Fuzzy logic: mathematical tools for approximate reasoning
Fuzzy logic: mathematical tools for approximate reasoning
Fuzzy implicative and Boolean filters of R0 algebras
Information Sciences—Informatics and Computer Science: An International Journal
Function Algebras on Finite Sets: Basic Course on Many-Valued Logic and Clone Theory (Springer Monographs in Mathematics)
TL-filters of integral residuated l-monoids
Information Sciences: an International Journal
Redefined fuzzy implicative filters
Information Sciences: an International Journal
On v-filters and normal v-filters of a residuated lattice with a weak vt-operator
Information Sciences: an International Journal
Fuzzy filters and fuzzy prime filters of bounded Rl-monoids and pseudo BL-algebras
Information Sciences: an International Journal
Functional completeness of bounded structures of fuzzy logic with wvt-operators
Fuzzy Sets and Systems
Systemic approach to fuzzy logic formalization for approximate reasoning
Information Sciences: an International Journal
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We consider certain finite universal algebras arising from algebraic semantics in implicational logics. They contain a binary operation - and two constants 0 and 1 satisfying the axioms 0-x=x-1=x-x=1 and 1-x=x valid in most implicational logics. We characterize the completeness (also called primality) of such algebras, i.e. the property that every finitary operation on their universe is a term operation of the algebra (in other words, it is a composition of the basic operations of the algebra). Using clone theory and the knowledge of maximal clones we describe completeness (functional completeness) in terms of nonpreservation of three types of specific relations. If - has a simple property and the algebra contains a binary operation @? with a neutral element 1 and a unary operation @? satisfying @?(1)=0 and @?x=1 otherwise, the algebra is functionally complete.