Interval-valued Information Systems Research Articles

Graph-Based Unsupervised Feature Selection for Interval-Valued Information System.

Feature selection has become one of the hot research topics in the era of big data. At the same time, as an extension of single-valued data, interval-valued data with its inherent uncertainty tend to be more applicable than single-valued data in some fields for characterizing inaccurate and ambiguous information, such as medical test results and qualified product indicators. However, there are relatively few studies on unsupervised attribute reduction for interval-valued information systems (IVISs), and it remains to be studied how to effectively control the dramatic increase of time cost in feature selection of large sample datasets. For these reasons, we propose a feature selection method for IVISs based on graph theory. Then, the model complexity could be greatly reduced after we utilize the properties of the matrix power series to optimize the calculation of the original model. Our approach can be divided into two steps. The first is feature ranking with the principles of relevance and nonredundancy, and the second is selecting top-ranked attributes when the number of features to keep is fixed as a priori. In this article, experiments are performed on 14 public datasets and the corresponding seven comparative algorithms. The results of the experiments verify that our algorithm is effective and efficient for feature selection in IVISs.

Interval-valued fuzzy discernibility pair approach for attribute reduction in incomplete interval-valued information systems

Interval-valued information systems provide rich semantic interpretation and greater flexibility compared to real-valued information systems. Meanwhile, incomplete interval-valued information systems containing missing values exist widely in reality. One of the key issues in handling incomplete interval-valued information systems is attribute reduction. Unfortunately, there are few studies on attribute reduction for incomplete interval-valued information systems. Moreover, most of the existing studies use fuzzy similarity relations to measure the similarity of objects. Due to the complexity of incomplete interval-valued information systems, traditional fuzzy similarity relations cannot adequately represent the information contained within incomplete interval-valued information systems. To address this issue, this study proposes interval-valued fuzzy min-max similarity relations for incomplete interval-valued information systems, along with two attribute reduction algorithms based on interval-valued fuzzy discernibility pairs model for incomplete interval-valued information systems. Firstly, this study defines interval-valued fuzzy min-max similarity relations using distance-based extended restricted equivalence functions. Secondly, this study presents the interval-valued fuzzy discernibility pairs and discerning ability measure for attribute sets. Furthermore, an attribute reduction algorithm is proposed for incomplete interval-valued information systems. Thirdly, taking into account decision attributes, the relative interval-valued fuzzy discernibility pairs and an attribute reduction algorithm for incomplete interval-valued decision information systems are proposed. Finally, the effectiveness of the proposed method is compared to four representative attribute reduction algorithms in experiments. The experimental results illustrate that our method is effective and has advantages over the compared algorithms.

Three-way decisions method based on matrices approaches oriented dynamic interval-valued information system

Interval-valued Information Systems (IvIS) reflect the uncertain information in real scene, in which the attribute value of objects are all interval values rather than single values. Data information analysed by three-way decisions is not static but dynamically changing in IvIS, which results in the updating of positive region, boundary region and negative region of decision class X. In this paper, a matrix computational framework based on λ-similarity relation is proposed on the variation of the attribute set, attribute value and object set. Based on the framework, some incremental algorithms are proposed to calculate the positive, boundary and negative region of X in dynamic IvIS. Finally, comparative experiments on data sets from UCI are conducted when attribute set, attribute value and object set are updating over time, respectively. Experimental results show that in comparison with the traditional algorithm, the proposed algorithms can effectively save time for the computation of positive, boundary and negative region of X in dynamic IvIS.

Dynamic information fusion in multi-source incomplete interval-valued information system with variation of information sources and attributes

Interval-valued data describe the random phenomenon that abounds in the real world, a pivotal research orientation in uncertainty processing. With the rapid development of big data, we may gather information from multiple information sources. To effectively acquire knowledge from multiple information sources, information fusion is commonly used to get a unified representation. However, sometimes data gathered from multiple sources may be lost; it is meaningful and necessary to study the fusion of multi-source incomplete interval-valued data. We propose a novel information fusion method based on information entropy for multi-source incomplete interval-valued data and four incremental fusion mechanisms characterized by the change in information sources and attributes. The corresponding static and dynamic fusion algorithms are designed, and their time complexities are analyzed. Experimental results show that the proposed method outperforms the mean, max, and min fusion methods. Furthermore, the four incremental fusion mechanisms reduced the runtime compared with the static fusion mechanism.

