Transactions on Rough Sets XVIII

herausgegeben von: James F. Peters, Andrzej Skowron, Tianrui Li, Yan Yang, JingTao Yao, Hung Son Nguyen

Verlag: Springer Berlin Heidelberg

Buchreihe : Lecture Notes in Computer Science

Enthalten in: Springer Professional "Wirtschaft+Technik" , Springer Professional "Technik" , Springer Professional "Wirtschaft"

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Über dieses Buch

The LNCS journal Transactions on Rough Sets is devoted to the entire spectrum of rough sets related issues, from logical and mathematical foundations, through all aspects of rough set theory and its applications, such as data mining, knowledge discovery, and intelligent information processing, to relations between rough sets and other approaches to uncertainty, vagueness, and incompleteness, such as fuzzy sets and theory of evidence.

Volume XVIII includes extensions of papers from the Joint Rough Set Symposium (JRS 2012), which was held in Chengdu, China, in August 2012. The seven papers that constitute this volume deal with topics such as: rough fuzzy sets, intuitionistic fuzzy sets, multi-granulation rough sets, decision-theoretic rough sets, three-way decisions and their applications in attribute reduction, feature selection, overlapping clustering, data mining, cost-sensitive learning, face recognition, and spam filtering.

Inhaltsverzeichnis

Frontmatter

On the Intuitionistic Fuzzy Topological Structures of Rough Intuitionistic Fuzzy Sets

Abstract

A rough intuitionistic fuzzy set is the result of approximation of an intuitionistic fuzzy set with respect to a crisp approximation space. In this paper, we investigate topological structures of rough intuitionistic fuzzy sets. We first show that a reflexive crisp rough approximation space can induce an intuitionistic fuzzy Alexandrov space. It is proved that the lower and upper rough intuitionistic fuzzy approximation operators are, respectively, an intuitionistic fuzzy interior operator and an intuitionistic fuzzy closure operator if and only if the binary relation in the crisp approximation space is reflexive and transitive. We then verify that a similarity crisp approximation space can produce an intuitionistic fuzzy clopen topological space. We further examine sufficient and necessary conditions that an intuitionistic fuzzy interior (closure, respectively) operator derived from an intuitionistic fuzzy topological space can associate with a reflexive and transitive crisp relation such that the induced lower (upper, respectively) rough intuitionistic fuzzy approximation operator is exactly the intuitionistic fuzzy interior (closure, respectively) operator.

You-Hong Xu, Wei-Zhi Wu, Guoyin Wang

Feature Selection with Positive Region Constraint for Test-Cost-Sensitive Data

Abstract

In many data mining and machine learning applications, data are not free, and there is a test cost for each data item. Due to economic, technological and legal reasons, it is neither possible nor necessary to obtain a classifier with 100 % accuracy. In this paper, we consider such a situation and propose a new constraint satisfaction problem to address it. With this in mind, one has to minimize the test cost to keep the accuracy of the classification under a budget. The constraint is expressed by the positive region, whereas the object is to minimizing the total test cost. The new problem is essentially a dual of the test cost constraint attribute reduction problem, which has been addressed recently. We propose a heuristic algorithm based on the information gain, the test cost, and a user specified parameter \(\lambda \) to deal with the new problem. The algorithm is tested on four University of California - Irvine datasets with various test cost settings. Experimental results indicate that the algorithm finds optimal feature subset in most cases, the rational setting of \(\lambda \) is different among datasets, and the algorithm is especially stable when the test cost is subject to the Pareto distribution.

Jiabin Liu, Fan Min, Hong Zhao, William Zhu

A Rough Neurocomputing Approach for Illumination Invariant Face Recognition System

Abstract

To surmount the issue of illumination variation in face recognition, this paper proposes a rough neurocomputing recognition system, namely, RNRS for an illumination invariant face recognition. The main focus of the proposed work is to address the problem of variations in illumination through the strength of the rough sets to recognize the faces under varying effects of illumination. RNRS uses geometric facial features and an approximation-decider neuron network as a recognizer. The novelty of the proposed RNRS is that the correct face match is estimated at the approximation layer itself based on the highest rough membership function value. On the contrary, if it is not being done at this layer then decider neuron does this against reduced number of sample faces. The efficiency and robustness of the proposed RNRS are demonstrated on different standard face databases and are compared with state-of-art techniques. Our proposed RNRS has achieved 93.56 % recognition rate for extended YaleB face database and 85 % recognition rate for CMU-PIE face database for larger degree of variations in illumination.

