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

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
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