New Measures of Uncertainty for Interval-Valued Data With Application to Attribute Reduction

Uncertainty measurement (UM) gives a brand-new perspective on attribute reduction in an information system (IS). Interval-valued data is a kind of very vital data in rough set theory (RST). Rough set model based on tolerance relations can be considered to deal with interval-valued data. However, these kinds of tolerance relations have deficiencies when they are used in fuzzy rough computation. This paper studies new UM for an interval-valued information system (IVIS) and considers its attribute reduction. Firstly, a novel fuzzy symmetry relation on the object set of an IVIS is established based on “The similarity between information values that is fed back to the attribute set”. Secondly, λ-information granules on the basis of a fuzzy symmetry relation are obtained. Then, four UMs for an IVIS are investigated. Next, numerical experiments and statistical tests are used to evaluate the performance of the proposed UMs. Moreover, attribute reduction in an IVIS is studied and the relevant algorithms are proposed. Finally, clustering analysis on the reduced IVIS is conducted. Experimental results indicate that the proposed algorithms are effective based on evaluation indicators of clustering performance. This paper provides a novel viewpoint for the establishment of fuzzy symmetry relation and attribute reduction algorithms.

Attribute significance based on inclusion degree for incomplete information systems and their applications to MADM problems

Attribute significance is very important in multiple-attribute decision-making (MADM) problems. In a MADM problem, the significance of attributes is often different. In order to overcome the shortcoming that attribute significance is usually given artificially. The purpose of this paper is to give attribute significance computation formulas based on inclusion degree. We note that in the real-world application, there is a lot of incomplete information due to the error of data measurement, the limitation of data understanding and data acquisition, etc. Firstly, we give a general description and the definition of incomplete information systems. We then establish the tolerance relation for incomplete linguistic information system, with the tolerance classes and inclusion degree, significance of attribute is proposed and the corresponding computation formula is obtained. Subsequently, for incomplete fuzzy information system and incomplete interval-valued fuzzy information system, the dominance relation and interval dominance relation is established, respectively. And the dominance class and interval dominance class of an element are got as well. With the help of inclusion degree, the computation formulas of attribute significance for incomplete fuzzy information system and incomplete interval-valued fuzzy information system are also obtained. At the same time, results show that the reduction of attribute set can be obtained by computing the significance of attributes in these incomplete information systems. Finally, as the applications of attribute significance, the attribute significance is viewed as attribute weights to solve MADM problems and the corresponding TOPSIS methods for three incomplete information systems are proposed. The numerical examples are also employed to illustrate the feasibility and effectiveness of the proposed approaches.

Dynamic fuzzy neighborhood rough set approach for interval-valued information systems with fuzzy decision

Nowadays, many extended rough set models are proposed to acquire valuable knowledge from interval-valued information system. These existing models mainly focus on different forms of similarity relations. However, most of these similarity relations are qualitative rather than quantitative, which is not reasonable in some practical cases. In addition, with the arrival of new objects and the removal of obsolete objects, the interval-valued information system with fuzzy decision (IvIS_FD) is always changing with time. Therefore, how to efficiently mining knowledge from dynamic IvIS_FD is a meaningful topic. Motivated by these two issues, we study the dynamic fuzzy neighborhood rough set approach for IvIS_FD, aiming to effectively update the rough approximations when the IvIS_FD evolves over time. Firstly, δ-fuzzy neighborhood relation is defined to describe the similarity relation between objects quantitatively. Secondly, we introduce a novel fuzzy neighborhood rough set model and its matrix representation suitable for IvIS_FD. On this basis, we discuss the incremental mechanisms to update fuzzy neighborhood approximations when multiple objects are added to or deleted from an IvIS_FD, respectively. Meanwhile, corresponding dynamic algorithms are designed and explained. Finally, experiments are performed on nine public data sets to evaluate the performance of the dynamic fuzzy neighborhood rough set model. Experimental results verify that the proposed model is effective and efficient for updating rough approximations in dynamic IvIS_FD.

