JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (04): 36-41.doi: 10.6040/j.issn.1671-9352.0.2014.482

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A one-to-one correspondence between fuzzy G-ideals and fuzzy Galois connections on fuzzy complete lattices

SHEN Chong, YAO Wei   

  1. Department of Mathematics, Hebei University of Science and Technology, Shijiazhuang 050018, Hebei, China
  • Received:2014-11-04 Revised:2015-03-03 Online:2015-04-20 Published:2015-04-17

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Abstract: This paper deals with fuzzy G-ideals on fuzzy complete lattices. Firstly, the concept of fuzzy G-ideals is defined and it is proved that the set of all fuzzy G-ideals of X×Y is a fuzzy complete lattice with respect to fuzzy in clusion order. Secondly, by making use of the intrinsic fuzzy inclusion orders on fuzzy G-ideals, the relationship between fuzzy Galois connections and fuzzy G-ideals is studied. It is shown that the fuzzy poset of fuzzy Galois connections between fuzzy complete lattices X and Y is order-isomorphic to the fuzzy poset of all fuzzy G-ideals of X×Y.

Key words: fuzzy G-ideal, fuzzy Galois connection, fuzzy complete lattice, commutative unital quantale

CLC Number: 

  • O159
[1] SCHMIDT J. Beitraezur filter theorie[J]. II, Mathematische Nachrichten, 1953, 10(1):197-232.
[2] ORE O. Galois connexions[J]. Transactions of the American Mathematical Society, 1944, 55(0):493-513.
[3] SHMUELY Z. The structure of Galois connections[J]. Pacific J Math, 1974, 54(2):209-225.
[4] PICADO J. The quantale of Galois connections[J]. Algebra Universalis, 2004, 52(4):527-540.
[5] YAO Wei, LU Lingxia. Fuzzy Galois connections on fuzzy posets[J]. Mathematical Logic Quarterly, 2009, 55(1):105-112.
[6] ROSENTHAL K I. Quantales and their applications[M]. New York: Addison Wesley Longman, 1990.
[7] LAI Hongliang, ZHANG Dexue. Complete and directed complete Ω-categories[J]. Theoretical Computer Science, 2007, 388(1-3):1-25.
[8] BELOHLAVEK R. Fuzzy relation systems: foundations and principles[M]. New York: Kluwer Academic Publishers, 2002.
[9] GOGUEN J A. L-fuzzy sets[J]. Journal of Mathematical Analysis and Applications, 1967, 18(1):145-174.
[10] ZHANG Qiye, FAN Lei. Continuity in quantitative domains[J]. Fuzzy Sets and Systems, 2005, 154(1):118-131.
[11] ZHANG Qiye, XIE Weixian. Section-retraction-pairs between fuzzy domains[J]. Fuzzy Sets and Systems, 2007, 158(1):99-114.
[12] BELOHLAVEK R. Concept lattices and order in fuzzy logic[J]. Annals of Pure and Applied Logic, 2004, 128(1-3):227-298.
[13] ZHANG Dexue. An enriched category approach to many valued topology[J]. Fuzzy Sets and Systems, 2007, 158(4):1-25.
[1] ZHOU Yi-hui1, MA Jue2. The products and coproducts in the category of fuzzy complete lattices [J]. J4, 2012, 47(8): 122-126.
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