JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (8): 48-52.doi: 10.6040/j.issn.1671-9352.0.2016.491

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Characterizations of n-fold positive implicative filter in residuated lattice

LIU Li-jun   

  1. School of Mathematics and Computer Science, Shaanxi Sci-Tech University, Hanzhong 723001, Shaanxi, China
  • Received:2016-11-03 Online:2017-08-20 Published:2017-08-03

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Abstract: The concept of n-fold implicative filter and n-fold positive implicative filter are introduced in residuated lattice. By studying their properties, a series of characterization theorems are given. On this basis, the sufficient and necessary condition that non-empty subsets of residuated lattice become n-fold(positive)implicative filter are proposed. And the relation between n-fold implicative filter and n-fold positive implicative filter is discussed. The results of the study further extend the filter theory of the residuated lattice. It is important theoretical foundation for the application of algebraic logic and computer information processing.

Key words: n-fold positive implicative filter, residuated lattice, filter, n-fold implicative filter

CLC Number: 

  • O159
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