Sequential Three-way Decisions Research Articles

Intuitionistic Fuzzy Sequential Three-Way Decision Model in Incomplete Information Systems

As an effective method for uncertain knowledge discovery and decision-making, the three-way decisions model has attracted extensive attention from scholars. However, in practice, the existing sequential three-way decision model often faces challenges due to factors such as missing data and unbalanced attribute granularity. To address these issues, we propose an intuitionistic fuzzy sequential three-way decision (IFSTWD) model, which introduces several significant contributions: (1) New intuitionistic fuzzy similarity relations. By integrating possibility theory, our model defines similarity and dissimilarity in incomplete information systems, establishing new intuitionistic fuzzy similarity relations and their cut relations. (2) Granulation method innovation. We propose a density neighborhood-based granulation method to partition decision attributes and introduce a novel criterion for evaluating attribute importance. (3) Enhanced decision process. By incorporating sequential three-way decision theory and developing a multi-level granularity structure, our model replaces the traditional equivalent relation in the decision-theoretic rough sets model, thus advancing the model’s applicability and effectiveness. The practical utility of our model is demonstrated through an example analysis of “Chinese + vocational skills” talent competency and validated through simulation experiments on the UCI dataset, showing superior performance compared to existing methods.

Sequential three-way decision with automatic threshold learning for credit risk prediction

Machine learning algorithms treat credit risk prediction as a binary classification problem. However, two-way decisions with a single threshold force to make either a default or non-default decision may be inappropriate. To reduce the risk of decision errors, this study introduces three-way decisions and proposes a sequential three-way decision model with automatic threshold learning to evaluate credit risk. Initially, the model uses the loan amount and interest to determine the decision loss of the three-way decision, assigning distinct decision thresholds to different samples. Subsequently, the model employs decision cost and information gain to formulate an objective for threshold optimisation. Finally, the model continuously optimises the classification process by using the outcomes of certain decisions as supplementary information. In addition, to validate our model, we conduct comparative experiments with various methods on a real credit dataset from a Chinese bank. The results indicate that the model not only enhances classification performance across several metrics but also assists financial institutions in reducing decision error costs.

Sequential three-way group decision-making for double hierarchy hesitant fuzzy linguistic term set

Group decision-making (GDM) characterized by complexity and uncertainty is an essential part of various life scenarios. Most existing researches lack tools to fuse information quickly and interpret decision results for partially formed decisions. This limitation is particularly noticeable when there is a need to improve the efficiency of GDM. To address this issue, a novel multi-level sequential three-way decision for group decision-making (S3W-GDM) method is constructed from the perspective of granular computing. This method simultaneously considers the vagueness, hesitation, and variation of GDM problems under double hierarchy hesitant fuzzy linguistic term sets (DHHFLTS) environment. First, for fusing information efficiently, a novel multi-level expert information fusion method is proposed, and the concepts of expert decision table and the extraction/aggregation of decision-leveled information based on the multi-level granularity are defined. Second, the neighborhood theory, outranking relation and regret theory (RT) are utilized to redesign the calculations of conditional probability and relative loss function. Then, the granular structure of DHHFLTS based on the sequential three-way decision (S3WD) is defined to improve the decision-making efficiency, and the decision-making strategy and interpretation of each decision-level are proposed. Furthermore, the algorithm of S3W-GDM is given. Finally, an illustrative example of diagnosis is presented, and the comparative and sensitivity analysis with other methods are performed to verify the efficiency and rationality of the proposed method.

A sequential multiple attribute three-way group decision-making method to heterogeneous MAGDM problems with unknown weight information

As a decision model to depict the human cognitive process, three-way decision (3WD) provides a reasonable semantic interpretation for solving practical multi-attribute group decision-making (MAGDM) problems. At the same time, there often exist different types of information due to the subjective and objective criteria in practical decision-making problems, thus it is necessary to develop some efficient frameworks to deal with the MAGDM problems with heterogeneous information. In this paper, based on 3WD theory and sequential strategy, we propose a sequential multiple attribute three-way group decision-making (SMA3WGD) method for the heterogeneous MAGDM problem with unknown weight information to achieve this goal. At first, we compute the weights of decision-makers by using the consensus degree between each of the decision-makers in a group. Then, we calculate the collective evaluation result of multiple decision-makers by utilizing the mathematical planning method with two objectives of minimum difference and high similarity between group evaluation values and individual evaluation values. Meanwhile, a nested sequence of the set of attributes is constructed according to the attribute values offered by decision-makers that have different degrees of consensus on different attributes. On this basis, a multilevel granular structure for the heterogeneous MAGDM problems is constructed, and then the compute of the cost functions and conditional probability is explored in a single level of granular structure, and the thresholds and three-way decision rules of alternatives are further determined depending on the principle of cost minimization. Furthermore, by using a sequential strategy, we obtain a sequential three-way decision result of the heterogeneous MAGDM problems under the multilevel granular structure. At last, the practicality and advantages of the suggested method are demonstrated via a blockchain service provider selection case study, a parameter sensitivity analysis along with a comparison analysis.

