12,236 research outputs found
Homomorphisms between fuzzy information systems revisited
Recently, Wang et al. discussed the properties of fuzzy information systems
under homomorphisms in the paper [C. Wang, D. Chen, L. Zhu, Homomorphisms
between fuzzy information systems, Applied Mathematics Letters 22 (2009)
1045-1050], where homomorphisms are based upon the concepts of consistent
functions and fuzzy relation mappings. In this paper, we classify consistent
functions as predecessor-consistent and successor-consistent, and then proceed
to present more properties of consistent functions. In addition, we improve
some characterizations of fuzzy relation mappings provided by Wang et al.Comment: 10 page
Entailment systems for stably locally compact locales
The category SCFrU of stably continuous frames and preframe ho-momorphisms (preserving ¯nite meets and directed joins) is dual to the Karoubi envelope of a category Ent whose objects are sets and whose
morphisms X ! Y are upper closed relations between the ¯nite powersets FX and FY . Composition of these morphisms is the \cut composition" of Jung et al. that interfaces disjunction in the codomains with conjunctions in the domains, and thereby relates to their multi-lingual sequent
calculus. Thus stably locally compact locales are represented by \entailment systems" (X; `) in which `, a generalization of entailment relations,is idempotent for cut composition.
Some constructions on stably locally compact locales are represented
in terms of entailment systems: products, duality and powerlocales.
Relational converse provides Ent with an involution, and this gives a simple treatment of the duality of stably locally compact locales. If A and B are stably continuous frames, then the internal preframe hom A t B is isomorphic to e A B where e A is the Hofmann-Lawson dual.
For a stably locally compact locale X, the lower powerlocale of X is shown to be the dual of the upper powerlocale of the dual of X
Boolean Coverings of Quantum Observable Structure: A Setting for an Abstract Differential Geometric Mechanism
We develop the idea of employing localization systems of Boolean coverings,
associated with measurement situations, in order to comprehend structures of
Quantum Observables. In this manner, Boolean domain observables constitute
structure sheaves of coordinatization coefficients in the attempt to probe the
Quantum world. Interpretational aspects of the proposed scheme are discussed
with respect to a functorial formulation of information exchange, as well as,
quantum logical considerations. Finally, the sheaf theoretical construction
suggests an opearationally intuitive method to develop differential geometric
concepts in the quantum regime.Comment: 25 pages, Late
Covering rough sets based on neighborhoods: An approach without using neighborhoods
Rough set theory, a mathematical tool to deal with inexact or uncertain
knowledge in information systems, has originally described the indiscernibility
of elements by equivalence relations. Covering rough sets are a natural
extension of classical rough sets by relaxing the partitions arising from
equivalence relations to coverings. Recently, some topological concepts such as
neighborhood have been applied to covering rough sets. In this paper, we
further investigate the covering rough sets based on neighborhoods by
approximation operations. We show that the upper approximation based on
neighborhoods can be defined equivalently without using neighborhoods. To
analyze the coverings themselves, we introduce unary and composition operations
on coverings. A notion of homomorphismis provided to relate two covering
approximation spaces. We also examine the properties of approximations
preserved by the operations and homomorphisms, respectively.Comment: 13 pages; to appear in International Journal of Approximate Reasonin
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