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http://dx.doi.org/10.11568/kjm.2019.27.4.1109

FUZZY CONNECTIONS ON ADJOINT TRIPLES  

Ko, Jung Mi (Department of Mathematics Gangneung-Wonju National)
Kim, Yong Chan (Department of Mathematics Gangneung-Wonju National)
Publication Information
Korean Journal of Mathematics / v.27, no.4, 2019 , pp. 1109-1118 More about this Journal
Abstract
In this paper, we introduce the notion of residuated and Galois connections on adjoint triples and investigate their properties. Using the properties of residuated and Galois connections, we solve fuzzy relation equations and give their examples.
Keywords
Adjoint triples; residuated connections; Galois connections; fuzzy relational erosion(dilation); fuzzy closure (interior) operator;
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1 R. Belohlavek, Fuzzy Relational Systems, Kluwer Academic Publishers, New York, 2002.
2 M.E. Cornejo, J. Medina, E. Ramirez, A comparative study of adjoint triples, Fuzzy Sets and Systems, 211 (2013), 1-14.   DOI
3 M.E. Cornejo, J. Medina and E. Ramirez, Multi-adjoint algebras versus non-commutative residuated structures, International Journal of Approximate Reasoning 66 (2015), 119-138.   DOI
4 N. Madrid, M. Ojeda-Aciego, J. Medina and I. Perfilieva, L-fuzzy relational mathematical morphology based on adjoint triples, Information Sciences 474 (2019), 75-89.   DOI
5 P. Hajek, Metamathematices of Fuzzy Logic, Kluwer Academic Publishers, Dordrecht, 1998.
6 U. Hohle, E.P. Klement, Non-classical logic and their applications to fuzzy subsets, Kluwer Academic Publishers, Boston, 1995.
7 U. Hohle, S.E. Rodabaugh, Mathematics of Fuzzy Sets, Logic, Topology and Measure Theory, The Handbooks of Fuzzy Sets Series, Kluwer Academic Publishers, Dordrecht, 1999.
8 Y.C. Kim, Join-meet preserving maps and Alexandrov fuzzy topologies, Journal of Intelligent and Fuzzy Systems 28 (2015), 457-467.   DOI
9 M. Kryszkiewicz, Rough set approach to incomplete information systems, Information Sciences 112 (1998), 39-49.   DOI
10 Z. Pawlak, Rough sets, Internat. J. Comput. Inform. Sci., 11 (1982), 341-356.   DOI
11 Z. Pawlak, Rough sets: Theoretical Aspects of Reasoning about Data, System Theory, Knowledge Engineering and Problem Solving, Kluwer Academic Publishers, Dordrecht, The Netherlands (1991)
12 B.S. Shieh, Solutions of fuzzy relation equations based on continuous t-norms, Information Sciences, 177 (2007), 4208-4215.   DOI
13 I. Perfilieva, Finitary solvability conditions for systems of fuzzy relation equations, Information Sciences, 234 (2013), 29-43.   DOI
14 I. Perfilieva and L. Noskova, System of fuzzy relation equations with infcomposition: Commplete set of solutions, Fuzzy Sets and Systems 159 (2008), 2256-2271.   DOI
15 E. Sanchez, Resolution of composite fuzzy relation equations, Inform. and Control 30 (1976), 38-48.   DOI
16 P. Sussner, Lattice fuzzy transforms from the perspective of mathematical morphology, Fuzzy Sets and Systems, 288 (2016), 115-128.   DOI
17 S. P. Tiwari, I. Perfilieva and A.P. Singh, Generalized residuated lattices based F-transformation, Iranian Journal of Fuzzy Systems 15 (2) (2018), 165-182.
18 M.Ward, R.P. Dilworth, Residuated lattices, Trans. Amer. Math. Soc. 45 (1939), 335-354,   DOI
19 A.A. Abdel-Hamid, N.N. Morsi, Associatively tied implications, Fuzzy Sets and Systems, 136 (3) (2003), 291-311.   DOI