Showing papers on "Rough set published in 2013"

Building the fundamentals of granular computing: A principle of justifiable granularity

Abstract: The study introduces and discusses a principle of justifiable granularity, which supports a coherent way of designing information granules in presence of experimental evidence (either of numerical or granular character) The term ''justifiable'' pertains to the construction of the information granule, which is formed in such a way that it is (a) highly legitimate (justified) in light of the experimental evidence, and (b) specific enough meaning it comes with a well-articulated semantics (meaning) The design process associates with a well-defined optimization problem with the two requirements of experimental justification and specificity A series of experiments is provided as well as a number of constructs carried for various formalisms of information granules (intervals, fuzzy sets, rough sets, and shadowed sets) are discussed as well

Another approach to soft rough sets

Abstract: Theories of soft sets and rough sets are two different approaches to vagueness. A possible fusion of rough sets and soft sets is proposed by F.Feng et al. They introduce the concept of soft rough sets, where parametrized subsets of a universe set are basic building blocks for lower and upper approximations of a subset. In the present paper, a new approach is being introduced to study roughness through soft sets. In this new technique of finding approximations of a set, flavour of both theories of soft sets and rough sets is retained. This new model may be called modified soft rough set. It is shown that in this new model, information granules are finer than soft rough sets. Some results which were not valid in soft rough sets can be proved in MSR-sets. Finally concept of approximations of an information system with respect to another information system is studied.

Attribute reduction: A dimension incremental strategy

Abstract: Many real data sets in databases may vary dynamically. With the rapid development of data processing tools, databases increase quickly not only in rows (objects) but also in columns (attributes) nowadays. This phenomena occurs in several fields including image processing, gene sequencing and risk prediction in management. Rough set theory has been conceived as a valid mathematical tool to analyze various types of data. A key problem in rough set theory is executing attribute reduction for a data set. This paper focuses on attribute reduction for data sets with dynamically-increasing attributes. Information entropy is a common measure of uncertainty and has been widely used to construct attribute reduction algorithms. Based on three representative entropies, this paper develops a dimension incremental strategy for redcut computation. When an attribute set is added to a decision table, the developed algorithm can find a new reduct in a much shorter time. Experiments on six data sets downloaded from UCI show that, compared with the traditional non-incremental reduction algorithm, the developed algorithm is effective and efficient.

Attribute reduction for dynamic data sets

Abstract: Many real data sets in databases may vary dynamically. With such data sets, one has to run a knowledge acquisition algorithm repeatedly in order to acquire new knowledge. This is a very time-consuming process. To overcome this deficiency, several approaches have been developed to deal with dynamic databases. They mainly address knowledge updating from three aspects: the expansion of data, the increasing number of attributes and the variation of data values. This paper focuses on attribute reduction for data sets with dynamically varying data values. Information entropy is a common measure of uncertainty and has been widely used to construct attribute reduction algorithms. Based on three representative entropies, this paper develops an attribute reduction algorithm for data sets with dynamically varying data values. When a part of data in a given data set is replaced by some new data, compared with the classic reduction algorithms based on the three entropies, the developed algorithm can find a new reduct in a much shorter time. Experiments on six data sets downloaded from UCI show that the algorithm is effective and efficient.

Incremental updating approximations in dominance-based rough sets approach under the variation of the attribute set

Abstract: Dominance-based Rough Sets Approach (DRSA) is a generalized model of the classical Rough Sets Theory (RST) which may handle information with preference-ordered attribute domain. The attribute set in the information system may evolve over time. Approximations of DRSA used to induce decision rules need updating for knowledge discovery and other related tasks. We firstly introduce a kind of dominance matrix to calculate P-dominating sets and P-dominated sets in DRSA. Then we discuss the principles of updating P-dominating sets and P-dominated sets when some attributes are added into or deleted from the attribute set P. Furthermore, we propose incremental approaches and algorithms for updating approximations in DRSA. The proposed incremental approaches effectively reduce the computational time in comparison with the non-incremental approach are validated by experimental evaluations on different data sets from UCI.

An intelligent supplier evaluation, selection and development system

Abstract: Supplier evaluation and selection process has a critical role and significant impact on purchasing management in supply chain. It is also a complex multiple criteria decision making problem which is affected by several conflicting factors. Due to multiple criteria effects the evaluation and selection process, deciding which criteria have the most critical roles in decision making is a very important step for supplier selection, evaluation and particularly development. With this study, a hybridization of fuzzy c-means (FCM) and rough set theory (RST) techniques is proposed as a new solution for supplier selection, evaluation and development problem. First the vendors are clustered with FCM algorithm then the formed clusters are represented by their prototypes that are used for labeling the clusters. RST is used at the next step of modeling where we discover the primary features in other words the core evaluation criteria of the suppliers and extract the decision rules for characterizing the clusters. The obtained results show that the proposed method not only selects the best supplier(s), also clusters all of the vendors with respect to fuzzy similarity degrees, decides the most critical criteria for supplier evaluation and extracts the decision rules about data.

