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Formal concept analysis is a widely studied mathematical tool for performing data analysis and processing. Three-way decision is a model of decision making based on human cognition, which decomposes the problem to be solved into three elements and then reprocesses them. Hesitant fuzzy sets use some possible values instead of one, which can reflect the hesitation and uncertainty of the decision makers. This paper combines the three elements together for the first time and proposes a hesitant fuzzy three-way concept lattice model, which not only extends the concept lattice model but also provides a new way to deal with imprecise data. Firstly, the hesitant fuzzy three-way concept lattice model is proposed and the related properties are investigated. Further, two methods of constructing the hesitant fuzzy three-way concept lattice are studied, and the related construction algorithms are given. Thirdly, the attribute reduction based on the hesitant fuzzy three-way concept lattice is proposed, and a heuristic reduction algorithm is given. Finally, the effectiveness of the proposed algorithms for constructing the hesitant fuzzy three-way concept lattice is verified through some experiments, and the efficiency of the algorithm is compared. [ABSTRACT FROM AUTHOR]

Multi-criteria Decision Making (MCDM) plays a very vital role in many application fields. There are many classical methods to solve the MCDM problems if the available information is crisp. However, the uncertainty and ambiguity inherent in the MCDM often makes these methods unsuitable for solving this kind of problem. Aims at the failures of TOPSIS method that can not rank the alternatives completely in a Hesitant Fuzzy β-Covering Approximation Space (HFβCAS), we develop an improved TOPSIS method. First, we define two pairs of hesitant fuzzy relationship based on hesitant fuzzy β-neighborhood, and construct the corresponding hesitant fuzzy covering rough set models; further we discuss the properties and relationships between the models. Second, we introduce a new comprehensive weight determination method by using the precision degree of hesitant fuzzy covering rough set and the maximizing deviation method. Third, we construct a γ-βCHF-TOPSIS method to MCDM which generalizes the TOPSIS method in an HFβCAS. Finally, two real decision-making problems are used to illustrate the concrete implementation process of γ-βCHF-TOPSIS method, and demonstrate its effectiveness and reasonability. [ABSTRACT FROM AUTHOR]

A rule is an effective representation of knowledge in formal concept analysis (FCA), which can express the relations between concepts. One of the main research directions of FCA is to develop rule-based classification algorithms. Rule-based algorithms in FCA lack effective methods for analyze their generalization capability, which can provide an effective learning guarantee for the algorithm. To solve this problem and effectively improve the classification performance of rule-based algorithms in terms of speed and accuracy, this paper combines formal concept analysis with online learning theory to design an online rule fusion model based on FCA, named ORFM. First, the weak granular decision rule is proposed based on rule confidence. Second, the purpose of each iteration is to reduce the difference between the prediction rules extracted from the ORFM and the weak granular decision rules as much as possible so that the classifier model can be adjusted to the direction of the minimum regret growth rate, and the regret growth rate is 0 under the ideal state at the end of iteration. Third, it is proven that the regret of ORFM has an upper bound; that is, in an ideal state, the regret growth rate decreases rapidly with the increase in the number of iterations, eventually making the regret of the model no longer grow. This provides an effective learning guarantee for ORFM. Finally, experimental results on 16 datasets show that ORFM has better classification performance than other classifier models. [ABSTRACT FROM AUTHOR]

Recommender system plays an increasingly important role in identifying the individual's preference and accordingly makes a personalized recommendation. Matrix factorization is currently the most popular model-based collaborative filtering (CF) method that achieves high recommendation accuracy. However, similarity computation hinders the development of CF-based recommendation systems. Preference obtained only depends on the explicit rating without considering the implicit content feature, which is the root cause of preference bias. In this paper, the content feature of items described by fuzzy sets is integrated into the similarity computation, which helps to improve the accuracy of user preference modeling. The importance of a user is then defined according to preferences, which serves as a baseline standards of the core users selection. Furthermore, core users based matrix factorization model (CU-FHR) is established, then genetic algorithm is used to predict the missing rating on items. Finally, MovieLens is used to test the performance of our proposed method. Experiments show CU-FHR achieves better accuracy in prediction compared with the other recommendation methods. [ABSTRACT FROM AUTHOR]

Logistic regression model is a commonly used data correlation analysis model in statistical analysis methods which has been widely used in economics, medicine, sociology, psychology and other fields. Information fusion method based on granular computing is an important big data analysis method in which clustering ensemble method is an important branch. Clustering ensemble method can granulate a data set into a multi granular structure, integrate multiple clustering results, and obtain a better clustering effect than a single clustering algorithm. However it is only applicable to specific data sets and the clustering results have no practical significance, and therefore it is difficult to construct a consistent fusion function. To solve the above problems, this paper proposes a multi-granularity information fusion method based on logistic regression model and D-S evidence theory, and applies it to multi-attribute group decision-making. Firstly, the data set is granulated into multi granular structure by using logistic regression model, and the output result is the probability that each object belongs to each category at different granularities; Secondly, the output results are used to construct the mass functions of all objects at each granularity, and the Dempster synthesis formula in evidence theory is used to fuse the mass functions at each granularity. Then, a multi-granularity information fusion algorithm (LDIF) based on logistic regression model and D-S evidence theory is proposed, and the complexity and experimental analysis of the algorithm are carried out. Finally, the multi-granularity information fusion method based on logistic regression model and D-S evidence theory is applied to multi-attribute group decision-making. The results show that compared with other methods, this method has the advantages of simple calculation, convenient construction of mass function and high classification accuracy. It is very suitable for multi-attribute group decision-making problems and has excellent performance. [ABSTRACT FROM AUTHOR]

