Abstract: Some invariant properties of incomplete information systems homomorphism are studied in this paper. Demand conditions of tolerance class, attribute reduction, indispensable attribute and dispensable attribute being invariant under homomorphism in incomplete information system are revealed and discussed. The existing condition of endohomomorphism on an incomplete information system is also explored. It establishes some theoretical foundations for further investigations on incomplete information systems in rough set theory, like in information systems.
Abstract: This paper illustrates an application of granular computing approach, namely rough set theory in data mining. The paper outlines the formalism of granular computing and elucidates the mathematical underpinning of rough set theory, which has been widely used by the data mining and the machine learning community. A real-world application is illustrated, and the classification performance is compared with other contending machine learning algorithms. The predictive performance of the rough set rule induction model shows comparative success with respect to other contending algorithms.
Abstract: Branch of modern mathematics, graphs represent instruments
for optimization and solving practical applications in
various fields such as economic networks, engineering, network optimization,
the geometry of social action, generally, complex systems
including contemporary urban problems (path or transport efficiencies,
biourbanism, & c.). In this paper is studied the interconnection
of some urban network, which can lead to a simulation problem of a
digraph through another digraph. The simulation is made univoc or
more general multivoc. The concepts of fragment and atom are very
useful in the study of connectivity in the digraph that is simulation
- including an alternative evaluation of k- connectivity. Rough set
approach in (bi)digraph which is proposed in premier in this paper
contribute to improved significantly the evaluation of k-connectivity.
This rough set approach is based on generalized rough sets - basic
facts are presented in this paper.
Abstract: Some properties of approximation sets are studied in multi-granulation optimist model in rough set theory using maximal compatible classes. The relationships between or among lower and upper approximations in single and multiple granulation are compared and discussed. Through designing Boolean functions and discernibility matrices in incomplete information systems, the lower and upper approximation sets and reduction in multi-granulation environments can be found. By using examples, the correctness of computation approach is consolidated. The related conclusions obtained are suitable for further investigating in multiple granulation RSM.
Abstract: Rough set theory is used to handle uncertainty and incomplete information by applying two accurate sets, Lower approximation and Upper approximation. In this paper, the rough clustering algorithms are improved by adopting the Similarity, Dissimilarity–Similarity and Entropy based initial centroids selection method on three different clustering algorithms namely Entropy based Rough K-Means (ERKM), Similarity based Rough K-Means (SRKM) and Dissimilarity-Similarity based Rough K-Means (DSRKM) were developed and executed by yeast dataset. The rough clustering algorithms are validated by cluster validity indexes namely Rand and Adjusted Rand indexes. An experimental result shows that the ERKM clustering algorithm perform effectively and delivers better results than other clustering methods. Outlier detection is an important task in data mining and very much different from the rest of the objects in the clusters. Entropy based Rough Outlier Factor (EROF) method is seemly to detect outlier effectively for yeast dataset. In rough K-Means method, by tuning the epsilon (ᶓ) value from 0.8 to 1.08 can detect outliers on boundary region and the RKM algorithm delivers better results, when choosing the value of epsilon (ᶓ) in the specified range. An experimental result shows that the EROF method on clustering algorithm performed very well and suitable for detecting outlier effectively for all datasets. Further, experimental readings show that the ERKM clustering method outperformed the other methods.
Abstract: One of the global combinatorial optimization
problems in machine learning is feature selection. It concerned with
removing the irrelevant, noisy, and redundant data, along with
keeping the original meaning of the original data. Attribute reduction
in rough set theory is an important feature selection method. Since
attribute reduction is an NP-hard problem, it is necessary to
investigate fast and effective approximate algorithms. In this paper,
we proposed two feature selection mechanisms based on memetic
algorithms (MAs) which combine the genetic algorithm with a fuzzy
record to record travel algorithm and a fuzzy controlled great deluge
algorithm, to identify a good balance between local search and
genetic search. In order to verify the proposed approaches, numerical
experiments are carried out on thirteen datasets. The results show that
the MAs approaches are efficient in solving attribute reduction
problems when compared with other meta-heuristic approaches.
Abstract: In the era of rapidly increasing notebook market, consumer electronics manufacturers are facing a highly dynamic and competitive environment. In particular, the product appearance is the first part for user to distinguish the product from the product of other brands. Notebook product should differ in its appearance to engage users and contribute to the user experience (UX). The UX evaluates various product concepts to find the design for user needs; in addition, help the designer to further understand the product appearance preference of different market segment. However, few studies have been done for exploring the relationship between consumer background and the reaction of product appearance. This study aims to propose a data mining framework to capture the user’s information and the important relation between product appearance factors. The proposed framework consists of problem definition and structuring, data preparation, rules generation, and results evaluation and interpretation. An empirical study has been done in Taiwan that recruited 168 subjects from different background to experience the appearance performance of 11 different portable computers. The results assist the designers to develop product strategies based on the characteristics of consumers and the product concept that related to the UX, which help to launch the products to the right customers and increase the market shares. The results have shown the practical feasibility of the proposed framework.
Abstract: A learning content management system (LCMS) is an
environment to support web-based learning content development.
Primary function of the system is to manage the learning process as
well as to generate content customized to meet a unique requirement
of each learner. Among the available supporting tools offered by
several vendors, we propose to enhance the LCMS functionality to
individualize the presented content with the induction ability. Our
induction technique is based on rough set theory. The induced rules
are intended to be the supportive knowledge for guiding the content
flow planning. They can also be used as decision rules to help
content developers on managing content delivered to individual
learner.