Rough-Fuzzy Clustering for Grouping Functionally Similar Genes from Microarray Data

Abstract: Gene expression data clustering is one of the important tasks of functional genomics as it provides a powerful tool for studying functional relationships of genes in a biological process. Identifying coexpressed groups of genes represents the basic challenge in gene clustering problem. In this regard, a gene clustering algorithm, termed as robust rough-fuzzy $(c)$-means, is proposed judiciously integrating the merits of rough sets and fuzzy sets. While the concept of lower and upper approximations of rough sets deals with uncertainty, vagueness, and incompleteness in cluster definition, the integration of probabilistic and possibilistic memberships of fuzzy sets enables efficient handling of overlapping partitions in noisy environment. The concept of possibilistic lower bound and probabilistic boundary of a cluster, introduced in robust rough-fuzzy $(c)$-means, enables efficient selection of gene clusters. An efficient method is proposed to select initial prototypes of different gene clusters, which enables the proposed $(c)$-means algorithm to converge to an optimum or near optimum solutions and helps to discover coexpressed gene clusters. The effectiveness of the algorithm, along with a comparison with other algorithms, is demonstrated both qualitatively and quantitatively on 14 yeast microarray data sets.

Incremental approaches for updating approximations in set-valued ordered information systems

Abstract: Incremental learning is an efficient technique for knowledge discovery in a dynamic database, which enables acquiring additional knowledge from new data without forgetting prior knowledge. Rough set theory has been successfully used in information systems for classification analysis. Set-valued information systems are generalized models of single-valued information systems, which can be classified into two categories: disjunctive and conjunctive. Approximations are fundamental concepts of rough set theory, which need to be updated incrementally while the object set varies over time in the set-valued information systems. In this paper, we analyze the updating mechanisms for computing approximations with the variation of the object set. Two incremental algorithms for updating the approximations in disjunctive/conjunctive set-valued information systems are proposed, respectively. Furthermore, extensive experiments are carried out on several data sets to verify the performance of the proposed algorithms. The results indicate the incremental approaches significantly outperform non-incremental approaches with a dramatic reduction in the computational speed.

Attribute selection based on a new conditional entropy for incomplete decision systems

Abstract: Shannon's entropy and its variants have been applied to measure uncertainty in rough set theory from the viewpoint of information theory. However, few studies have been done on attribute selection in incomplete decision systems based on information-theoretical measurement of attribute importance. In this paper, we introduce a new form of conditional entropy to measure the importance of attributes in incomplete decision systems. Based on the introduced conditional entropy, we construct three attribute selection approaches, including an exhaustive search strategy approach, a greedy (heuristic) search strategy approach and a probabilistic search approach for incomplete decision systems. To test the effectiveness of these methods, experiments on several real-life incomplete data sets are conducted. The results indicate that two of these methods are effective for attribute selection in incomplete decision system.

jMAF - Dominance-Based Rough Set Data Analysis Framework

Abstract: We present a rough set data analysis software jMAF. It employs java Rough Set (jRS) library in which are implemented data analysis methods provided by the (variable consistency) Dominance-based Rough Set Approach (DRSA). The chapter also provides some basics of the DRSA and of its variable consistency extension.

Multi-granulation rough sets based on tolerance relations

Abstract: The original rough set model is primarily concerned with the approximations of sets described by a single equivalence relation on the universe. Some further investigations generalize the classical rough set model to rough set model based on a tolerance relation. From the granular computing point of view, the classical rough set theory is based on a single granulation. For some complicated issues, the classical rough set model was extended to multi-granulation rough set model (MGRS). This paper extends the single-granulation tolerance rough set model (SGTRS) to two types of multi-granulation tolerance rough set models (MGTRS). Some important properties of the two types of MGTRS are investigated. From the properties, it can be found that rough set model based on a single tolerance relation is a special instance of MGTRS. Moreover, the relationship and difference among SGTRS, the first type of MGTRS and the second type of MGTRS are discussed. Furthermore, several important measures are presented in two types of MGTRS, such as rough measure and quality of approximation. Several examples are considered to illustrate the two types of multi-granulation tolerance rough set models. The results from this research are both theoretically and practically meaningful for data reduction.

Dynamic Maintenance of Approximations in Dominance-Based Rough Set Approach under the Variation of the Object Set

Abstract: Dominance-based rough sets approach (DRSA) is an effective tool to deal with information with preference-ordered attribute domains and decision classes. Any information system may evolve when new objects enter into or old objects get out. Approximations of DRSA need update for decision analysis or other relative tasks. Incremental updating is a feasible and effective technique to update approximations. The purpose of this paper is to present an incremental approach for updating approximations of DRSA. The approach is applicable to dynamic information systems when the set of objects varies over time. In this paper, we discuss the principles of incrementally updating P -dominating sets and P -dominated sets and propose an incremental approach for updating approximations of DRSA. A numerical example is given to illustrate the incremental approach. The experimental evaluations on data sets from UCI show that the incremental approach outperforms the original nonincremental one. C � 2013 Wiley Periodicals, Inc.

Knowledge representation and processing with formal concept analysis

Abstract: During the last three decades, formal concept analysis (FCA) became a well-known formalism in data analysis and knowledge discovery because of its usefulness in important domains of knowledge discovery in databases (KDD) such as ontology engineering, association rule mining, machine learning, as well as relation to other established theories for representing knowledge processing, like description logics, conceptual graphs, and rough sets. In early days, FCA was sometimes misconceived as a static crisp hardly scalable formalism for binary data tables. In this paper, we will try to show that FCA actually provides support for processing large dynamical complex (may be uncertain) data augmented with additional knowledge. © 2013 Wiley Periodicals, Inc.