Xibei Yang

Dominance-based rough set approach and knowledge reductions in incomplete ordered information system

Many methods based on the rough set to deal with incomplete information systems have been proposed in recent years. However, they are only suitable for the incomplete systems with regular attributes whose domains are not preference-ordered. This paper thus attempts to present research focusing on a complex incomplete information system-the incomplete ordered information system. In such incomplete information systems, all attributes are considered as criterions. A criterion indicates an attribute with preference-ordered domain. To conduct classification analysis in the incomplete ordered information system, the concept of similarity dominance relation is first proposed. Two types of knowledge reductions are then formed for preserving two different notions of similarity dominance relations. With introduction of the approximate distribution reduct into the incomplete ordered decision system, the judgment theorems and discernibility matrixes associated with four novel approximate distribution reducts are obtained. A numerical example is employed to substantiate the conceptual arguments.

Dominance-based rough set approach to incomplete interval-valued information system

Since preference order is a crucial feature of data concerning decision situations, the classical rough set model has been generalized by replacing the indiscernibility relation with a dominance relation. The purpose of this paper is to further investigate the dominance-based rough set in incomplete interval-valued information system, which contains both incomplete and imprecise evaluations of objects. By considering three types of unknown values in the incomplete interval-valued information system, a data complement method is used to transform the incomplete interval-valued information system into a traditional one. To generate the optimal decision rules from the incomplete interval-valued decision system, six types of relative reducts are proposed. Not only the relationships between these reducts but also the practical approaches to compute these reducts are then investigated. Some numerical examples are employed to substantiate the conceptual arguments.

Neighborhood systems-based rough sets in incomplete information system

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.

Updating multigranulation rough approximations with increasing of granular structures

Dynamic updating of the rough approximations is a critical factor for the success of the rough set theory since data is growing at an unprecedented rate in the information-explosion era. Though many updating schemes have been proposed to study such problem, few of them were carried out in a multigranulation environment. To fill such gap, the updating of the multigranulation rough approximations is firstly explored in this paper. Both naive and fast algorithms are presented for updating the multigranulation rough approximations with the increasing of the granular structures. Different from the naive algorithm, the fast algorithm is designed based on the monotonic property of the multigranulation rough approximations. Experiments on six microarray data sets show us that the fast algorithm can effectively reduce the computational time in comparison with the naive algorithm when facing high dimensional data sets. Moreover, it is also shown that fast algorithm is useful in decreasing the computational time of finding both traditional reduct and attribute clustering based reduct.

On multigranulation rough sets in incomplete information system

Multigranulation rough set is a new and interesting topic in the theory of rough set. In this paper, the multigranulation rough sets approach is introduced into the incomplete information system. The tolerance relation, the similarity relation and the limited tolerance relations are employed to construct the optimistic and the pessimistic multigranulation rough sets, respectively. Not only the properties about these multigranulation rough sets are discussed, but also the relationships among these multigranulation rough sets models are explored. It is shown that by the multigranulation rough sets theory, the limited tolerance relations based multigranulation lower approximations fall between the tolerance and the similarity relations based multigranulation lower approximations, the limited tolerance relations based multigranulation upper approximations fall between the similarity and the tolerance relations based multigranulation upper approximations. Such results are consistent to those in single-granulation based rough sets models.

Generalization of Soft Set Theory: From Crisp to Fuzzy Case

The traditional soft set is a mapping from parameter to the crisp subset of universe. However, the situation may be more complex in real world because the fuzzy characters of parameters. In this paper, the traditional soft set theory is expanded to be a fuzzy one, the fuzzy membership is used to describe parameter-approximate elements of fuzzy soft set. Furthermore, basic fuzzy logic operators are used to define generalized operators on fuzzy soft set and then the DeMorgan’s laws are proved. Finally, the parametrization reduction of fuzzy soft set is defined, a decision-making problem is analyzed to indicate the validity of the fuzzy soft set.

