Fundamenta Informaticae - Volume 111, issue 1

Authors: Wu, Wei-Zhi | Ślęzak, Dominik | Nguyen, Hung Son

Article Type: Other

DOI: 10.3233/FI-2011-549

Citation: Fundamenta Informaticae, vol. 111, no. 1, pp. v-vi, 2011

Authors: Haruna, Taichi | Gunji, Yukio-Pegio

Article Type: Research Article

Abstract: We explore lattice theoretic aspects in rough set theory in terms of the duality between algebra and representation. Approximation spaces are dual to complete atomic Boolean algebras in the sense that there is an adjunction between corresponding suitable categories. This is an analogy with the adjunction between the category of topological spaces and the opposite of the category of frames in pointless topology. In this paper we consider a generalization of approximation spaces called double approximation systems. A double approximation system consists of a set and two equivalence relations on it. We construct an adjunction generalizing this concept for approximation …spaces. To achieve this goal, we first introduce a natural generalization of complete atomic Boolean algebras called complete prime lattices. Then we select double approximation systems that can be dual to complete prime lattices and prove the adjunction. Show more

Keywords: rough sets, approximation spaces, complete lattices, adjunction, equivalence of categories

DOI: 10.3233/FI-2011-550

Citation: Fundamenta Informaticae, vol. 111, no. 1, pp. 1-14, 2011

Authors: Li, Tong-Jun | Wu, Wei-Zhi

Article Type: Research Article

Abstract: This paper proposes an approach to attribute reduction in formal contexts via a covering rough set theory. The notions of reducible attributes and irreducible attributes of a formal context are first introduced and their properties are examined. Judgment theorems for determining all attribute reducts in the formal context are then obtained. According to the attribute reducts, all attributes of the formal context are further classified into three types and the characteristic of each type is characterized by the properties of irreducible classes of the formal context. Finally, by using the discernibility attribute sets, a method of distinguishing the reducible attributes …and the irreducible attributes in formal contexts is presented. Show more

Keywords: Attribute reduction, concept lattice, covering rough sets, formal contexts, rough sets

DOI: 10.3233/FI-2011-551

Citation: Fundamenta Informaticae, vol. 111, no. 1, pp. 15-32, 2011

Authors: Yao, Yanqing | Mi, Jusheng | Li, Zhoujun | Xie, Bin

Article Type: Research Article

Abstract: Formal concept analysis and rough set analysis are two complementary approaches for analyzing data. This paper studies approaches to constructing fuzzy concept lattices based on generalized fuzzy rough approximation operators. For a residual implicator θ satisfying θ(a, b) = θ(1 − b, 1 − a) and its dual σ, a pair of (θ, σ)-fuzzy rough approximation operators is defined. We then propose three kinds of fuzzy operators, and examine some of their basic properties. Thus, three complete fuzzy concept lattices can be produced, for which the properties are analogous to those of the classical concept lattices.

Keywords: Fuzzy concept lattices, Approximation operators, (θ, σ)-fuzzy rough sets, Galois connections

DOI: 10.3233/FI-2011-552

Citation: Fundamenta Informaticae, vol. 111, no. 1, pp. 33-45, 2011

Authors: Wu, Zhengjiang | Li, Tianrui | Qin, Keyun | Ruan, Da

Article Type: Research Article

Abstract: Approximation operators play a vital role in rough set theory. Their three elements, namely, binary relation in the universe, basis algebra and properties, are fundamental in the study of approximation operators. In this paper, the interrelations among the three elements of approximation operators in L-fuzzy rough sets are discussed under the constructive approach, the axiomatic approach and the basis algebra choosing approach respectively. In the constructive approach, the properties of the approximation operators depend on the basis algebra and the binary relation. In the axiomatic approach, the induced binary relation is influenced by the axiom set and the basis algebra. …In the basis algebra choosing approach, the basis algebra is constructed by properties of approximation operators and specific binary relations. Show more

Keywords: L-fuzzy rough sets, approximation operators, basis algebra, binary relation, residuated lattice

DOI: 10.3233/FI-2011-553

Citation: Fundamenta Informaticae, vol. 111, no. 1, pp. 47-63, 2011

Authors: Du, Yong | Hu, Qinghua | Chen, Degang | Ma, Peijun

Article Type: Research Article

Abstract: Driver fatigue detection based on computer vision is considered as one of the most hopeful applications of image recognition technology. The key issue is to extract and select useful features from the driver images. In this work, we use the properties of image sequences to describe states of drivers. In addition, we introduce a kernelized fuzzy rough sets based technique to evaluate quality of candidate features and select the useful subset. Fuzzy rough sets are widely discussed in dealing with uncertainty in data analysis. We construct an algorithm for feature evaluation and selection based on fuzzy rough set model. Two …classification algorithms are introduced to validate the selected features. The experimental results show the effectiveness of the proposed techniques. Show more

Keywords: fatigue detection, image recognition, fuzzy rough sets, feature selection, classification

DOI: 10.3233/FI-2011-554

Citation: Fundamenta Informaticae, vol. 111, no. 1, pp. 65-79, 2011

Authors: Yu, Jian | Yang, Miin-Shen | Hao, Pengwei

Article Type: Research Article

Abstract: Cluster analysis is a tool for data analysis. It is a method for finding clusters of a data set with most similarity in the same group and most dissimilarity between different groups. In general, there are two ways, mixture distributions and classification maximum likelihood method, to use probability models for cluster analysis. However, the corresponding probability distributions to most clustering algorithms such as fuzzy c-means, possibilistic c-means, mode-seeking methods, etc., have not yet been found. In this paper, we construct a multimodal probability distribution model and then present the relationships between many clustering algorithms and the proposed model via the …maximum likelihood estimation. Moreover, we also give the theoretical properties of the proposed multimodal probability distribution. Show more

Keywords: Cluster analysis, probability density function

DOI: 10.3233/FI-2011-555

Citation: Fundamenta Informaticae, vol. 111, no. 1, pp. 81-90, 2011

Authors: Mishra, Deepti | Mishra, Alok

Article Type: Research Article

Abstract: It is important to identify modules that are fault prone or exhibit evidence of high cognitive complexity as these modules require corrective actions such as increased source code inspection, refactoring or performing more exhaustive testing. This can lead to a better quality software system. It has been found that inheritance has an impact on the cognitive complexity of a software system. In this paper, two inheritance metrics based on cognitive complexity, one at class level CCI (Class Complexity due to Inheritance) and another at program level ACI (Average Complexity of a program due to Inheritance), have been proposed for object-oriented …software systems. Additionally, one more metric MC (Method Complexity) has been proposed to calculate the complexity of a method. These proposed metrics are compared with some well known object-oriented inheritance metrics by calculating their values for three random C++ programs. It has been observed that CCI and ACI are better to represent cognitive complexity due to inheritance than other well known class level and program level inheritance metrics. Show more

Keywords: cognitive complexity, software metrics, object-oriented systems

DOI: 10.3233/FI-2011-556

Citation: Fundamenta Informaticae, vol. 111, no. 1, pp. 91-117, 2011