, B-9000, Gent, Belgium
Pages 343-360 | Received 10 Dec 2002, Accepted 04 Mar 2003, Published online: 17 Oct 2011

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J. M. Gallardo, N. Jiménez & A. Jiménez-Losada. (2017) Fuzzy restrictions and an application to cooperative games with restricted cooperation. International Journal of General Systems 46:7, pages 772-790.
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A. A. Ramadan, E. H. Elkordy & M. A. Usama. (2021) On L-fuzzy closure operators and L-fuzzy pre-proximities. Journal of the Egyptian Mathematical Society 29:1.
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Michal Holčapek, Nicole Škorupová & Martin Štěpnička. (2021) Fuzzy Interpolation with Extensional Fuzzy Numbers. Symmetry 13:2, pages 170.
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Jiří Močkoř. (2020) Functors among Relational Variants of Categories Related to L-Fuzzy Partitions, L-Fuzzy Pretopological Spaces and L-Fuzzy Closure Spaces. Axioms 9:2, pages 63.
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Kai Zhang, Jianming Zhan & Wei-Zhi Wu. (2020) Novel fuzzy rough set models and corresponding applications to multi-criteria decision-making. Fuzzy Sets and Systems 383, pages 92-126.
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Jiří Močkoř. 2020. Information Processing and Management of Uncertainty in Knowledge-Based Systems. Information Processing and Management of Uncertainty in Knowledge-Based Systems 189 197 .
Ahmed Ramadan, Enas Elkordy, Usama Abdel-Hameed & Reham Ahmed. (2019) On Alexandrov L-fuzzy nearness. Journal of Intelligent & Fuzzy Systems 37:4, pages 5113-5128.
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Ivana Micić, Zorana Jančić & Stefan Stanimirović. (2018) Computation of the greatest right and left invariant fuzzy quasi-orders and fuzzy equivalences. Fuzzy Sets and Systems 339, pages 99-118.
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Vilem Vychodil. (2017) Closure structures parameterized by systems of isotone Galois connections. International Journal of Approximate Reasoning 91, pages 1-21.
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Martin Štěpnička & Balasubramaniam Jayaram. (2016) Interpolativity of at-least and at-most models of monotone fuzzy rule bases with multiple antecedent variables. Fuzzy Sets and Systems 297, pages 26-45.
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Antonín Dvořák, Martin Štěpnička & Lenka Štěpničková. (2015) On redundancies in systems of fuzzy/linguistic IF–THEN rules under perception-based logical deduction inference. Fuzzy Sets and Systems 277, pages 22-43.
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N. Carmona, J. Elorza, J. Recasens & J. Bragard. (2015) Permutable fuzzy consequence and interior operators and their connection with fuzzy relations. Information Sciences 310, pages 36-51.
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Jelena Ignjatović, Miroslav Ćirić, Branimir Šešelja & Andreja Tepavčević. (2015) Fuzzy relational inequalities and equations, fuzzy quasi-orders, closures and openings of fuzzy sets. Fuzzy Sets and Systems 260, pages 1-24.
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Bernadette Bouchon-Meunier & Christophe Marsala. 2015. Fifty Years of Fuzzy Logic and its Applications. Fifty Years of Fuzzy Logic and its Applications 51 63 .
Dao-wu Pei. (2014) On uniqueness of (fuzzy) relation in some generalized rough set model. Applied Mathematics-A Journal of Chinese Universities 29:3, pages 253-264.
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Jorge Jiménez, Susana Montes, Branimir Šešelja & Andreja Tepavčević. (2014) Fuzzy correspondence inequations and equations. Fuzzy Sets and Systems 239, pages 81-90.
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M. Štěpnička & B. De Baets. (2013) Implication-based models of monotone fuzzy rule bases. Fuzzy Sets and Systems 232, pages 134-155.
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Martin Štěpnička & Bernard De Baets. (2013) Interpolativity of at-least and at-most models of monotone single-input single-output fuzzy rule bases. Information Sciences 234, pages 16-28.
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Jelena Ignjatović, Miroslav Ćirić & Vesna Simović. (2013) Fuzzy relation equations and subsystems of fuzzy transition systems. Knowledge-Based Systems 38, pages 48-61.
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Neus Carmona, Jorge Elorza, Jordi Recasens & Jean Bragard. 2013. Modeling Decisions for Artificial Intelligence. Modeling Decisions for Artificial Intelligence 237 247 .
