37,618 research outputs found
Some characteristics of matroids through rough sets
At present, practical application and theoretical discussion of rough sets
are two hot problems in computer science. The core concepts of rough set theory
are upper and lower approximation operators based on equivalence relations.
Matroid, as a branch of mathematics, is a structure that generalizes linear
independence in vector spaces. Further, matroid theory borrows extensively from
the terminology of linear algebra and graph theory. We can combine rough set
theory with matroid theory through using rough sets to study some
characteristics of matroids. In this paper, we apply rough sets to matroids
through defining a family of sets which are constructed from the upper
approximation operator with respect to an equivalence relation. First, we prove
the family of sets satisfies the support set axioms of matroids, and then we
obtain a matroid. We say the matroids induced by the equivalence relation and a
type of matroid, namely support matroid, is induced. Second, through rough
sets, some characteristics of matroids such as independent sets, support sets,
bases, hyperplanes and closed sets are investigated.Comment: 13 page
A reusable iterative optimization software library to solve combinatorial problems with approximate reasoning
Real world combinatorial optimization problems such as scheduling are
typically too complex to solve with exact methods. Additionally, the problems
often have to observe vaguely specified constraints of different importance,
the available data may be uncertain, and compromises between antagonistic
criteria may be necessary. We present a combination of approximate reasoning
based constraints and iterative optimization based heuristics that help to
model and solve such problems in a framework of C++ software libraries called
StarFLIP++. While initially developed to schedule continuous caster units in
steel plants, we present in this paper results from reusing the library
components in a shift scheduling system for the workforce of an industrial
production plant.Comment: 33 pages, 9 figures; for a project overview see
http://www.dbai.tuwien.ac.at/proj/StarFLIP
A temporal semantics for Nilpotent Minimum logic
In [Ban97] a connection among rough sets (in particular, pre-rough algebras)
and three-valued {\L}ukasiewicz logic {\L}3 is pointed out. In this paper we
present a temporal like semantics for Nilpotent Minimum logic NM ([Fod95,
EG01]), in which the logic of every instant is given by {\L}3: a completeness
theorem will be shown. This is the prosecution of the work initiated in [AGM08]
and [ABM09], in which the authors construct a temporal semantics for the
many-valued logics of G\"odel ([G\"od32], [Dum59]) and Basic Logic ([H\'aj98]).Comment: 19 pages, 2 table
A comprehensive study of implicator-conjunctor based and noise-tolerant fuzzy rough sets: definitions, properties and robustness analysis
© 2014 Elsevier B.V. Both rough and fuzzy set theories offer interesting tools for dealing with imperfect data: while the former allows us to work with uncertain and incomplete information, the latter provides a formal setting for vague concepts. The two theories are highly compatible, and since the late 1980s many researchers have studied their hybridization. In this paper, we critically evaluate most relevant fuzzy rough set models proposed in the literature. To this end, we establish a formally correct and unified mathematical framework for them. Both implicator-conjunctor-based definitions and noise-tolerant models are studied. We evaluate these models on two different fronts: firstly, we discuss which properties of the original rough set model can be maintained and secondly, we examine how robust they are against both class and attribute noise. By highlighting the benefits and drawbacks of the different fuzzy rough set models, this study appears a necessary first step to propose and develop new models in future research.Lynn D’eer has been supported by the Ghent University Special Research Fund, Chris Cornelis was partially supported by the Spanish Ministry of Science and Technology under the project TIN2011-28488 and the Andalusian Research Plans P11-TIC-7765 and P10-TIC-6858, and by project PYR-2014-8 of the Genil Program of CEI BioTic GRANADA and Lluis Godo has been partially supported by the Spanish MINECO project EdeTRI TIN2012-39348-C02-01Peer Reviewe
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