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Galois connections between a fuzzy preordered structure and a general fuzzy structure

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Abstract
We continue the study of (isotone) Galois connections, also called adjunctions, in the framework of fuzzy preordered structures, which generalize fuzzy preposets by considering underlying fuzzy equivalence relations. Specifically, we present necessary and sufficient conditions so that, given amapping f :A -> B from a fuzzy preordered structure A = < A, approximate to(A),rho(A)> into a fuzzy structure < B, approximate to(B)>, it is possible to construct a fuzzy relation rho(B) that induces a suitable fuzzy preorder structure on B and such that there exists a mapping g : B -> A such that the pair (f, g) constitutes an Galois connection.
Keywords
Fuzzy sets, Galois connection, preorder, KNOWLEDGE DISCOVERY, CONCEPT LATTICES, ADJUNCTIONS, CLASSIFICATION, CONSTRUCTION, TREES

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Citation

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Chicago
Cabrera, Inma P, Pablo Cordero, Francisca Garcia-Pardo, Manuel Ojeda-Aciego, and Bernard De Baets. 2018. “Galois Connections Between a Fuzzy Preordered Structure and a General Fuzzy Structure.” Ieee Transactions on Fuzzy Systems 26 (3): 1274–1287.
APA
Cabrera, I. P., Cordero, P., Garcia-Pardo, F., Ojeda-Aciego, M., & De Baets, B. (2018). Galois connections between a fuzzy preordered structure and a general fuzzy structure. IEEE TRANSACTIONS ON FUZZY SYSTEMS, 26(3), 1274–1287.
Vancouver
1.
Cabrera IP, Cordero P, Garcia-Pardo F, Ojeda-Aciego M, De Baets B. Galois connections between a fuzzy preordered structure and a general fuzzy structure. IEEE TRANSACTIONS ON FUZZY SYSTEMS. 2018;26(3):1274–87.
MLA
Cabrera, Inma P, Pablo Cordero, Francisca Garcia-Pardo, et al. “Galois Connections Between a Fuzzy Preordered Structure and a General Fuzzy Structure.” IEEE TRANSACTIONS ON FUZZY SYSTEMS 26.3 (2018): 1274–1287. Print.
@article{8578995,
  abstract     = {We continue the study of (isotone) Galois connections, also called adjunctions, in the framework of fuzzy preordered structures, which generalize fuzzy preposets by considering underlying fuzzy equivalence relations. Specifically, we present necessary and sufficient conditions so that, given amapping f :A -{\textrangle} B from a fuzzy preordered structure A = {\textlangle} A, approximate to(A),rho(A){\textrangle} into a fuzzy structure {\textlangle} B, approximate to(B){\textrangle}, it is possible to construct a fuzzy relation rho(B) that induces a suitable fuzzy preorder structure on B and such that there exists a mapping g : B -{\textrangle} A such that the pair (f, g) constitutes an Galois connection.},
  author       = {Cabrera, Inma P and Cordero, Pablo and Garcia-Pardo, Francisca and Ojeda-Aciego, Manuel and De Baets, Bernard},
  issn         = {1063-6706},
  journal      = {IEEE TRANSACTIONS ON FUZZY SYSTEMS},
  language     = {eng},
  number       = {3},
  pages        = {1274--1287},
  title        = {Galois connections between a fuzzy preordered structure and a general fuzzy structure},
  url          = {http://dx.doi.org/10.1109/tfuzz.2017.2718495},
  volume       = {26},
  year         = {2018},
}

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