In multi-label learning, samples of practical classification task may associated with multiple labels, it is challenging to acquire all labels of the training samples, the rapid expansion of the label space and the significant increase in annotation costs have exacerbated the issue of missing labels in multi-label learning. By utilizing the low rank structure of the label matrix, missing labels can be effectively recovered with matrix factorization technique. Nevertheless, current approaches disregard the potential correlation between the feature space and the multi-dimensional label data. In this paper, key features associated to different labels are extracted and then a non-negative matrix factorization algorithm is proposed for recover missing labels. Firstly, the fuzzy rough set theory is used to analyze the consistency between label matrix and feature space, potential feature information is employed to determine the latent variable dimension in non-negative matrix decomposition and the symbolic label matrix is also converted to a numerical one by means of the lower approximation operator. Then, feature-based manifold regularization and local label correlations are used to model the multi-label completion algorithm. In order to verify the effectiveness in dealing incomplete label data, comparison experiments with varying levels of missing values are designed, the experiments show that compared with the state-of-the-art algorithm, the proposed algorithm is effective in the completion of missing labels. In addition, the sensitivity analysis experiments also show that the proposed method has good stability.

The three-way decision theory provides a three-way philosophical thinking to solve problems, and the regret theory quantifies the risk preferences of decision makers under different psychological behaviors. On the one hand, the combination of these two theories makes models more practical by considering the psychological behaviors of decision makers. On the other hand, we can effectively combine the advantages of the three-way decision theory with the regret theory to highlight the interpretability of decision-making processes. In this article, we propose a novel approximate estimation method for incomplete utility values via the regret theory and establish a wide sense of a three-way decision model on incomplete multiscale decision information systems. First, the degree of consistency for each scale is measured via using the dependence degree, then the optimal subsystem is selected by evaluating the scale selection cost. Furthermore, the incomplete multiscale evaluation information is transformed into triangular fuzzy numbers via linguistic term sets. Second, in light of fuzzy evaluation values and tradeoff factors, an estimation method for incomplete fuzzy subsystems is constructed, which can be used to calculate the utility difference and regret-rejoicing values for pairwise comparisons. Finally, from the perspective of human cognition, the tripartition and the corresponding decision rules are built by the tolerance degree, and the ranking of objects is calculated by the relative closeness degree. Additionally, multiaspect comparative and experimental analyses are performed by extensive experiments, and the feasibility, validity, and stability of the constructed model are shown by parametric analyses.

In multi-label classification, the expansion of output dimension seriously interferes learning performance, and even fails to build a joint prediction model. In order to restrain the proliferation of multi-label classifier’s hypothesis space, the current works focus on the application of global positive label correlation. However, the “black or white” mechanism ignore other possible forms of label correlation, such as negative or neutral correlation. By introducing the doctrine of the mean, three-way decision (3WD) theory provides a solution for in-depth research on local label correlation, and aims to handle the uncertainty of multi-label learning tasks. In this paper, a novel learning algorithm for multi-label joint classification, namely ML-3WD, is proposed by considering the 3WD label correlation from the perspective of samples. According to the weights of different features on any label, the comprehensive loss of each sample to three action strategies can be measured. Obviously, the 3WD rules for any label variable in multi-label output space is obtained. By aggregating the cutting thresholds between different labels, the division principles of 3WD label correlation are further established. Given any multi-label sample, the local fuzzy membership to co-occurrence or mutual state for label pair is examined based on kernelized fuzzy rough sets. The 3WD local label relevance of each sample is confirmed, that is, positive, negative or neutral. The global application strategy for multi-label classification is utilized to avoid over-fitting induced by local mining strategy. Based on the integral mean of the distribution of 3WD local label relevance in multi-label sample space, two different versions of empirical label relevance are constructed. By constraining the relative position between sub-separation hyperplanes, the 3WD label correlation distribution-based model for multi-label joint classification is designed. The experiment results on fifteen real world multi-label datasets reflect that our algorithm achieves good classification ability and versatility. The impact of core parameters on learning performance is also dissected.

