Three-way decision based on confidence level change in rough set

A three-way decision model on incomplete single-valued neutrosophic information tables

In this paper, we focus on the three-way decision model on incomplete single-valued neutrosophic information tables. Firstly, we define the minimum and maximum similarity measures between single-valued neutrosophic numbers (SVNNs) which may contain unknown values. On this basis, the notion of θ-weak similarity measure is given. Then, we introduce the conception of an incomplete single-valued neutrosophic information table (ISVNIT). For an incomplete single-valued neutrosophic information table, a new similarity relation is proposed based on the θ-weak similarity measure. Some properties are also studied. By using Bayesian decision theory and this similarity relation, we construct a three-way decision model on an ISVNIT. Finally, an example of choosing product service providers is explored to illustrate the rationality and feasibility of the proposed model. We also discuss the influence of parameters in the model on decision results.

Rough set approximations based on a matroidal structure over three sets

Pawlak's classical model of rough set approximations provides an efficient tool for extracting information exactly by employing available knowledge (i.e., known knowledge) in an information system, since many problems in rough set theory are NP-hard and their solution process is therefore greedy and approximate. Many extensions of Pawlak's classical model have been proposed in recent years. Most of them are considered over one or two sets, that is, one- or two-dimensional space or one- or two-dimensional data. Aided by relation-based rough set models, a few of these extensions are considered over three sets. However, the real world is in three-dimensional space. Therefore, it is necessary to solve these problems with other models, such as covering rough set models. For this purpose, we propose the TP-matroid-a matroidal structure over three sets. Employing the family of feasible sets of a TP-matroid as the available knowledge, a pair of rough set approximations-lower and upper approximations-is provided. In addition, for an information system defined over three sets, assisted by formal concept analysis, we establish a pair of rough set approximations. Furthermore, two TP-matroids are established based on the above pair of rough set approximations. The integration between the two pairs of rough set approximations presented here is discussed. The results show that for an information system in three-dimensional space, the rough set approximations provided here can effectively explore unknown knowledge by using available knowledge based on the family of feasible sets of a TP-matroid.

Dynamic Dual-Threshold Virtual Machine Merging Method Based on Three-Way Decision

Cloud computing, an emerging computing paradigm, has been widely considered due to its high scalability and availability. An essential stage of cloud computing is the cloud virtual machine migration technology. Nevertheless, the current trigger timing of virtual machine migration in cloud data centers is inaccurate, resulting in insufficient virtual machine consolidation. Furthermore, the high and low workload fluctuations are also a potential symmetrical problem worthy of attention. This paper proposes a virtual machine energy-saving merging method based on a three-way decision (ESMM-3WD). Firstly, we need to calculate the load fluctuation of the physical machine and divide the load fluctuation into three parts. Furthermore, the corresponding mathematical model predicts the load according to the different classification categories. Then, the predicted load value is used to dynamically adjust the threshold to improve the virtual machine merge probability. Finally, the simulation experiment is carried out on the cloud computing simulation platform cloudsim plus. The experimental results show that the virtual machine energy-saving merging method based on the three-way decision proposed in this paper can better reduce the number of migrations, increase the number of physical machines shut down, better improve the probability of virtual machine merger, and achieve the purpose of reducing the energy consumption of the data center.

Intuitionistic Fuzzy-Based Three-Way Label Enhancement for Multi-Label Classification

Multi-label classification deals with the determination of instance-label associations for unseen instances. Although many margin-based approaches are delicately developed, the uncertainty classifications for those with smaller separation margins remain unsolved. The intuitionistic fuzzy set is an effective tool to characterize the concept of uncertainty, yet it has not been examined for multi-label cases. This paper proposed a novel model called intuitionistic fuzzy three-way label enhancement (IFTWLE) for multi-label classification. The IFTWLE combines label enhancement with an intuitionistic fuzzy set under the framework of three-way decisions. For unseen instances, we generated the pseudo-label for label uncertainty evaluation from a logical label-based model. An intuitionistic fuzzy set-based instance selection principle seamlessly bridges logical label learning and numerical label learning. The principle is hierarchically developed. At the label level, membership and non-membership functions are pair-wisely defined to measure the local uncertainty and generate candidate uncertain instances. After upgrading to the instance level, we select instances from the candidates for label enhancement, whereas they remained unchanged for the remaining. To the best of our knowledge, this is the first attempt to combine logical label learning with numerical label learning into a unified framework for minimizing classification uncertainty. Extensive experiments demonstrate that, with the selectively reconstructed label importance, IFTWLE achieves statistically superior over the state-of-the-art multi-label classification algorithms in terms of classification accuracy. The computational complexity of this algorithm is On2mk, where n, m, and k denote the unseen instances count, label count, and average label-specific feature size, respectively.