Algorithms and Computations in BL-Algebras

Algorithms and Computations in BL-Algebras

Celestin Lele
Copyright: © 2010 |Pages: 19
DOI: 10.4018/jalr.2010100103
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Abstract

In this paper, the authors study the notion of n-fold implicative and fuzzy n-fold implicative filters, which correspond to various sets of provable formulaes, in BL-algebras. Several characterizations of fuzzy n-fold implicative filters are given and the authors analyse some relationships with various n-fold and fuzzy n-fold filters in BL-algebras, while constructing some algorithms for studying the foldness of filters in BL-algebras. The authors describe the relation between fuzzy n-fold implicative filters and fuzzy (n+1)-fold implicative filters and establish the extension property for fuzzy n-fold implicative filters in BL-algebras.
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Preliminaries

A BL-algebra is a structure jalr.2010100103.m01in which X is a non empty set with four binary operations jalr.2010100103.m02 and two constants 0 and 1 satisfying the following axioms:

  • BL-1 (X,∧,∨,0,1) is a bounded lattice;

  • BL-2 (X,∗,1) is an abelian monoid, i. e., ∗ is commutative and associative with x∗1=x;

  • BL-3 x∗y≤z iff jalr.2010100103.m03(Residuation);

  • BL-4 jalr.2010100103.m04 (Divisibility);

  • BL-5 jalr.2010100103.m05 (Prelinearity).

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