A fuzzy [formula omitted]-similarity relation-based attribute reduction approach in incomplete interval-valued information systems

As generalizations of single-valued information systems, interval-valued information systems (IVISs) can better express the real data with uncertainty in some applications. Attribute reduction methods for complete IVISs or complete interval-valued decision systems (IVDSs) have been developed. However, there are few researches on attribute reduction for incomplete interval-valued information systems (IIVISs). The paper aims to investigate the attribute reduction issue in IIVISs. Firstly, the maximal and minimal distances, which characterize the difference between two interval values, are defined, and the maximal and minimal similarity degrees are given. Secondly, the fuzzy α-similarity relation is defined based on similarity between interval values, and the concept of α-equivalence relation is raised. Thirdly, entropy measures are investigated for IIVISs in view of α-equivalence relations. Fourthly, a new attribute reduction approach for IIVISs is proposed by using conditional entropy, and its corresponding algorithm is given. Finally, experiments to verify the effectiveness and feasibility of the newly proposed approach for attribute reduction in IIVISs are presented. These results will be helpful to perfect the uncertainty measurement model, and provide an approach for attribute reduction in IIVISs.

Feature Selection for Interval-Valued Data Based on D-S Evidence Theory

Feature selection is one basic and critical technology for data mining, especially in current “big data era". Rough set theory (RST) is sensitive to noise in feature selection due to the strict condition of equivalence relation. However, D-S evidence theory is flexible to measure uncertainty of information. This paper introduces robust feature evaluation metrics “belief function" and “plausibility function" into feature selection algorithm to avoid the defect that classification effect is affected by noise. First of all, similarity between information values in an interval-valued information system (IVIS) is given and a variable parameter to control the similarity of samples is introduced. Then, θ-lower approximation and θ-upper approximation in IVIS are put forward. Next, belief function and plausibility function based on θ-lower approximation and θ-upper approximation are put forward. Finally, four feature selection algorithms in an IVIS based on D-S evidence theory are proposed. The experimental results on four real interval-valued datasets show that the proposed metrics are robust to noise, and the proposed algorithms are more effective than the existing algorithms.

Attribute selection approaches for incomplete interval-value data

Attribute selection in an information system (IS) is an important issue when dealing with a large amount of data. An IS with incomplete interval-value data is called an incomplete interval-valued information system (IIVIS). This paper proposes attribute selection approaches for an IIVIS. Firstly, the similarity degree between two information values of a given attribute in an IIVIS is proposed. Then, the tolerance relation on the object set with respect to a given attribute subset is obtained. Next, θ-reduction in an IIVIS is studied. What is more, connections between the proposed reduction and information entropy are revealed. Lastly, three reduction algorithms base on θ-discernibility matrix, θ-information entropy and θ-significance in an IIVIS are given.

Unsupervised attribute reduction based on $$\alpha $$-approximate equal relation in interval-valued information systems

As generalizations of single-valued information systems, interval-valued information systems (IVISs) can better express real data. At present, numerous unsupervised attribute reduction approaches for single-valued information systems have been considered, but there are few researches on unsupervised attribute reduction for IVISs. In this article, we investigate a new fuzzy relation by means of similarity between interval values, and propose the concept of $$\alpha $$ -approximate equal relation in view of the fuzzy similarity class. Then the equivalence relation induced by $$\alpha $$ -approximate equal relation is used to define the information entropy, which is used to construct the unsupervised attribute reduction method together with mutual information for IVISs. Finally, experiments demonstrate that the advanced unsupervised attribute reduction method is effective and feasible in IVISs.

