JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2016, Vol. 51 ›› Issue (2): 102-107.doi: 10.6040/j.issn.1671-9352.0.2015.116

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〈,(-overQ)〉-fuzzy filter and its characterization of the non-commutative residual lattices on the interval sets

QIAO Xi-min1, WU Hong-bo2   

  1. 1. School of Mathematics and Computer Application, Shangluo University, Shangluo 726000, Shaanxi, China;
    2. School of Mathematics and Information Science, Shaanxi Normal University, Xian 710062, Shaanxi, China
  • Received:2014-03-18 Online:2016-02-16 Published:2016-03-11

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Abstract: Taking the thought of interval sets as the research tool, the theories of non-commutative residual lattices are discussed on the interval sets and filters. The concepts of non-commutative residual lattices are introduced on interval sets and fuzzy filters of non-commutative residual lattices on interval sets. The algebraic structure of the 〈,(-overQ)〉-fuzzy filters of non-commutative residual lattices is provided on interval sets, and several equivalent characterization are received. A detailed demonstration for the necessary and sufficient conditions of the representation theorem is given.

Key words: non-commutative fuzzy logic, non-commutative residual lattices on the interval sets, characterization, 〈,(-overQ)〉-fuzzy filters, interval sets

CLC Number: 

  • O141
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