Singh Kavita, Zaveri Mukesh, Raghuwanshi Mukesh

Variable Precision Multigranulation Rough Set and Attributes Reduction

Abstract

Multigranulation rough set is a new expansion of the classical rough set since the former uses a family of the binary relations instead of single one for the constructing of approximations. In this paper, the model of the variable precision rough set is introduced into the multigranulation environment and then the concept of the variable precision multigranulation rough set is proposed, which include optimistic and pessimistic cases. Not only basic properties of variable precision multigranulation rough set are investigated, but also the relationships among variable precision rough set, multigranulation rough set and variable precision multigranulation rough set are examined. Finally, a heuristic algorithm is presented for computing reducts of variable precision multigranulation rough set, it is also tested on five UCI data sets.

Hengrong Ju, Xibei Yang, Huili Dou, Jingjing Song

Three-Way Decisions Versus Two-Way Decisions on Filtering Spam Email

Abstract

A three-way decisions solution and a two-way decisions solution for filtering spam emails are examined in this paper. Compared to two-way decisions, the spam filtering is no longer viewed as a binary classification problem, and each incoming email is accepted as a legitimate or rejected as a spam or undecided as a further-examined email in the three-way decisions. One advantage of the three-way decisions solution for spam filtering is that it can reduce the error rate of classifying a legitimate email to spam with minimum misclassification cost. The other one is that the solution can provide a more meaningful decision procedure for users while it is not restricted to a specific classifier. Experimental results on several corpus show that the three-way decisions solution can get a lower error rate and a lower misclassification cost.

Xiuyi Jia, Lin Shang

A Three-Way Decisions Approach to Density-Based Overlapping Clustering

Abstract

Most of clustering methods assume that each object must be assigned to exactly one cluster, however, overlapping clustering is more appropriate than crisp clustering in a variety of important applications such as the network structure analysis and biological information. This paper provides a three-way decisions approach for overlapping clustering based on the decision-theoretic rough set model, where each cluster is described by an interval set which is defined by a pair of sets called the lower and upper bounds, and the overlapping objects usually are distributed in the region between the lower and upper regions. Besides, a density-based clustering algorithm is proposed using the approach considering the advantages of the density-based clustering algorithms in finding the arbitrary shape clusters. The results of comparison experiments show that the three-way decisions approach is not only effective to overlapping clustering but also good at discovering the arbitrary shape clusters.

Hong Yu, Ying Wang, Peng Jiao

Three-Way Decisions in Stochastic Decision-Theoretic Rough Sets

Abstract

In the previous decision-theoretic rough sets (DTRS), its loss function values are precise. This paper extends the precise values of loss functions to a more realistic stochastic environment. The stochastic loss functions are induced to decision-theoretic rough set theory based on the bayesian decision theory. A model of stochastic decision-theoretic rough set theory (SDTRS) is built with respect to the minimum bayesian expected risk. The corresponding propositions and criteria of SDTRS are also analyzed. Furthermore, we investigate two special SDTRS models under the uniform distribution and the normal distribution, respectively. Finally, an empirical study of Public-Private Partnerships (PPP) project investment validates the reasonability and effectiveness of the proposed models.

Dun Liu, Tianrui Li, Decui Liang

Correction to: Transactions on Rough Sets XVIII

James F. Peters, Andrzej Skowron, Tianrui Li, Yan Yang, JingTao Yao, Hung Son Nguyen

Backmatter

Titel: Transactions on Rough Sets XVIII
herausgegeben von: James F. Peters
Andrzej Skowron
Tianrui Li
Yan Yang
JingTao Yao
Hung Son Nguyen
Verlag: Springer Berlin Heidelberg
Electronic ISBN: 978-3-662-44680-5
Print ISBN: 978-3-662-44679-9
DOI: https://doi.org/10.1007/978-3-662-44680-5