New measures of uncertainty for an interval-valued information system

An information system as a database that represents relationships between objects and attributes is an important mathematical model. An interval-valued information system is a generalized model of single-valued information systems. As important evaluation tools in the field of machine learning, measures of uncertainty can quantify the dependence and similarity between two targets. However, the existing measures of uncertainty for interval-valued information systems have not been thoroughly researched. This paper is devoted to the study of new measures of uncertainty for an interval-valued information system. Information structures are first introduced in a given interval-valued information system. Then, the dependence between two information structures is depicted. Next, new measures of uncertainty for an interval-valued information system are investigated by using the information structures. As an application of the proposed measures, the rough entropy of a rough set is proposed by means of information granulation. Finally, a numerical experiment on the Face recognition dataset is presented to demonstrate the feasibility of the proposed measures, and a statistical effectiveness analysis is conducted. The results are helpful for understanding the essence of uncertainty in interval-valued information systems.

Rough Set Model for Cognitive Expectation Embedded Interval‐Valued Decision Systems

Interval-valued information system is a kind of knowledge representation model for uncertain information. An interval-valued attribute has an expectation by experience or background knowledge, called cognitive expectation. There are few studies aiming at intervalvalued attributes with cognitive expectations. We propose the concept of Interval-valued decision system with expectations (IDSE). A new dominance relation based on the distances between expectations and interval values is constructed. Based on the constructed dominance relation, a rough set model for IDSE is investigated. Attribute reduction in IDSE is also examined by using discernibility matrices and discernibility functions.

Multigranulation Decision-theoretic Rough Set Based on Incomplete Interval-valued Information Systems

Most of the previous results about decision-theoretic rough set do not take a variety of decision maker’s attitude into consideration, which is vulnerable environmental impact in reality. To solve such problems, a strategy is firstly introduced into multigranulation decision-theoretic rough set by the definition of decision function. Firstly, the equivalence classes are replaced with maximal consistent classes to establish the decision-theoretic rough set in an incomplete interval-valued information system. Then, based on the definition of decision function, the Sigmoid-multigranulation decision-theoretic rough set model and generalized multigranulation decision-theoretic rough set model are proposed and some properties of two models are studied in an incomplete interval-valued information system. Finally, the relation is illustrated between generalized multigranulation decision-theoretic rough set model and other related rough set models. This study suggests potential application areas and new research trends concerning decision-theoretic rough set.

Uncertainty measurement for incomplete interval-valued information systems based on α-weak similarity

Rough set theory is a powerful mathematical tool to deal with uncertainty in data analysis. Interval-valued information systems are generalized models of single-valued information systems. Recently, uncertainty measures for complete interval-valued information systems or complete interval-valued decision systems have been developed. However, there are few studies on uncertainty measurements for incomplete interval-valued information systems. This paper aims to investigate the uncertainty measures in incomplete interval-valued information systems based on an α-weak similarity. Firstly, the maximum and the minimum similarity degrees are defined when interval-values information systems are incomplete based on the similarity relation. The concept of α-weak similarity relation is also defined. Secondly, the rough set model is constructed. Based on this model, accuracy, roughness and approximation accuracy are given to evaluate the uncertainty in incomplete interval-valued information systems. Furthermore, experimental analysis shows the effectiveness of the constructed uncertainty measures for incomplete interval-valued information systems.

Intelligent reasoning and management decision making with grey rough influence diagrams