A sequential three-way risk sorting model with the cautionary principle under probabilistic linguistic environment

Risk assessment plays a crucial role in managing risks associated with systems, products and services. In practical risk assessment, the cautionary principle is widely adopted by individuals to prevent accidents, and the degree of caution varies with the risk level of potential hazardous activities (PHAs). Therefore, it is necessary to explore a sequential risk assessment model integrating the cautionary principle. To this end, we design an improved risk assessment model based on sequential three-way decision (STWD) model and cautionary principle. Firstly, a risk distance measure under probabilistic linguistic environment is proposed to effectively reflect varying degrees of caution when individuals analyzed PHAs of different risk levels. Then, a comprehensive risk weight optimization model is constructed on the consideration of the importance ranking and correlations of risk attributes. Subsequently, STWD and the as low as reasonably practicable (ALARP) principle are integrated to build the risk sorting model, and both the risk prioritization and classification of PHAs are obtained from the sequential risk sorting process. Finally, we verify the reliability of our proposed model through an example of a floating offshore wind turbine system. The findings validate the crucial role of cautionary principle in risk assessment.

Research on multi-view clustering algorithm based on sequential three-way decision

Multi-view clustering has achieved many applications in recent years. But the existing multi-view clustering methods face two problems, firstly, the traditional multi-view clustering uses a hard clustering method, which cannot describe the uncertainty between the samples and the clusters, and secondly how to perform effective incremental learning on multi-view data when the number of views increases. Therefore to address the above two problems, we firstly propose a three-way fuzzy spectral clustering algorithm based on fuzzy clustering, which can perform three-way clustering on multi-views and get soft clustering results, thus describing the uncertainty between samples and clusters. Then based on the sequential decision making approach, an incremental learning mechanism is designed for multi-view clustering when the number of views increases. Finally, these two works are combined to propose a multi-view clustering algorithm based on sequential three-way decision making. The experimental results demonstrate that the method proposed in this paper has better clustering accuracy and efficiency compared to the traditional multi-view clustering algorithm.

M3W: Multistep Three-Way Clustering.

Three-way clustering has been an active research topic in the field of cluster analysis in recent years. Some efforts are focused on the technique due to its feasibility and rationality. We observe, however, that the existing three-way clustering algorithms struggle to obtain more information and limit the fault tolerance excessively. Moreover, although the one-step three-way allocation based on a pair of fixed, global thresholds is the most straightforward way to generate the three-way cluster representations, the clusters derived from a pair of global thresholds cannot exactly reveal the inherent clustering structure of the dataset, and the threshold values are often difficult to determine beforehand. Inspired by sequential three-way decisions, we propose an algorithm, called multistep three-way clustering (M3W), to address these issues. Specifically, we first use a progressive erosion strategy to construct a multilevel structure of data, so that lower levels (or external layers) can gather more available information from higher levels (or internal layers). Then, we further propose a multistep three-way allocation strategy, which sufficiently considers the neighborhood information of every eroded instance. We use the allocation strategy in combination with the multilevel structure to ensure that more information is gradually obtained to increase the probability of being assigned correctly, capturing adaptively the inherent clustering structure of the dataset. The proposed algorithm is compared with eight competitors using 18 benchmark datasets. Experimental results show that M3W achieves superior performance, verifying its advantages and effectiveness.

