Sequential Three-way Decision Model Research Articles

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.

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.

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.

Generalized multigranulation sequential three-way decision models for hierarchical classification

Hierarchical classification is an important research hotspot in machine learning due to the widespread existence of data with hierarchical class structures. The existing sequential three-way decision models mainly constructed the hierarchical condition information granules via concept hierarchy tree to discuss the three probabilistic regions for flat classification. However, in real-world applications, one may face not only the tree-structured data with hierarchical condition attributes but also more often the multi-level data with hierarchical decision attribute (hierarchical class labels). How to obtain acceptable decisions under different levels of granularity is the most important issue within the multi-level and multi-view data. To this end, we construct a generalized hierarchical decision table and propose a generalized hierarchical multigranulation sequential three-way decision model by combining multi-granularity and sequential three-way decisions. Specifically, we first design a generalized hierarchical decision table using concept hierarchy trees of all conditional attributes and decision attribute, and explore some basic properties. Then we decompose and aggregate condition and decision granules under different levels of granularity, propose the optimistic and pessimistic generalized hierarchical multigranulation three-way decision models to update the three probabilistic regions for flat and hierarchical classification, and discuss the relationships between these two models. Finally, the experimental results demonstrate that the proposed models are more suitable for different applications. These models will provide a novel insight and enrich the development of multigranulation three-way decisions from the perspective of multi-level and multi-view.

Optimal Scale Combination Selection Integrating Three-Way Decision With Hasse Diagram.

Multi-scale decision system (MDS) is an effective tool to describe hierarchical data in machine learning. Optimal scale combination (OSC) selection and attribute reduction are two key issues related to knowledge discovery in MDSs. However, searching for all OSCs may result in a combinatorial explosion, and the existing approaches typically incur excessive time consumption. In this study, searching for all OSCs is considered as an optimization problem with the scale space as the search space. Accordingly, a sequential three-way decision model of the scale space is established to reduce the search space by integrating three-way decision with the Hasse diagram. First, a novel scale combination is proposed to perform scale selection and attribute reduction simultaneously, and then an extended stepwise optimal scale selection (ESOSS) method is introduced to quickly search for a single local OSC on a subset of the scale space. Second, based on the obtained local OSCs, a sequential three-way decision model of the scale space is established to divide the search space into three pair-wise disjoint regions, namely the positive, negative, and boundary regions. The boundary region is regarded as a new search space, and it can be proved that a local OSC on the boundary region is also a global OSC. Therefore, all OSCs of a given MDS can be obtained by searching for the local OSCs on the boundary regions in a step-by-step manner. Finally, according to the properties of the Hasse diagram, a formula for calculating the maximal elements of a given boundary region is provided to alleviate space complexity. Accordingly, an efficient OSC selection algorithm is proposed to improve the efficiency of searching for all OSCs by reducing the search space. The experimental results demonstrate that the proposed method can significantly reduce computational time.

Cost-sensitive sequential three-way decision for information system with fuzzy decision

Sequential three-way decision (S3WD) regarded as a dynamic multi-stage decision-making model, includes three critical components: evaluation function, threshold pair, and granularity structure. In this model, the construction of granularity structure, as the basis for decision execution, is closely related to the order in which the attributes are joined, while different features may require different costs in many real-world applications. Besides, the fuzziness of label space is widespread in information systems, however, the S3WD problem of information system with fuzzy decision has received little attention. Therefore, a cost-sensitive sequential three-way decision model for the information system with fuzzy decision is proposed in this paper. Firstly, a novel granulation method is proposed based on the density neighborhood for information system with fuzzy decision, which can obtain hidden connections of different objects. On this basis, a new evaluation criterion of attribute significance is presented by considering attribute dependence and test cost simultaneously. With three different test cost distributions, a cost-sensitive sequential three-way decision model is proposed by optimizing the information granularity. Finally, experimental results indicate that the performance of this model is affected by the granulation parameter. Compared with other S3WDs, the proposed model can achieve better classification performance with lower test costs.