Irina Perfilieva, Didier Dubois, Henri Prade, Francesc Esteva, Lluis Godo & Petra Hoďáková. (2012) Interpolation of fuzzy data: Analytical approach and overview. Fuzzy Sets and Systems 192, pages 134-158.
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A.A. Ramadan. (2011) -fuzzy interior systems . Computers & Mathematics with Applications 62:12, pages 4301-4307.
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Wei Yao & Bin Zhao. (2011) Kernel systems on L-ordered sets. Fuzzy Sets and Systems 182:1, pages 101-109.
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Jorge Jiménez, Susana Montes, Branimir Šešelja & Andreja Tepavčević. (2011) Lattice-valued approach to closed sets under fuzzy relations: Theory and applications. Computers & Mathematics with Applications 62:10, pages 3729-3740.
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Martina Dankova, Martin Stepnicka & Bernard De Baets. (2011) Grades of Monotonicity of Fuzzy Relations and Their Application to Fuzzy Rule Bases. Grades of Monotonicity of Fuzzy Relations and Their Application to Fuzzy Rule Bases.
Jorge Jiménez, Susana Montes, Branimir Šešelja & Andreja Tepavčević. 2011. Symbolic and Quantitative Approaches to Reasoning with Uncertainty. Symbolic and Quantitative Approaches to Reasoning with Uncertainty 606 615 .
Jorge Jiménez, Susana Montes, Branimir Šešelja & Andreja Tepavčević. (2010) On lattice valued up-sets and down-sets. Fuzzy Sets and Systems 161:12, pages 1699-1710.
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Jinghua Han & Gang Liu. 2010. Fuzzy Information and Engineering 2010. Fuzzy Information and Engineering 2010 667 673 .
Libor Běhounek & Martina Daňková. (2009) Relational compositions in Fuzzy Class Theory. Fuzzy Sets and Systems 160:8, pages 1005-1036.
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Tong-Jun Li. (2008) Rough approximation operators on two universes of discourse and their fuzzy extensions. Fuzzy Sets and Systems 159:22, pages 3033-3050.
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Tong-Jun Li, Yee Leung & Wen-Xiu Zhang. (2008) Generalized fuzzy rough approximation operators based on fuzzy coverings. International Journal of Approximate Reasoning 48:3, pages 836-856.
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Libor Běhounek, Ulrich Bodenhofer & Petr Cintula. (2008) Relations in Fuzzy Class Theory:. Fuzzy Sets and Systems 159:14, pages 1729-1772.
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ULRICH BODENHOFER & MUSTAFA DEMIRCI. (2011) STRICT FUZZY ORDERINGS WITH A GIVEN CONTEXT OF SIMILARITY. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems 16:02, pages 147-178.
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Jinming Fang & Yue Qiu. (2008) Fuzzy orders and fuzzifying topologies. International Journal of Approximate Reasoning 48:1, pages 98-109.
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Fang Jinming. (2007) -fuzzy Alexandrov topologies and specialization orders. Fuzzy Sets and Systems 158:21, pages 2359-2374.
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Jinming Fang & Piwei Chen. (2007) One-to-one correspondence between fuzzifying topologies and fuzzy preorders. Fuzzy Sets and Systems 158:16, pages 1814-1822.
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Martine De Cock, Chris Cornelis & Etienne E. Kerre. (2007) Fuzzy Rough Sets: The Forgotten Step. IEEE Transactions on Fuzzy Systems 15:1, pages 121-130.
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Dexue Zhang. (2007) An enriched category approach to many valued topology. Fuzzy Sets and Systems 158:4, pages 349-366.
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Etienne E. Kerre. 2007. Modeling Decisions for Artificial Intelligence. Modeling Decisions for Artificial Intelligence 1 13 .
Hongliang Lai & Dexue Zhang. (2006) Fuzzy preorder and fuzzy topology. Fuzzy Sets and Systems 157:14, pages 1865-1885.
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Martina Daňková. (2004) Generalized extensionality of fuzzy relations. Fuzzy Sets and Systems 148:2, pages 291-304.
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M. De Cock, C. Cornelis & E. Kerre. (2004) Fuzzy rough sets: beyond the obvious. Fuzzy rough sets: beyond the obvious.

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