A robust one-stage detector for SAR ship detection with sequential three-way decisions and multi-granularity

Synthetic Aperture Radar (SAR) images are widely used in ship detection because of their all-weather and all-day imaging characteristics. However, there are two challenges for SAR ship detection. One is coherent speckle noise, causing ship confusion with similar objects and raising false alarms. The other is multi-scale ship detection, particularly in small ships, which suffers from insufficient accuracy. To address these challenges, this paper proposes a robust one-stage detector, S3MDet, for SAR ship detection with sequential three-way decisions (S3WDs) and multi-granularity. First, to effectively eliminate the interference of coherent speckle noise, a noise classification and denoising module (NCDM) S3WD-based is designed. This module can accurately classify the noise level of the image and only perform denoising on the images identified as noisy, avoiding unnecessary operations on noise-free images. Then, to solve the problem of multi-scale ship detection, a multi-granularity group attention module (MGAM) is designed to obtain a richer representation of multi-granularity features. This module adopts a multi-granularity group convolution structure and channel-wise attention weights to efficiently extract ship features of different scales from SAR images. Extensive experiments on four SAR ship datasets, including SAR-Ship-Dataset, HRSID, SSDD, and LS-SSDD-v1.0, validate the robustness of S3MDet, demonstrating that it achieves state-of-the-art performance.

A Novel Approach for Sequential Three-Way Decision Using Chi-Square Statistic as the Assessment Metric

A Novel Approach for Sequential Three-Way Decision Using Chi-Square Statistic as the Assessment Metric

A novel grey relational clustering model under sequential three-way decision framework

In the context of addressing clustering problems with small samples, grey relational clustering (GRC) plays a crucial role. Currently, a three-way GRC has gained popularity, particularly for its ability to handle the uncertain relationship between objects and classes. However, explicit clustering for some objects may not be achievable when employing the one-step decision, which is often a coarse-grained approach. In such cases, re-clustering these objects with a finer granularity becomes necessary. This is where the sequential three-way decision (STWD) proves to be an effective solution. Therefore, this paper is dedicated to designing a novel GRC under the STWD framework, namely GRC-STWD. Specifically, recognizing that some existing threshold calculations in GRCs can be overly subjective and that a pair-wise global threshold may not efficiently leverage available information for accurate object clustering, we introduce a novel threshold algorithm to address these limitations. Furthermore, we propose a conditional probability calculation method combining TOPSIS and grey relational degrees for clustering data lacking decision attributes or class labels. As the development of GRC within portfolio environments remains relatively nascent, we apply the proposed model to portfolio strategy construction. Finally, comparative and experimental analyses validate the model's effectiveness and feasibility. Notably, the developed model serves as a generalization of GRC, contributing to the broader advancement of GRC and STWD methodologies.

A sequential three-way decision model for classification with multilevel information gain and regret value optimization

The sequential three-way decision (S3WD) model plays a vital role in solving classification problems. This model comprises three fundamental elements, namely, conditional probability, cost function, and decision thresholds. The typical conditional probability estimation methods are bifurcated into two branches: equivalence class-based methods, which coincide with human recognition, and machine learning-based methods that rely on big data for high precision. This study synergizes two branches by introducing a novel algorithm that integrates the K-nearest neighbor method and Bayes rule for estimating conditional probabilities, enhancing both interpretability and precision. Regarding the cost function and decision thresholds, the inherent weak point in existing cost-sensitive S3WD models is the computation of three pairwise adjacent regions with subjectively given cost values and decision thresholds. To overcome the subjective arbitrariness bottleneck, an objective function is established by extending the definitions of information gain and regret value across a multilevel granularity structure. Subsequently, an adapted particle swarm optimization algorithm is utilized to optimize the decision thresholds and tri-partitions. Accordingly, a novel framework of the S3WD model is constructed. Finally, extensive experimental results substantiate the effectiveness and superiority of the proposed model in the realm of classification, as evidenced from both technical and empirical standpoints.

A TOPSIS method based on sequential three-way decision

A TOPSIS method based on sequential three-way decision

Multi-level personalized k-anonymity privacy-preserving model based on sequential three-way decisions

K-anonymity is a widely used privacy-preserving technique which defends against linking attacks by suppression and generalization. The existing k-anonymity algorithms prevent attackers from illegally obtaining private information by constraining at least k records in an equivalence group. However, this unified anonymity method ignores individual differences and leads to a large amount of information loss. To this end, we introduce sequential three-way decisions into k-anonymity, using a dynamic k-value sequence instead of the fixed k-value to achieve personalized k-anonymity. Specifically, we first construct a hierarchical decision table for k-anonymity by attribute generalization trees and sensitive decision values provided with users. Then, we propose a multi-level personalized k-anonymity privacy-preserving model based on sequential three-way decisions, where we anonymize the partitioning granular data with a dynamic k-value sequence, respectively. Furthermore, we present three practical algorithms to implement the proposed model and discuss the differences between them. Finally, the experimental results demonstrate that the proposed model not only provides a more flexible anonymization method to achieve personalized anonymity, but greatly reduces the information loss. This study provides a complete framework for multi-level privacy protection and enriches the application of sequential three-way decisions.