A Novel Sequential Three-Way Decision Model for Medical Diagnosis

In the sequential three-way decision model (S3WD), conditional probability and decision threshold pair are two key elements affecting the classification results. The classical model calculates the conditional probability based on the strict equivalence relationship, which limits its application in reality. In addition, little research has studied the relationship between the threshold change and its cause at different granularity levels. To deal with these deficiencies, we propose a novel sequential three-way decision model and apply it to medical diagnosis. Firstly, we propose two methods of calculating conditional probability based on similarity relation, which satisfies the property of symmetry. Then, we construct an S3WD model for a medical information system and use three different kinds of cost functions as the basis for modifying the threshold pair at each level. Subsequently, the rule of the decision threshold pair change is explored. Furthermore, two algorithms used for implementing the proposed S3WD model are introduced. Finally, extensive experiments are carried out to validate the feasibility and effectiveness of the proposed model, and the results show that the model can achieve better classification performance.

Sequential optimization three-way decision model with information gain for credit default risk evaluation

To categorize credit applications into defaulters or non-defaulters, most credit evaluation models have employed binary classification methods based on default probabilities. However, while some loan applications can be directly accepted or rejected, there are others on which immediate accurate credit status decisions cannot be made using existing information. To resolve these issues, this study developed an optimized sequential three-way decision model. First, an information gain objective function was built for the three-way decision, after which a genetic algorithm (GA) was applied to determine the optimal decision thresholds. Then, appropriate accept or reject decisions for some applicants were made using basic credit information, with the remaining applicants, whose credit status was difficult to determine, being divided into a boundary region (BND). Supplementary information was then added to reevaluate the credit applicants in the BND, and a sequential optimization process was employed to ensure more accurate predictions. Therefore, the model’s predictive abilities were improved and the information acquisition costs controlled. The empirical results demonstrated that the proposed model was able to outperform other benchmarking credit models based on performance indicators.

Hierarchical sequential three-way decision model

Knowledge acquisition is one of the important issues in granular computing. In recent years, scholars have paid much attention to this problem and proposed the rule-based acquisition algorithms. However, a large number of the decision rules mined by the existing algorithms are not comprehensible. At the same time, the long detailed rules are easy to lead to over-fitting. In order to generate simpler and easier-to-comprehensible rules and improve human decision-making, a hierarchical sequential three-way decision model is proposed by combining sequential three-way decisions with hierarchical rough set model. Specifically, we generalize the concepts of the conditional attributes through the concept hierarchy tree, design the multi-hierarchical decision table with multiple levels of granularity, and illustrate the corresponding algorithm to acquire the generalized rules step by step. The experimental results demonstrate that the proposed model can mine hierarchical sequential three-way decision rules under different levels of granularity.

Data-driven sequential three-way decisions for unlabeled information system

Based on the granular computing and three-way decisions theory, the sequential three-way decisions (S3WD) model implements the idea of progressive computing. However, almost S3WD models are established based on labeled information system, and there is still a lack of S3WD model for processing unlabeled information system (UIS). In this paper, to solve the issue of given accepted number for UIS, a data-driven sequential three-way decisions (DDS3WD) model is proposed. Firstly, from the perspective of similarity computed by TOPSIS, a general three-way decisions model for UIS based on decision risk is presented and its shortcomings are analyzed. Then, a concept of optimal density difference is defined to establish the DDS3WD model for UIS by updating attributes. Finally, the related experiments show that DDS3WD is feasible and effective for dealing with UIS under the condition of given accepted number of objects.

A sequential three-way decision model based on hesitant fuzzy sets

As a new extended model of fuzzy sets, hesitant fuzzy set theory is a useful tool to process uncertain information in decision making problems. The traditional hesitant fuzzy multi-attribute decision making (MADM) can only choose an optimal strategy, which is not suitable for all of the complex scenarios. Typically, in practical application, decision making problems may be more complicated involving three options of acceptance, non-commitment and rejection decisions. Three-way decisions, which divide universe into three disjoint regions by a pair of thresholds, are more efficient to deal with these problems. Therefore, how to utilize three-way decision theory to process hesitant fuzzy information is an essential issue to be studied. In this paper, from the perspective of hesitant fuzzy distance, a hesitant fuzzy three-way decision model is proposed. First, because hesitant fuzzy element (HFE) is a set of several possible membership degrees, it cannot be compared with thresholds directly. Hence, this paper converts it into the comparison between the distance and the thresholds. Then, to calculate thresholds more reasonably, shadowed set theory is introduced to avoid the subjectivity of threshold acquisition. Furthermore, sequential strategy is adopted to solve the multi-attribute decision making problems. Finally, an example of medical diagnosis and simulation experiments are given to prove the accuracy and efficiency of the proposed hesitant fuzzy three-way decision model.

