305 research outputs found
Interval valued (\in,\ivq)-fuzzy filters of pseudo -algebras
We introduce the concept of quasi-coincidence of a fuzzy interval value with
an interval valued fuzzy set. By using this new idea, we introduce the notions
of interval valued (\in,\ivq)-fuzzy filters of pseudo -algebras and
investigate some of their related properties. Some characterization theorems of
these generalized interval valued fuzzy filters are derived. The relationship
among these generalized interval valued fuzzy filters of pseudo -algebras
is considered. Finally, we consider the concept of implication-based interval
valued fuzzy implicative filters of pseudo -algebras, in particular, the
implication operators in Lukasiewicz system of continuous-valued logic are
discussed
Disjoint-union partial algebras
Disjoint union is a partial binary operation returning the union of two sets
if they are disjoint and undefined otherwise. A disjoint-union partial algebra
of sets is a collection of sets closed under disjoint unions, whenever they are
defined. We provide a recursive first-order axiomatisation of the class of
partial algebras isomorphic to a disjoint-union partial algebra of sets but
prove that no finite axiomatisation exists. We do the same for other signatures
including one or both of disjoint union and subset complement, another partial
binary operation we define.
Domain-disjoint union is a partial binary operation on partial functions,
returning the union if the arguments have disjoint domains and undefined
otherwise. For each signature including one or both of domain-disjoint union
and subset complement and optionally including composition, we consider the
class of partial algebras isomorphic to a collection of partial functions
closed under the operations. Again the classes prove to be axiomatisable, but
not finitely axiomatisable, in first-order logic.
We define the notion of pairwise combinability. For each of the previously
considered signatures, we examine the class isomorphic to a partial algebra of
sets/partial functions under an isomorphism mapping arbitrary suprema of
pairwise combinable sets to the corresponding disjoint unions. We prove that
for each case the class is not closed under elementary equivalence.
However, when intersection is added to any of the signatures considered, the
isomorphism class of the partial algebras of sets is finitely axiomatisable and
in each case we give such an axiomatisation.Comment: 30 page
State morphism MV-algebras
We present a complete characterization of subdirectly irreducible MV-algebras
with internal states (SMV-algebras). This allows us to classify subdirectly
irreducible state morphism MV-algebras (SMMV-algebras) and describe single
generators of the variety of SMMV-algebras, and show that we have a continuum
of varieties of SMMV-algebras
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