Purpose Influence diagrams (IDs) have been widely applied as a form of knowledge expression and a decision analysis tool in the management and engineering fields. Relationship measurements and expectation values are computed depending on probability distributions in traditional IDs, however, most information systems in the real world are nondeterministic, and data in information tables can be interval valued, multiple valued and even incomplete. Consequently, conventional numeric models of IDs are not suitable for information processing with respect to imprecise data whose boundaries are uncertain. The paper aims to discuss these issues. Design/methodology/approach The grey system theory and rough sets have proved to be effective tools in the data processing of uncertain information systems, approximate knowledge acquisition and representation are also the objectives in intelligent reasoning and decision analysis. Hence, this study proposes a new mathematical model by combining grey rough sets with IDs, and approximate measurements are used instead of probability distribution, an implicational relationship is utilized instead of an indiscernible relationship, and all of the features of the proposed approach contribute to deal with uncertain problems. Findings The focus of this paper is to provide a more comprehensive framework for approximate knowledge representation and intelligent decision analysis in uncertain information systems and an example of decision support in product management systems with the new approach is illustrated. Originality/value Collaboration of IDs and grey rough sets is first proposed, which provides a new mathematical and graphical tool for approximate reasoning and intelligent decision analysis within interval-valued information systems.

Incremental updating of rough approximations in interval-valued information systems under attribute generalization

Interval-valued Information System (IvIS) is a generalized model of single-valued information system, in which the attribute values of objects are all interval values instead of single values. The attribute set in IvIS is not static but rather dynamically changing over time with the collection of new information, which results in the continuous updating of rough approximations for rough set-based data analysis. In this paper, on the basis of the similarity-based rough set model in IvIS, we develop incremental approaches for updating rough approximations in IvIS under attribute generalization, which refers to the dynamic changing of attributes. Firstly, increment relationships between the original rough approximations and the updated ones when adding or deleting an attribute set are analyzed, respectively. And the incremental mechanisms for updating rough approximations in IvIS are introduced, which carry out the computation using the previous results from the original data set along with new results. Then, the corresponding incremental algorithms are designed based on the proposed mechanisms. Finally, comparative experiments on data sets from UCI as well as artificial data sets are conducted, respectively. Experimental results show that the proposed incremental algorithms can effectively reduce the running time for the computation of rough approximations in comparison with the static algorithm.

Attribute reduction in interval-valued information systems based on information entropies

Interval-valued data appear as a way to represent the uncertainty affecting the observed values. Dealing with interval-valued information systems is helpful to generalize the applications of rough set theory. Attribute reduction is a key issue in analysis of interval-valued data. Existing attribute reduction methods for single-valued data are unsuitable for interval-valued data. So far, there have been few studies on attribute reduction methods for interval-valued data. In this paper, we propose a framework for attribute reduction in interval-valued data from the viewpoint of information theory. Some information theory concepts, including entropy, conditional entropy, and joint entropy, are given in interval-valued information systems. Based on these concepts, we provide an information theory view for attribute reduction in interval-valued information systems. Consequently, attribute reduction algorithms are proposed. Experiments show that the proposed framework is effective for attribute reduction in interval-valued information systems.

A Ranking Method Based on Extended Possibility Degree Dominance Relation

Dominance relation is an important method in incomplete interval-valued information systems. In order to solve the problem that too many attributes maybe result in the ranking failure in the incomplete interval-valued information systems, the concepts of extended possibility degree, extended possibility degree dominance relation and average comprehensive dominance degree are defined. Based on them, a ranking method based on extended possibility degree dominance relation is proposed. Finally, comparing with other ranking methods, this new ranking method based on extended possibility degree dominance relation not only has stronger differentiation degree, but also can make ranking results more objective and reasonable.

A novel approach for ranking in interval-valued information systems

In decision making analysis, ranking decision with anti-noise capability is a very desirable issue. This paper focuses on analysing data in interval-valued information systems. A new approach ranking with weighted standardized cardinality (WSC) and inclusion indicator in interval-valued information systems is proposed. It is a novel generalization of ranking method based on dominance classes. The new approach overcomes the drawback of sensitivity to noise for raking using dominance classes-based method. In this paper, each object with all attribute values is regarded as an interval-valued fuzzy set (IVF-set). By defining WSC with controlling parameters and single interval inclusion indicator, two kinds of inclusion indicators of the IVF-set are constructed. The approach is based on the novel idea of raking with WSC and inclusion indicator rather than dominance classes. Experiments verify that the new approach is noise-resistant.