In multi-label classification, multiple label variables in output space are equally important and can be predicted according to a common set of input variables. To improve the accuracy and efficiency of multi-label learner, measuring and utilizing label correlation is the core breakthrough. Extensive research on label correlation focuses on the co-occurrence or mutual exclusion frequency of label values in output space. In this paper, to handle the multi-label learning tasks, a novel method, named FL-MLC, is proposed by considering the influence of feature-label dependencies on inter-label correlations. In order to describe the intrinsic relationship between feature variable and label variable, the discriminant weight of any feature to label is first defined. Therefore, the concept of feature distribution for inputs on label is proposed to reflect the discriminant weights of features to the label. The corresponding calculation process is also designed based on multiple kernel learning and kernel alignment. Furthermore, the feature distributions on different labels are integrated into the feature distribution-based label correlation by using two different aggregation strategies. Obviously, arbitrary label variables with highly similar feature distributions have strong relevance. Thus, the feature distribution-based label correlation is applied to adjust the distance between the parameters for different labels in the predictive learner of FL-MLC method. Finally, the experimental results on twelve real-world datasets demonstrate that our methods achieves good effectiveness and versatility for multi-label classification. [ABSTRACT FROM AUTHOR]

Attribute reduction in formal decision contexts has become one of the key issues in the research and development of formal concept analysis (FCA) and its applications. As far as we know, however, most of the existing reduction methods for formal decision contexts are time-consuming especially for the large-scale data. This paper investigates the attribute reduction method for large-scale formal decision contexts. The computation of a discernibility matrix is an important step in the development of the corresponding reduction method. A simple and powerful method to efficiently calculate the discernibility matrix of formal decision contexts is first presented. In addition, a heuristic algorithm for searching the optimal reduct is then proposed. Thirdly, as an application of the new results, we discuss the problem of finding the minimal subbases of finite topological spaces. It has shown that the method of attribute reduction in formal decision contexts can be used to obtain all the minimal subbases of a finite topological space. Furthermore, we present an algorithm for computing the minimal subbase of a topological space, based on the attribute reduction method proposed in this paper. Finally, two groups of experiments are carried out on some large-scale data sets to verify the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

Granular computing ( GrC ) is one of the key issues in the field of information sciences. Research on the theory and algorithms of granular computing has very important practical significance in huge amounts of information. In multi-granulation rough set theory, two subsets are calculated to approximate the target concept, which are extremely time-consuming for large-scale data. In this paper, to address the issue above, we propose efficient algorithms for updating the lower approximation when a single object is added into or deleted from the target concept in an incomplete information system. Firstly, adjustable multi-granulation rough sets ( AMGRSs ) are introduced in an incomplete information system, and the related properties and theorems are explored. Secondly, it is proved that local- AMGRSs and AMGRSs are equivalent in an incomplete information system. Finally, dynamic algorithms for updating the lower approximation are proposed, and the efficiency of these algorithms is verified by an experiment. [ABSTRACT FROM AUTHOR]

Rough set is a data evaluation methodology to take care of uncertainty in data. Attribute reduction with rough set goals to achieve a compact and informative attribute set for a given data sets, and incremental mechanism is reasonable selection for attribute reduction in dynamic data sets. This paper focuses on introducing incremental mechanism to develop effective incremental algorithm during the arrival of new attributes in terms of approach of discerning samples. The traditional definition of discernibility matrix is improved first to address fewer samples to be discerned. Based on this improvement, discernible relation is developed for every attribute and utilized to characterize attribute reduction. For dynamic data sets with the dynamically increasing of attributes, an incremental mechanism is introduced to judge and ignore unnecessary new arriving attributes. For necessary new arriving attributes, the original reduct is updated in terms of updating of discernible relations instead of information granular or information entropy. The efficiency and effectiveness of developed incremental algorithm based on this mechanism is demonstrated through experimental comparisons in this paper in terms of running time. [ABSTRACT FROM AUTHOR]

The traditional k-means, which unambiguously assigns an object precisely to a single cluster with crisp boundary, does not adequately show the fact that a cluster may not have a well-defined cluster boundary. This paper presents a three-way k-means clustering algorithm based on three-way strategy. In the proposed method, an overlap clustering is used to obtain the supports (unions of the core regions and the fringe regions) of the clusters and perturbation analysis is applied to separate the core regions from the supports. The difference between the support and the core region is regarded as the fringe region of the specific cluster. Therefore, a three-way explanation of the cluster is naturally formed. Davies–Bouldin index (DB), Average Silhouette index (AS) and Accuracy (ACC) are computed by using core region to evaluate the structure of three-way k-means result. The experimental results on UCI data sets and USPS data sets show that such strategy is effective in improving the structure of clustering results. [ABSTRACT FROM AUTHOR]

The multiple granular structures in multigranulation approximation space can be integrated by different approximation operators. These operators are induced by multigranulation rough set or others. In this paper, numerical algorithms of attributes set reduction are developed by using evidence theory or minimal elements of discernibility matrix, respectively. Firstly, a pair of multi-source rough approximation operators and their corresponding multigranulation rough approximation operators are defined based on a bijective and new transitional domain. Then, we propose attributes set reduction with respect to multi-source rough approximation. It is based on the relationship between multi-source rough approximations and evidence theory. Therefore, a heuristic algorithm of attributes set reduction for multi-source lower rough approximation is given. Secondly, we define a multigranulation variable precision rough set (MVRS) by considering weight of each attributes set relative to all of attributes sets. Finally, we investigate attributes set reduction with MVRS by combing the minimal elements of discernibility matrix and distribution discernibility function. There are some illustrative examples to elaborate the operation mechanism of above conclusions. [ABSTRACT FROM AUTHOR]