Folding Theory for Fantastic Filters in BL-Algebras

Celestin Lele (University of Dschang, Cameroon)

Source Title: Investigations into Living Systems, Artificial Life, and Real-World Solutions

DOI: 10.4018/978-1-4666-3890-7.ch021

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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 in which is a non-empty set with four binary operations and two constants 0 and 1 satisfying the following axioms:

BL-1: is a bounded lattice;
BL-2: is an abelian monoid; which means that $\ast $ is commutative and associative with ;
BL-3: iff (residuation);
BL-4: (divisibility);
BL-5: (prelinearity);