1,543 research outputs found
Pseudo MV-algebras and Lexicographic Product
We study algebraic conditions when a pseudo MV-algebra is an interval in the
lexicographic product of an Abelian unital -group and an -group
that is not necessary Abelian. We introduce -perfect pseudo MV-algebras
and strong -perfect pseudo MV-algebras, the latter ones will have a
representation by a lexicographic product. Fixing a unital -group
, the category of strong -perfect pseudo MV-algebras is
categorically equivalent to the category of -groups.Comment: arXiv admin note: text overlap with arXiv:1304.074
Kite Pseudo Effect Algebras
We define a new class of pseudo effect algebras, called kite pseudo effect
algebras, which is connected with partially ordered groups not necessarily with
strong unit. In such a case, starting even with an Abelian po-group, we can
obtain a noncommutative pseudo effect algebra. We show how such kite pseudo
effect algebras are tied with different types of the Riesz Decomposition
Properties. Kites are so-called perfect pseudo effect algebras, and we define
conditions when kite pseudo effect algebras have the least non-trivial normal
ideal
States on pseudo effect algebras and integrals
We show that every state on an interval pseudo effect algebra satisfying
some kind of the Riesz Decomposition Properties (RDP) is an integral through a
regular Borel probability measure defined on the Borel -algebra of a
Choquet simplex . In particular, if satisfies the strongest type of
(RDP), the representing Borel probability measure can be uniquely chosen to
have its support in the set of the extreme points of $K.
Lexicographic Effect Algebras
In the paper we investigate a class of effect algebras which can be
represented in the form of the lexicographic product \Gamma(H\lex G,(u,0)),
where is an Abelian unital po-group and is an Abelian directed
po-group. We study algebraic conditions when an effect algebra is of this form.
Fixing a unital po-group , the category of strong -perfect effect
algebra is introduced and it is shown that it is categorically equivalent to
the category of directed po-group with interpolation. We show some
representation theorems including a subdirect product representation by
antilattice lexicographic effect algebras
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
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