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.

In realistic decision-making environments, human behaviors bring influences to various decision-making procedures, and classic multiattribute decision-making approaches based on utility decisions own some deviations from actual situations. The behavioral decision theory modifies classic decision-making theories to make the new method more applicable. Regret theory, as one of the important components in behavioral decision theories, has been widely used in theories and applications. Based on regret theory, we establish a generalized three-way decision method on incomplete multiscale decision information systems with interval fuzzy numbers. First, we select an incomplete optimal subsystem for the incomplete multiscale information system, and convert the multiscale evaluation information into an interval fuzzy number by using a linguistic term set. Second, based on the probability distribution of evaluation values and tradeoff factors, we propose a target-dependent approximation estimation method for the incomplete interval fuzzy subsystem. Then, the regret–rejoicing preferences between objects are obtained. Finally, a tripartition and ranking method based on a max-bipartition and preference index is established. Moreover, the incompleteness experiments show that the decision-making results of our method can still maintain more than 97% consistency in an incomplete information system with a missing rate of at most 20%. In addition, the parameter analysis shows that the proposed method maintains an accuracy rate of more than 98% and a classification error rate of no more than 0.6%.

Multi-scale information systems (MSISs) contain more comprehensive evaluations with different scales than general single-scale counterparts, thus multi-criteria decision-making (MCDM) problems from MSISs are in line with practical scenarios. However, the loss problem of information encountered in decision-making processes brings certain troubles to MCDM. Due to this limitation, a ranking method based on a preference relation in incomplete multi-scale information systems (IMSISs) is proposed in this article. The core idea of the preference ranking organization method for enrichment evaluation II (PROMETHEE II method) is first introduced into IMSISs and a process on dealing with incomplete information in an IMSIS is developed. Then, a corresponding MCDM method is constructed into IMSISs. Finally, a numerical example with different parameters is employed to verify the usefulness of the constructed method, and a comparative study of the constructed method with other MCDM methods is explored to demonstrate the effectiveness of the newly presented method.

In an uncertain and complex decision-making environment, limited by the scope of human cognition, traditional utility decision-making has a certain deviation to actual decision-making. The revision of behavioral decision-making (BDM) to traditional rational decision-making theory makes the new model more universal. In light of this point, we reveal a new three-way decision (3WD) model by virtue of prospect theory (PT) on multi-scale information systems (MS-ISs) for persuing multi-attribute decision-making (MADM) problems. By utilizing an expected evaluation, our newly designed value function can not only reflect the relative position of the object but also avoid the drawbacks of the reference point being too subjective. Through the value function, we obtain a more reasonable avail function to replace the loss function in the traditional 3WD model. At the same time, the weighting function of the object in different states can be calculated, by synthesizing avail function and the weighting function under different decision attitudes. The comprehensive prospect value and classification conditions of the object are calculated. Then, through data selected from the UCI database, we verify the effectiveness of the constructed method. Comparative and experimental analyses are also used to illustrate the superiority and stability of our designed method.

Three-way decision (3WD) provides a new perspective and methodology for solving multi-attribute decision-making (MADM) problem. In this paper, we introduce 3WD into a multi-scale decision information system (MS-DIS), which provides a new idea for solving MADM issues in MS-DISs. By using fuzzy membership functions, a multi-scale evaluation information table is first converted into a numerical evaluation value table. To calculate loss functions at two states generated by the decision class partition, a distance-based cost measurement is then defined. With reference to fuzzy σ-neighborhood classes, conditional probabilities are further calculated and 3WD rules from MS-DISs can be unravelled. As a result, the ranking about all objects in the data is obtained according to expected losses. Finally, a specific numerical example is used to illustrate the effectiveness of the proposed method comparing with other ones. An experimental analysis is also used to describe the superiority of the proposed method.