A novel sequential three-way decision model with autonomous error correction

As an approach to granular computing, the sequential three-way decision (S3WD) model has been widely studied in practical applications. In terms of improving the accuracy of the S3WD model, existing studies have achieved fruitful results. However, the two types of classification errors and two types of uncertain classifications caused by a probabilistic rough set model have received less consideration, which will result in a higher error classification rate (ECR) in the decision process. In this paper, from the perspective of the subdivision of granules, a new sequential three-way decision model with autonomous error correction (S3WD-AEC) is proposed to reduce the ECR. First, two types of errors correction and two types of effective classifications in the S3WD model are defined. Next, according to the process of information granulation, four subdivisions of equivalence classes are discussed in detail. Subsequently, the total ECR composed of the positive and negative regions in each granularity layer is proved to gradually decrease with the subdivision of the equivalence classes. Then, during the S3WD process, four commonly used clustering algorithms are introduced to select a portion of the equivalence classes near the boundary region for further subdivision, implementing an error correction for some misclassified objects. Finally, the experimental results show that the S3WD-AEC model has a smaller ECR compared with the S3WD model.

Optimal scale combination selection for multi-scale decision tables based on three-way decision

Optimal scale combination selection plays a critical role for knowledge discovery in multi-scale decision tables (MDTs) and has attracted considerable attention. However, searching for all optimal scale combinations from the scale collection may result in a combinatorial explosion, and the existing approaches are time-consuming. The main goal of this study is to improve the efficiency of searching for all optimal scale combinations. To this end, a sequential three-way decision model of the scale collection and an extended stepwise optimal scale selection method are proposed to quickly search for all optimal scale combinations. First, a sequential three-way decision model of the scale collection is proposed, and it can be proved that a local optimal scale combination on the boundary region is also a global optimal scale combination on the scale collection. Therefore, all optimal scale combinations of a MDT can be obtained by searching for a single local optimal scale combination on the boundary regions in a step-by-step manner. Second, an extended stepwise optimal scale selection method is introduced to quickly search for a single local optimal scale combination on the boundary region. Moreover, a necessary and sufficient condition under which a MDT has a unique optimal scale combination is given, and two efficient methods for computing the maximal elements of the boundary region are provided. Finally, an efficient optimal scale combination selection algorithm based on sequential three-way decision is presented to search for all optimal scale combinations. Experimental results demonstrate that the proposed algorithms can significantly reduce overall computational time.

BWM and MULTIMOORA-based multigranulation sequential three-way decision model for multi-attribute group decision-making problem

This paper proposes a sequential three-way decision-making approach based on BWM (best-worst method) and MULTIMOORA for multiple levels of granularity to deal with the multi-attribute group decision-making problems under uncertainty. First, using BWM to preprocess the attribute indicators of the decision problem, the relationship between the criteria important for decision problem is determined. Then, according to the importance of the determined level of granularity, from rough to clear, three-way decisions are made in sequence at each level. In this way, we obtain a lattice based three-way decision-making process. Also, in the process at each granularity, we consider the costs of both the decision process and the decision result. Thus, this paper builds a multigranulation sequential three-way decisions model with cost-sensitive. Next, based on the above-mentioned model, we propose a decision procedure and an algorithm for multi-attribute group decision making. It is worth noting that according to the research goals of the decision problem, MULTIMOORA is used to sort the classified alternatives. And a ranking result of the decision problem is given. Finally, the effectiveness and validity of the proposed model is verified by a multi-attribute group decision problem. The problem is the case of emergency diagnosis and treatment after a highway accident. And put forward reasonable suggestions for further development direction.

