122,739 research outputs found
Scalable approximate FRNN-OWA classification
Fuzzy Rough Nearest Neighbour classification with Ordered Weighted Averaging operators (FRNN-OWA) is an algorithm that classifies unseen instances according to their membership in the fuzzy upper and lower approximations of the decision classes. Previous research has shown that the use of OWA operators increases the robustness of this model. However, calculating membership in an approximation requires a nearest neighbour search. In practice, the query time complexity of exact nearest neighbour search algorithms in more than a handful of dimensions is near-linear, which limits the scalability of FRNN-OWA. Therefore, we propose approximate FRNN-OWA, a modified model that calculates upper and lower approximations of decision classes using the approximate nearest neighbours returned by Hierarchical Navigable Small Worlds (HNSW), a recent approximative nearest neighbour search algorithm with logarithmic query time complexity at constant near-100% accuracy. We demonstrate that approximate FRNN-OWA is sufficiently robust to match the classification accuracy of exact FRNN-OWA while scaling much more efficiently. We test four parameter configurations of HNSW, and evaluate their performance by measuring classification accuracy and construction and query times for samples of various sizes from three large datasets. We find that with two of the parameter configurations, approximate FRNN-OWA achieves near-identical accuracy to exact FRNN-OWA for most sample sizes within query times that are up to several orders of magnitude faster
Class Association Rules Mining based Rough Set Method
This paper investigates the mining of class association rules with rough set
approach. In data mining, an association occurs between two set of elements
when one element set happen together with another. A class association rule set
(CARs) is a subset of association rules with classes specified as their
consequences. We present an efficient algorithm for mining the finest class
rule set inspired form Apriori algorithm, where the support and confidence are
computed based on the elementary set of lower approximation included in the
property of rough set theory. Our proposed approach has been shown very
effective, where the rough set approach for class association discovery is much
simpler than the classic association method.Comment: 10 pages, 2 figure
"Possible Definitions of an ’A Priori’ Granule\ud in General Rough Set Theory" by A. Mani
We introduce an abstract framework for general rough set theory from a mereological perspective and consider possible concepts of ’a priori’ granules and granulation in the same. The framework is ideal for relaxing many of the\ud
relatively superfluous set-theoretic axioms and for improving the semantics of many relation based, cover-based and dialectical rough set theories. This is a\ud
relatively simplified presentation of a section in three different recent research papers by the present author.\u
A comparative study of the AHP and TOPSIS methods for implementing load shedding scheme in a pulp mill system
The advancement of technology had encouraged mankind to design and create useful
equipment and devices. These equipment enable users to fully utilize them in various
applications. Pulp mill is one of the heavy industries that consumes large amount of
electricity in its production. Due to this, any malfunction of the equipment might
cause mass losses to the company. In particular, the breakdown of the generator
would cause other generators to be overloaded. In the meantime, the subsequence
loads will be shed until the generators are sufficient to provide the power to other
loads. Once the fault had been fixed, the load shedding scheme can be deactivated.
Thus, load shedding scheme is the best way in handling such condition. Selected load
will be shed under this scheme in order to protect the generators from being
damaged. Multi Criteria Decision Making (MCDM) can be applied in determination
of the load shedding scheme in the electric power system. In this thesis two methods
which are Analytic Hierarchy Process (AHP) and Technique for Order Preference by
Similarity to Ideal Solution (TOPSIS) were introduced and applied. From this thesis,
a series of analyses are conducted and the results are determined. Among these two
methods which are AHP and TOPSIS, the results shown that TOPSIS is the best
Multi criteria Decision Making (MCDM) for load shedding scheme in the pulp mill
system. TOPSIS is the most effective solution because of the highest percentage
effectiveness of load shedding between these two methods. The results of the AHP
and TOPSIS analysis to the pulp mill system are very promising
Rough Set Theory for Real Estate Appraisal: An Application to Directional District of Naples
This paper proposes an application of Rough Set Theory (RST) to the real estate field, in order to highlight its operational potentialities for mass appraisal purposes. RST allows one to solve the appraisal of real estate units regardless of the deterministic relationship between characteristics that contribute to the formation of the property market price and the same real estate prices. RST was applied to a real estate sample (office units located in Directional District of Naples) and was also integrated with a functional extension so-called Valued Tolerance Relation (VTR) in order to improve its flexibility. A multiple regression analysis (MRA) was developed on the same real estate sample with the aim to compare RST and MRA results. The case study is followed by a brief discussion on basic theoretical connotations of this methodology
Parametric matroid of rough set
Rough set is mainly concerned with the approximations of objects through an
equivalence relation on a universe. Matroid is a combinatorial generalization
of linear independence in vector spaces. In this paper, we define a parametric
set family, with any subset of a universe as its parameter, to connect rough
sets and matroids. On the one hand, for a universe and an equivalence relation
on the universe, a parametric set family is defined through the lower
approximation operator. This parametric set family is proved to satisfy the
independent set axiom of matroids, therefore it can generate a matroid, called
a parametric matroid of the rough set. Three equivalent representations of the
parametric set family are obtained. Moreover, the parametric matroid of the
rough set is proved to be the direct sum of a partition-circuit matroid and a
free matroid. On the other hand, since partition-circuit matroids were well
studied through the lower approximation number, we use it to investigate the
parametric matroid of the rough set. Several characteristics of the parametric
matroid of the rough set, such as independent sets, bases, circuits, the rank
function and the closure operator, are expressed by the lower approximation
number.Comment: 15 page
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