Folding Theory for Fantastic Filters in BL-Algebras

Folding Theory for Fantastic Filters in BL-Algebras

Celestin Lele (University of Dschang, Cameroon)
DOI: 10.4018/978-1-4666-3890-7.ch021

Abstract

In this paper, the author examines the notion of n-fold fantastic and fuzzy n-fold fantastic filters in BL-algebras. Several characterizations of fuzzy n-fold fantastic filters are given. The author shows that every n-fold (fuzzy n-fold) fantastic filter is a filter (fuzzy filter), but the converse is not true. Using a level set of a fuzzy set in a BL-algebra, the author gives a characterization of fuzzy n-fold fantastic filters. Finally, the author establishes the extension property for n-fold and fuzzy n-fold fantastic filters in BL-algebras. The author also constructs some algorithms for folding theory applied to fantastic filters in BL-algebras.
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2. Preliminaries

A BL-algebra is a structure 978-1-4666-3890-7.ch021.m01 in which 978-1-4666-3890-7.ch021.m02 is a non-empty set with four binary operations 978-1-4666-3890-7.ch021.m03 and two constants 0 and 1 satisfying the following axioms:

  • BL-1:978-1-4666-3890-7.ch021.m04 is a bounded lattice;

  • BL-2: 978-1-4666-3890-7.ch021.m05 is an abelian monoid; which means that $\ast $ is commutative and associative with 978-1-4666-3890-7.ch021.m06;

  • BL-3:978-1-4666-3890-7.ch021.m07 iff 978-1-4666-3890-7.ch021.m08 (residuation);

  • BL-4:978-1-4666-3890-7.ch021.m09 (divisibility);

  • BL-5:978-1-4666-3890-7.ch021.m10 (prelinearity);

A BL-algebra 978-1-4666-3890-7.ch021.m11 is called a MV-algebra if 978-1-4666-3890-7.ch021.m12 or equivalently 978-1-4666-3890-7.ch021.m13 where 978-1-4666-3890-7.ch021.m14

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