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Multigranulation decision-theoretic rough sets

Tumor classification based on gene expression levels is important for tumor diagnosis. Since tumor data in gene expression contain thousands of attributes, attribute selection for tumor data in gene expression becomes a key point for tumor classification. Inspired by the concept of gain ratio in decision tree theory, an attribute selection method based on fuzzy gain ratio under the framework of fuzzy rough set theory is proposed. The approach is compared to several other approaches on three real world tumor data sets in gene expression. Results show that the proposed method is effective. This work may supply an optional strategy for dealing with tumor data in gene expression or other applications.

Attribute selection based on information gain ratio in fuzzy rough set theory with application to tumor classification

Many previous studies on face recognition attempted to seek a precise classifier to achieve a low misclassification error, which is based on an assumption that all misclassification costs are the same. In many real-world scenarios, however, this assumption is not reasonable due to the imbalanced misclassification cost and insufficient high-quality facial image information. To address this issue, we propose a sequential three-way decision method for cost-sensitive face recognition. The proposed method is based on a formal description of granular computing. It develops a sequential strategy in a decision process. In each decision step, it seeks a decision which minimizes the misclassification cost rather than misclassification error, and it incorporates the boundary decision into the decision set such that a delayed decision can be made if available high-quality facial image information is insufficient for a precise decision. To describe the granular information of the facial image in three-way decision steps, we develop a series of image granulation methods based on two-dimensional subspace projection methods including 2DPCA, 2DLDA and 2DLPP. The sequential three-way decisions and granulation methods present an applicable simulation on human decisions in face recognition, which simulate a sequential decision strategy from rough granule to precise granule. The experiments were conducted on two popular facial image database, which validated the effectiveness of the proposed methods.

Sequential three-way decision and granulation for cost-sensitive face recognition

We induce the incomplete information to DTRS and build a three-way decision model.We use a hybrid information table to deal with the integrated information system.We list the key steps and algorithm of the proposed three-way decision model. As a natural extension of three-way decisions with incomplete information, this paper provides a novel three-way decision model based on incomplete information system. First, we define a new relation to describe the similarity degree of incomplete information. Then, in view of the missing values presented in incomplete information system, we utilize interval number to acquire the loss function. A hybrid information table which consist both of the incomplete information and loss function, is used to deal with the new three-way decision model. The key steps and algorithm for constructing the integrated three-way decision model are also carefully investigated. An empirical study of medical diagnosis validates the reasonability and effectiveness of our proposed model.

A novel three-way decision model based on incomplete information system

NMGRS: Neighborhood-based multigranulation rough sets

Neighborhood system formalized the ancient intuition, infinitesimals, which led to the invention of calculus, topology and non-standard analysis. In this paper, the neighborhood system is researched from the view point of knowledge engineering and then each neighborhood is considered as a basic unit with knowledge. By using these knowledge in neighborhood system, the rough approximations and the corresponding properties are discussed. It is shown that in the incomplete information system, the smaller upper approximations can be obtained by neighborhood system based rough sets than by the methods in [Y. Leung, D.Y. Li, Maximal consistent block technique for rule acquisition in incomplete information systems, Information Sciences 115 (2003) 85-106] and [Y. Leung, W.Z. Wu, W.X. Zhang, Knowledge acquisition in incomplete information systems: a rough set approach, European Journal of Operational Research 168 (2006) 164-180]. Furthermore, a new knowledge operation is discussed in the neighborhood system, from which more knowledge can be derived from the initial neighborhood system. By such operations, the regions of lower and upper approximations are further expanded and narrowed, respectively. Some numerical examples are employed to substantiate the conceptual arguments.

Neighborhood systems-based rough sets in incomplete information system

Multi-granulation rough set: from crisp to fuzzy case

We propose a DTRS by a set of cost matrices.Optimistic and pessimistic cases are two special models of our approach.Two criterions based reducts are calculated by two different algorithms. By introducing the misclassification and delayed decision costs into the probabilistic approximations of the target, the model of decision-theoretic rough set is then sensitive to cost. However, traditional decision-theoretic rough set is proposed based on one and only one cost matrix, such model does not take the characteristics of multiplicity and variability of cost into consideration. To fill this gap, a multicost strategy is developed for decision-theoretic rough set. Firstly, from the viewpoint of the voting fusion mechanism, a parameterized decision-theoretic rough set is proposed. Secondly, based on the new model, the smallest possible cost and the largest possible cost are calculated in decision systems. Finally, both the decision-monotocity and cost criteria are introduced into the attribute reductions. The heuristic algorithm is used to compute decision-monotonicity reduct while the genetic algorithm is used to compute the smallest and the largest possible cost reducts. Experimental results on eight UCI data sets tell us: 1. compared with the raw data, decision-monotocity reduct can generate greater lower approximations and more decision rules; 2. the smallest possible cost reduct is much better than decision-monotocity reduct for obtaining smaller costs and more decision rules. This study suggests new research trends concerning decision-theoretic rough set theory.

Decision-theoretic rough set

A simple multigranulation rough set approach is to approximate the target through a family of binary relations. Optimistic and pessimistic multigranulation rough sets are two typical examples of such approach. However, these two multigranulation rough sets do not take frequencies of occurrences of containments or intersections into account. To solve such problem, by the motivation of the multiset, the model of the multiple multigranulation rough set is proposed, in which both lower and upper approximations are multisets. Such two multisets are useful when counting frequencies of occurrences such that objects belong to lower or upper approximations with a family of binary relations. Furthermore, not only the concept of approximate distribution reduct is introduced into multiple multigranulation rough set, but also a heuristic algorithm is presented for computing reduct. Finally, multiple multigranulation rough set approach is tested on eight UCI (University of California–Irvine) data sets. Experimental results show: 1. the approximate quality based on multiple multigranulation rough set is between approximate qualities based on optimistic and pessimistic multigranulation rough sets; 2. by comparing with optimistic and pessimistic multigranulation rough sets, multiple multigranulation rough set needs more attributes to form a reduct.

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Multigranulation rough set: A multiset based strategy

Presently, the greedy searching strategy has been widely accepted for obtaining reduct in the field of rough set. In the framework of greedy searching, the evaluation of the candidate attribute is crucial, because the evaluation can determine the final result of reduct to a large extent. However, most of the previous evaluations are designed by considering one and only one fixed granularity, which fails to make the multi-view based evaluation possible. To fill such gap, a Parameterized Multi-granularity Attribute Selector is proposed for obtaining reduct in this paper. Our attribute selector consists of two parts: one is the multi-granularity attribute selector which evaluates and selects attributes through using the information provided by multiple different granularities; the other is the data-guided parameterized granularity selector which generates multiple different parameterized granularities through taking the characteristics of data into account. The experimental results over 15 UCI data sets show the following: 1) compared with the state of the art approaches for obtaining reducts, our proposed attribute selector can contribute to reduct with higher stability; 2) our proposed attribute selector will not provide the reduct with poorer classification performance. This research suggests a new trend for the multi-granularity mechanism in the problem of attribute reduction.

Huili Dou

Papers

Neighborhood systems-based rough sets in incomplete information system

Multi-granulation rough set: from crisp to fuzzy case

Decision-theoretic rough set

Multigranulation rough set: A multiset based strategy

Data-guided multi-granularity selector for attribute reduction