Abstract: Effective employee selection is a critical component
of a successful organization. Many important criteria for personnel
selection such as decision-making ability, adaptability, ambition, and
self-organization are naturally vague and imprecise to evaluate. The
rough sets theory (RST) as a new mathematical approach to
vagueness and uncertainty is a very well suited tool to deal with
qualitative data and various decision problems. This paper provides
conceptual, descriptive, and simulation results, concentrating chiefly
on human resources and personnel selection factors. The current
research derives certain decision rules which are able to facilitate
personnel selection and identifies several significant features based
on an empirical study conducted in an IT company in Iran.
Abstract: Granular computing deals with representation of information in the form of some aggregates and related methods for transformation and analysis for problem solving. A granulation scheme based on clustering and Rough Set Theory is presented with focus on structured conceptualization of information has been presented in this paper. Experiments for the proposed method on four labeled data exhibit good result with reference to classification problem. The proposed granulation technique is semi-supervised imbibing global as well as local information granulation. To represent the results of the attribute oriented granulation a tree structure is proposed in this paper.
Abstract: Adopting Zakowski-s upper approximation operator
C and lower approximation operator C, this paper investigates
granularity-wise separations in covering approximation spaces. Some
characterizations of granularity-wise separations are obtained by
means of Pawlak rough sets and some relations among granularitywise
separations are established, which makes it possible to research
covering approximation spaces by logical methods and mathematical
methods in computer science. Results of this paper give further
applications of Pawlak rough set theory in pattern recognition and
artificial intelligence.
Abstract: Rough set theory is a very effective tool to deal with granularity and vagueness in information systems. Covering-based rough set theory is an extension of classical rough set theory. In this paper, firstly we present the characteristics of the reducible element and the minimal description covering-based rough sets through downsets. Then we establish lattices and topological spaces in coveringbased rough sets through down-sets and up-sets. In this way, one can investigate covering-based rough sets from algebraic and topological points of view.
Abstract: The theory of rough sets is generalized by using a
filter. The filter is induced by binary relations and it is used to
generalize the basic rough set concepts. The knowledge
representations and processing of binary relations in the style of
rough set theory are investigated.
Abstract: This paper shows that some properties of the decision
rules in the literature do not hold by presenting a counterexample. We
give sufficient and necessary conditions under which these properties
are valid. These results will be helpful when one tries to choose the
right decision rules in the research of rough set theory.
Abstract: This paper presents the idea of a rough controller with application to control the overhead traveling crane system. The structure of such a controller is based on a suggested concept of a fuzzy logic controller. A measure of fuzziness in rough sets is introduced. A comparison between fuzzy logic controller and rough controller has been demonstrated. The results of a simulation comparing the performance of both controllers are shown. From these results we infer that the performance of the proposed rough controller is satisfactory.
Abstract: Medical Decision Support Systems (MDSSs) are sophisticated, intelligent systems that can provide inference due to lack of information and uncertainty. In such systems, to model the uncertainty various soft computing methods such as Bayesian networks, rough sets, artificial neural networks, fuzzy logic, inductive logic programming and genetic algorithms and hybrid methods that formed from the combination of the few mentioned methods are used. In this study, symptom-disease relationships are presented by a framework which is modeled with a formal concept analysis and theory, as diseases, objects and attributes of symptoms. After a concept lattice is formed, Bayes theorem can be used to determine the relationships between attributes and objects. A discernibility relation that forms the base of the rough sets can be applied to attribute data sets in order to reduce attributes and decrease the complexity of computation.
Abstract: The distinction among urban, periurban and rural areas represents a classical example of uncertainty in land classification. Satellite images, geostatistical analysis and all kinds of spatial data are very useful in urban sprawl studies, but it is important to define precise rules in combining great amounts of data to build complex knowledge about territory. Rough Set theory may be a useful method to employ in this field. It represents a different mathematical approach to uncertainty by capturing the indiscernibility. Two different phenomena can be indiscernible in some contexts and classified in the same way when combining available information about them. This approach has been applied in a case of study, comparing the results achieved with both Map Algebra technique and Spatial Rough Set. The study case area, Potenza Province, is particularly suitable for the application of this theory, because it includes 100 municipalities with different number of inhabitants and morphologic features.
Abstract: Clustering in high dimensional space is a difficult
problem which is recurrent in many fields of science and
engineering, e.g., bioinformatics, image processing, pattern
reorganization and data mining. In high dimensional space some of
the dimensions are likely to be irrelevant, thus hiding the possible
clustering. In very high dimensions it is common for all the objects in
a dataset to be nearly equidistant from each other, completely
masking the clusters. Hence, performance of the clustering algorithm
decreases.
In this paper, we propose an algorithmic framework which
combines the (reduct) concept of rough set theory with the k-means
algorithm to remove the irrelevant dimensions in a high dimensional
space and obtain appropriate clusters. Our experiment on test data
shows that this framework increases efficiency of the clustering
process and accuracy of the results.
Abstract: Knowledge Discovery in Databases (KDD) has
evolved into an important and active area of research because of
theoretical challenges and practical applications associated with the
problem of discovering (or extracting) interesting and previously
unknown knowledge from very large real-world databases. Rough
Set Theory (RST) is a mathematical formalism for representing
uncertainty that can be considered an extension of the classical set
theory. It has been used in many different research areas, including
those related to inductive machine learning and reduction of
knowledge in knowledge-based systems. One important concept
related to RST is that of a rough relation. In this paper we presented
the current status of research on applying rough set theory to KDD,
which will be helpful for handle the characteristics of real-world
databases. The main aim is to show how rough set and rough set
analysis can be effectively used to extract knowledge from large
databases.