Classical rough set theory is considered a useful tool for dealing with the uncertainty of categorical data. The major deficiency of this model is that the classical rough set model is sensitive to noise in classification learning due to the stringent condition of equivalence relation. Thus, a class of fuzzy similarity relations was introduced to describe the similarity between samples with categorical attributes. However, these kinds of similarity relations also have deficiencies when they are used in fuzzy rough computation. In this article, we propose a new fuzzy-rough-set model for categorical data by introducing a variable parameter to control the similarity of samples. This model employs the iterative computation strategy to define fuzzy rough approximations and dependence functions. It is proved that the proposed rough dependence function is monotonic. Finally, the proposed model is applied to the attribute reduction of categorical data. The experimental results indicate that the proposed model is more effective for categorical data than some existing algorithms.

Fuzzy Rough Attribute Reduction for Categorical Data

Classical fuzzy rough set often uses fuzzy rough dependency as an evaluation function of feature selection. However, this function only retains the maximum member- ship degree of a sample to one decision class, it can not describe the classification error. Therefore, in this work, a novel criterion function for feature selection is proposed to overcome this weakness. To characterize the classification error rate, we first introduce a class of irreflexive and symmetric fuzzy binary relations to redefine the concepts of fuzzy rough approximations. Then, we propose a novel concept of dependency: inner product dependency to describe the classification error, and construct a criterion function to evaluate the importance of candidate features. The proposed criterion function not only can maintain a maximum dependency function, but also guarantees the minimum classification error. The experimental analysis shows that the proposed criterion function is effective for data sets with a large overlap between different categories.

Feature selection with fuzzy-rough minimum classification error criterion

Double-quantitative variable consistency dominance-based rough set approach

Double-quantitative rough sets, optimal scale selection and reduction in multi-scale dominance IF decision tables

The existing multiattribute decision-making (MADM) methods on multiscale information systems (MSISs) are generally studied from the utility point of view, which may cause two problems: 1) the objects are strictly classified into good or bad, which may lead to misclassification and 2) the risk attitude and psychological behaviors of decision makers are difficult to be reflected. In light of this, this article proposes a wide three-way decision (3WD) model on an MSIS, which combines 3WD theory and regret theory and can precisely make up for these two shortcomings. First, by virtue of regret theory, an outranking relation on the comprehensive MSIS is constructed according to the regret-rejoicing index. Second, objects in the outranking relation are classified into three different domains by a clustering method. In each domain, the ranking of objects can be calculated by using the relative closeness coefficient. Finally, we use the cases in the database to simulate the experiment to verify the decision-making effect of the proposed model. Comparative analysis and experimental analysis also show the effectiveness, superiority, and stability of the proposed model.

Regret-Theoretic Multiattribute Decision-Making Model Using Three-Way Framework in Multiscale Information Systems

A granular structure of intuitionistic fuzzy (IF) information presents simultaneously the similarity and diversity of samples. However, this structural representation has rarely displayed its technical capability in data mining and information processing due to the lack of suitable constructive methods and semantic interpretation for IF information with regard to real data. To pursue better performance of the IF-based technique in real-world data mining, in this article, we examine information granularity, information entropy of IF granular structures, and their applications to data reduction of IF information systems. First, several types of partial-order relations at different hierarchical levels are defined to reveal the granularity of IF granular structures. Second, the granularity invariance between different IF granular structures is characterized by using relational mappings. Third, Shannon's entropies are generalized to IF entropies and their relationships with the partial-order relations are addressed. Based on the theoretical analysis above, the significance of intuitionistic attributes using the information measures is then introduced and the information-preserving algorithm for data reduction of IF information systems is constructed. Finally, by inducing substantial IF relations from public datasets that take both the similarity/diversity between the samples from the same/different classes into account, a collection of numerical experiments is conducted to confirm the performance of the proposed technique.

Granularity and Entropy of Intuitionistic Fuzzy Information and Their Applications

Multigranulation rough set over two universes provides a new perspective to combine multiple granulation knowledge in a multigranulation space in practical reality. Note that there are always non-essential neighborhood granulations, which would affect the efficiency and quality of decision making. Therefore, selecting valuable granulations and reducing worthless ones are necessary for the application of multigranulation rough set in decision process. In this paper, we first define several measurements to compare the granularity of neighborhood granulations, using which the granulation selection with multigranulation rough set is characterized. Then, the selection algorithms in the multigranulation space are developed. Third, we generate “OR” and “AND” decision rules based on multigranulation fusion strategies. As an application, these decision rules are employed to make decisions in the presence of disease diagnosis problems. In the end, the effectiveness and efficiency of the proposed algorithms are examined with numerical experiments on selective data sets.

Suwei Shi

Papers

Granularity and Entropy of Intuitionistic Fuzzy Information and Their Applications

Granulation selection and decision making with multigranulation rough set over two universes