Research on multi-granularity sequential three-way decisions based on the fuzzy T-equivalence relation

The fuzzy decision-theoretic rough set (FDTRS) is a data processing method based on the fuzzy theory designed to handle decision problems with uncertainty and fuzziness. It simplifies the complexity of decision-making and provides decision strategies by integrating multiple sources of information. This approach makes the decision process more scientific and rational. The mainstream FDTRS model breaks the over restrictive limits of classical decision-theoretic rough sets, computes the fuzzy similarity relation between two objects utilizing the Gaussian kernel function, which is another major breakthrough and innovation in the field of decision-theoretic rough sets. However, this model suffers from the problems of insufficient decision information, single perspective and high decision-making cost when dealing with dynamic, complex and uncertain problems. Emerging in recent years, sequential three-way decisions not only provides a flexible mechanism to implement the idea of progressive computation, but also deals with dynamic, complex and uncertain problems. To this end, this paper proposes a sequential three-way decision model based on the fuzzy T-equivalence relation (FTE-based sequential three-way decision model) from the perspective of sequential three-way decisions, and gives relevant definitions and examples to effectively solve the problem of insufficient information. Then in order to solve the single-view problem, we extend the sequential three-way decisions to the case of multi-granularity, and propose FTE-based multi-granularity sequential three-way decisions in four aggregation strategies with the corresponding properties and algorithms. In addition, the rationality of models are tentatively analyzed through specific examples. Finally, six sets of UCI standard datasets are used to validate the proposed models, which demonstrate their good performance. These models contribute to the field of fuzzy decision-theoretic rough sets and sequential three-way decisions.

A sequential three-way classification model based on risk preference and decision correction

The sequential three-way decision (S3WD) model, which merges three-way decisions and granular computing, is increasingly crucial in classification. The risk attitude to the decision process and result costs affects the decisive actions in the S3WD model. Furthermore, decision conflict arises when there is a discrepancy between coarse-grained and fine-grained definite decision-making for the same object, which can potentially impact decision accuracy. However, current studies show incomplete risk preference research and a lack of decision correction strategies to address decision conflict. To address the limitation, four sequential three-way classifiers (S3WCs) are proposed. First, three prominent distance functions are employed to compute similarity classes for condition probability estimation. Second, optimistic, pessimistic, and weighted compromise sequential three-way classifiers are established to reflect the risk preference for the two types of costs. Third, four precision differences in the S3WCs are defined from local and global perspectives. An S3WC with decision correction is presented to improve precision by judging precision differences in adjacent granularity levels and the entire granular structure. Finally, a series of experiments are conducted to thoroughly analyze the characteristics and applications of these S3WCs. The superior classification performance of the proposed models on diverse datasets is demonstrated.

A multi-objective sequential three-way decision approach for real-time malware detection

A multi-objective sequential three-way decision approach for real-time malware detection

IoT-based generalized multi-granulation sequential three-way decisions

In the context of the Internet of Things (IoT), decision models and GRC (Governance, Risk, and Compliance) can be used for data processing and decision-making processes. The IoT involves a large number of sensors and devices, some of which enable “device-free” functionality, meaning that specific devices or sensors are not required to obtain the necessary information. This technology utilizes the signals present in the environment to determine the location of individuals without them carrying any specific devices. By incorporating “device-free” sensor data into decision models, we can process IoT data more efficiently and achieve accurate location positioning. The prevailing hierarchical sequential three-way decision models (STDM) follow a common pattern of constructing a hierarchical tree of conditional attributes to acquire knowledge. However, these models fail to meet the diverse needs of users when it comes to rule mining complex hierarchical data with multiple levels and views in real-world applications. Additionally, the pursuit of simplified rules remains a significant topic of interest. To address these challenges, we propose a novel approach that integrates multi-granularity, device-free localization, and STDM. By leveraging IoT and device-free localization, we collect data from various devices and sensors to accurately determine the positions of individuals. Using this data, we construct a generalized hierarchical decision table by creating a concept hierarchical tree with decision attributes. This framework offers a comprehensive solution for overcoming the challenges of device-free localization and IoT. Subsequently, we establish a granular structure by partitioning the complete set of attributes. In this paper, our proposed approach improves the efficiency and accuracy of data processing in machine learning models and enables users to better process and understand complex datasets. Finally, the performance is experimentally validated for the models in this paper. Such models greatly enrich the theoretical framework of three-way decision making. Overall, the abstract provides a concise and succinct overview, outlining the motivation behind the research and presenting the contributions made.

