763 research outputs found
Interval-valued algebras and fuzzy logics
In this chapter, we present a propositional calculus for several interval-valued fuzzy logics, i.e., logics having intervals as truth values. More precisely, the truth values are preferably subintervals of the unit interval. The idea behind it is that such an interval can model imprecise information. To compute the truth values of āp implies qā and āp and qā, given the truth values of p and q, we use operations from residuated lattices. This truth-functional approach is similar to the methods developed for the well-studied fuzzy logics. Although the interpretation of the intervals as truth values expressing some kind of imprecision is a bit problematic, the purely mathematical study of the properties of interval-valued fuzzy logics and their algebraic semantics can be done without any problem. This study is the focus of this chapter
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
On a New Construction of Pseudo BL-Algebras
We present a new construction of a class pseudo BL-algebras, called kite
pseudo BL-algebras. We start with a basic pseudo hoop . Using two injective
mappings from one set, , into the second one, , and with an identical
copy with the reverse order we construct a pseudo BL-algebra
where the lower part is of the form and the upper one is
. Starting with a basic commutative hoop we can obtain even a
non-commutative pseudo BL-algebra or a pseudo MV-algebra, or an algebra with
non-commuting negations. We describe the construction, subdirect irreducible
kite pseudo BL-algebras and their classification
The variety generated by all the ordinal sums of perfect MV-chains
We present the logic BL_Chang, an axiomatic extension of BL (see P. H\'ajek -
Metamathematics of fuzzy logic - 1998, Kluwer) whose corresponding algebras
form the smallest variety containing all the ordinal sums of perfect MV-chains.
We will analyze this logic and the corresponding algebraic semantics in the
propositional and in the first-order case. As we will see, moreover, the
variety of BL_Chang-algebras will be strictly connected to the one generated by
Chang's MV-algebra (that is, the variety generated by all the perfect
MV-algebras): we will also give some new results concerning these last
structures and their logic.Comment: This is a revised version of the previous paper: the modifications
concern essentially the presentation. The scientific content is substantially
unchanged. The major variations are: Definition 2.7 has been improved.
Section 3.1 has been made more compact. A new reference, [Bus04], has been
added. There is some minor modification in Section 3.
A Compactness Theorem for The Dual Gromov-Hausdorff Propinquity
We prove a compactness theorem for the dual Gromov-Hausdorff propinquity as a
noncommutative analogue of the Gromov compactness theorem for the
Gromov-Hausdorff distance. Our theorem is valid for subclasses of quasi-Leibniz
compact quantum metric spaces of the closure of finite dimensional
quasi-Leibniz compact quantum metric spaces for the dual propinquity. While
finding characterizations of this class proves delicate, we show that all
nuclear, quasi-diagonal quasi-Leibniz compact quantum metric spaces are limits
of finite dimensional quasi-Leibniz compact quantum metric spaces. This result
involves a mild extension of the definition of the dual propinquity to
quasi-Leibniz compact quantum metric spaces, which is presented in the first
part of this paper.Comment: 40 Pages. Version 4 includes several minor corrections and is
accepted in the Indiana University Mathematics Journa
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