153 research outputs found
Related Study of Soft Set and Its Application A Review
Abstract In the present paper some literature related to soft sets are collected. The literature is motivated by Molodsov
On the Dual Canonical Monoids
We investigate the conjugacy decomposition, nilpotent variety, the Putcha
monoid, as well as the two-sided weak order on the dual canonical monoids
Quantum Logic and the Histories Approach to Quantum Theory
An extended analysis is made of the Gell-Mann and Hartle axioms for a
generalised `histories' approach to quantum theory. Emphasis is placed on
finding equivalents of the lattice structure that is employed in standard
quantum logic. Particular attention is given to `quasi-temporal' theories in
which the notion of time-evolution is less rigid than in conventional
Hamiltonian physics; theories of this type are expected to arise naturally in
the context of quantum gravity and quantum field theory in a curved space-time.
The quasi-temporal structure is coded in a partial semi-group of `temporal
supports' that underpins the lattice of history propositions. Non-trivial
examples include quantum field theory on a non globally-hyperbolic spacetime,
and a simple cobordism approach to a theory of quantum topology.
It is shown how the set of history propositions in standard quantum theory
can be realised in such a way that each history proposition is represented by a
genuine projection operator. This provides valuable insight into the possible
lattice structure in general history theories, and also provides a number of
potential models for theories of this type.Comment: TP/92-93/39 36 pages + one page of diagrams (I could email Apple
laser printer postscript file for anyone who is especially keen
Rough sets and matroidal contraction
Rough sets are efficient for data pre-processing in data mining. As a
generalization of the linear independence in vector spaces, matroids provide
well-established platforms for greedy algorithms. In this paper, we apply rough
sets to matroids and study the contraction of the dual of the corresponding
matroid. First, for an equivalence relation on a universe, a matroidal
structure of the rough set is established through the lower approximation
operator. Second, the dual of the matroid and its properties such as
independent sets, bases and rank function are investigated. Finally, the
relationships between the contraction of the dual matroid to the complement of
a single point set and the contraction of the dual matroid to the complement of
the equivalence class of this point are studied.Comment: 11 page
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