Regret theory-based multivariate fusion prediction system and its application to interest rate estimation in multi-scale information systems

Estimating interest rates is a typical multivariate prediction problem that has garnered considerable attention in the finance industry. However, the rising complexity of the prediction environment has presented significant obstacles to the methodology and application of traditional single-scale rational prediction models. Considering this challenge, the paper presents a new multivariate fusion prediction system that aims to tackle the following issues: (1) How to mine prediction information from multi-scale information systems (MSISs)? (2) How to describe the irrational behavior of decision-makers (DMs) in prediction processes? (3) How to improve the prediction performance and generalization capability of the models? Specifically, the score function of each feature under MSISs is primarily established by applying scale rules, regret theory (RT), and dominance relations to thoroughly explore prediction information across varying scales. Second, an adaptive S3WD model is developed for feature selection, which leverages the feature score distribution and the sequential three-way decision (S3WD) concept to avoid the problem of dimensional disasters, thereby improving the accuracy of selected features and reducing the learning cost. Furthermore, to enhance the effectiveness and rationality of the kernel extreme learning machine (KELM), an improved version known as IKELM is developed, which combines the regret-based comprehensive score of each sample. Finally, a multivariate fusion prediction system is constructed and abbreviated as an S3WD-IKELM-PSO system, where the particle swarm optimization (PSO) algorithm is employed to determine optimal parameters. It is worth noting that actual interest rate estimation datasets are utilized to verify the feasibility and validity of the proposed prediction system. According to the experimental results, the S3WD-IKELM-PSO system exhibits superior prediction performance and generalization ability compared to existing machine learning models.

Real-Time Monitoring and Control of the Breakthrough Stage in Ultrafast Laser Drilling Based on Sequential Three-Way Decision

Real-time monitoring and control of breakthrough stage are essential issues in ultrafast laser drilling (ULD) process. This paper proposed a novel intelligent methodology to address the decision bias problem in monitoring and control of breakthrough stage. Eight time-domain statistical features were extracted after analyzing the correlation between the optical emission signal and the drilling process and data processing. To build the identification model of breakthrough stage, support vector machine (SVM) method was adopted and the identification accuracy can up to 98.42%. Even so, there is a large deviation between the prediction breakthrough time by the identification model and the actual breakthrough time, which can up to 3.81s. Considering the decision bias, the comprehensive Gaussian weight sequential three-way decision (CGW-S3WD) method was proposed for the first time. Compared to the actual breakthrough time, the mean decision time is only delayed by 0.375s based on the combination of the identification model and CGW-S3WD method under simulated conditions. Finally, the method was applied to monitoring and control of breakthrough stage in the actual ULD process. Experimental results demonstrate that the control delay time is only 0.354s and the high-quality holes and protection of the back wall can be achieved simultaneously. The research confirms that the method can reduce the decision bias and provides a new perspective for accurate monitoring of complex industrial scenarios.

STWD-SFNN: Sequential three-way decisions with a single hidden layer feedforward neural network

The three-way decisions strategy has been employed to construct network topology in a single hidden layer feedforward neural network (SFNN). However, this model has a general performance, and does not consider the process costs, since it has fixed threshold parameters. Inspired by the sequential three-way decisions (STWD), this paper proposes STWD with an SFNN (STWD-SFNN) to enhance the performance of networks on structured datasets. STWD-SFNN adopts multi-granularity levels to dynamically learn the number of hidden layer nodes from coarse to fine, and set the sequential threshold parameters. Specifically, at the coarse granular level, STWD-SFNN handles easy-to-classify instances by applying strict threshold conditions, and with the increasing number of hidden layer nodes at the fine granular level, STWD-SFNN focuses more on disposing of the difficult-to-classify instances by applying loose threshold conditions, thereby realizing the classification of instances. Moreover, STWD-SFNN considers and reports the process cost produced from each granular level. The experimental results verify that STWD-SFNN has a more compact network on structured datasets than other SFNN models, and has better generalization performance than the competitive models. All models and datasets can be downloaded from https://github.com/wuc567/Machine-learning/tree/main/STWD-SFNN.