Constructive and axiomatic approaches to hesitant fuzzy rough set

Hesitant fuzzy set is a generalization of the classical fuzzy set by returning a family of the membership degrees for each object in the universe. Since how to use the rough set model to solve fuzzy problems plays a crucial role in the development of the rough set theory, the fusion of hesitant fuzzy set and rough set is then firstly explored in this paper. Both constructive and axiomatic approaches are considered for this study. In constructive approach, the model of the hesitant fuzzy rough set is presented to approximate a hesitant fuzzy target through a hesitant fuzzy relation. In axiomatic approach, an operators-oriented characterization of the hesitant fuzzy rough set is presented, that is, hesitant fuzzy rough approximation operators are defined by axioms and then, different axiom sets of lower and upper hesitant fuzzy set-theoretic operators guarantee the existence of different types of hesitant fuzzy relations producing the same operators.

Relationships among generalized rough sets in six coverings and pure reflexive neighborhood system

Rough set is a useful tool to deal with partition related uncertainty, granularity, and incompleteness of knowledge. Although the classical rough set is constructed on the basis of an indiscernibility relation, it can also be generalized by using some weaker binary relations. In this paper, a systematic approach is used to study the generalized rough sets in six coverings and pure reflexive neighborhood system. After two steps, relationships among generalized rough sets in six coverings and pure reflexive neighborhood system are obtained. The first step is to study the generalized rough sets in six coverings, and to get relationships between every two covering rough set models. The second step is to study the relationships between generalized rough sets in each covering and in pure reflexive neighborhood system. The inclusion relations or equivalence relations among the seven upper/lower approximations could be acquired. Finally, the accuracy measures of generalized rough sets in six coverings and that in pure reflexive neighborhood system are compared. The relationships among seven accuracy measures are also obtained. Some illustrative examples are employed to demonstrate our arguments.

Cost-sensitive rough set: A multi-granulation approach

Abstract Cost is an important issue in real world data mining. In rough set community, test cost and decision cost are two popular costs which are addressed by many researchers. In recent years, these two costs have been widely discussed from the standpoint of attribute reduction. However, few works pay attention to the construction of cost-sensitive rough set model. In addition, it becomes apparent that multiple granulation approach plays a crucial role in dealing with involute information, such as heterogeneous data and multi-scale data. This study elaborates on a novel design of cost-sensitive rough set model with the aid of multi-granulation strategy. First, the lower and upper approximations of cost-sensitive multi-granulation are constructed, and it can be verified that in multi-granulation framework, the information granules and approximations are sensitive to decision costs and test costs, respectively. Second, along the approximations definitions, a semantic interpretation of the proposed model is studied. According to this interpretation, the settings of decision cost and test cost are presented in light of information entropy. For information reduction, we transform it to an optimization problem and investigate two pivotal reduction criteria. Theoretical analysis and experimental results show that: (a) the established model is a generalization of many existing models and quite close to real applications; (b) entropy based cost setting is much suitable for our model since it can increase classification quality or decrease decision cost; (c) considering different reduction approaches, decision monotonicity based reduction can increase the numbers of certainty rules and decrease the numbers of uncertainty rules while cost based reduction can obtain the minimal total costs. This study also shows an important philosophy in our life, i.e., the more you pay, the more you gain.

α-Dominance relation and rough sets in interval-valued information systems

Though rough set has been widely used to study systems characterized by insufficient and incomplete information, its performance in dealing with initial interval-valued data needs to be seriously considered for improving the suitability and scalability. The aim of this paper is to present a parameterized dominance-based rough set approach to interval-valued information systems. First, by considering the degree that an interval-valued data is dominating another one, we propose the concept of α-dominance relation. Second, we present the α-dominance based rough set model in interval-valued decision systems. Finally, we introduce lower and upper approximate reducts into α-dominance based rough set for simplifying decision rules, we also present the judgement theorems and discernibility functions, which describe how lower and upper approximate reducts can be calculated. This study suggests potential application areas and new research trends concerning rough set approach to interval-valued information systems.