Optimal scale selection and attribute reduction in multi-scale decision tables based on three-way decision

Optimal scale selection and attribute reduction are two key issues related to knowledge discovery in multi-scale decision tables (MDTs). The former is mainly used to obtain optimal scale combinations by selecting a suitable scale for each attribute, while the latter attempts to obtain reducts of these optimal scale combinations (i.e., optimal scale reducts). However, a search for all optimal scale reducts of a given MDT may result in a combinatorial explosion and existing approaches typically incur excessive time consumption. In this paper, a novel scale combination is defined to perform optimal scale selection and attribute reduction synchronously. Accordingly, an effective approach integrating sequential three-way decision with simplified MDTs is proposed to search for all optimal scale reducts. The efficiency of searching can be significantly improved by reducing the number of consistency checks required for single-scale decision tables and accelerating each check. First, a sequential three-way decision model of the scale space is proposed to search for all optimal scale reducts. Based on the trisecting-and-acting concept and a multi-step strategy, a large number of non-optimal scale reducts can be progressively transferred from the boundary regions to the negative regions. Second, an extended stepwise optimal scale selection method is introduced to quickly search for a single optimal scale reduct in the boundary region. Finally, a simplified MDT is proposed to accelerate the consistency checks for single-scale decision tables. Accordingly, an optimal scale selection algorithm integrating sequential three-way decision with simplified MDTs is proposed to improve the efficiency of searching for all optimal scale reducts. Experimental results demonstrate that the proposed algorithm can significantly reduce overall computational time.

A novel sequential three-way decisions model based on penalty function

In the sequential three-way decisions (S3WD) model, classification accuracy is an important issue. Based on the idea of minimum misclassification, loss functions have been used to calculate the thresholds. A lot of achievements have been achieved in the related research by using the idea of minimum misclassification. However, few researchers have focused on minimizing the misclassification by improving the classification precision in different granularity layers. In this paper, from the classification precision difference between two adjacent granularity layers, a new sequential three-way decisions model based on penalty function (S3WDPF) is proposed to improve the classification accuracy by modifying cost parameters. First, two types of negative benefit classification in the S3WD model are defined. Next, based on the idea of optimization, the penalty function is devised to optimize the cost parameters. Then, from the viewpoint of Bayesian minimum risk decision, a decision rule of mutually exclusive decision thresholds is designed, and the rules of three-way decisions are deduced. Further, the change rules of decision thresholds after modifying cost parameters are discussed in detail. Finally, the experimental results show that the performance of the S3WDPF model has improved classification accuracy compared with the current existing models.

Granularity-driven sequential three-way decisions: A cost-sensitive approach to classification

Sequential three-way decision (S3WD) is a multi-stage decision-making progress that emulates human cognition. S3WD employs coarse-to-fine information granularity and uses various types of costs to determine thresholds to make appropriate decisions. To date, however, few existing models discuss the construction of granules or consider costs in the decision process. This paper describes efforts to develop a granularity-driven sequential three-way decision model to address these two issues, and handle dual-constraint satisfaction problems considering both decision process and decision result costs. A key feature of the model is the incorporation of information granularity into the decision-making process. The model also incorporates a cost structure that accounts for the costs of both the decision process and the decision result. Using this model, we design two algorithms to minimize the cost of the decision process or the cost of the decision result. Our experimental results validate the effectiveness of the algorithms and the viability of the new model.

Sequential three-way decision based on multi-granular autoencoder features

Autoencoder network is an efficient representation learning method. In general, a finer feature set obtained from autoencoder leads to a lower error rate and lower total misclassification cost. However, the network is usually trained for a long time to obtain a finer feature set, leading to a high time cost and total cost. To address this issue, a Sequential Three-Way Decision (S3WD) model is developed to balance the misclassification cost and the time cost in autoencoder based classifications and decisions. To implement the tradeoff strategy, it is necessary to extract a multi-granular feature set. In the network, the associated discriminative information in the extracted features increases with training epochs, which constructs a multi-granular feature structure. An autoencoder-based multi-granular feature description definition is presented. Based on the definition, an autoencoder composed of restricted Boltzmann machines is adopted to extract the multi-granular features. Then, a new cost-sensitive S3WD model is proposed, which aims to find the optimal granule level with the lowest total cost. Finally, the experiments demonstrate the effectiveness of the proposed approaches.

Multigranulation sequential three-way decisions based on multiple thresholds

Three-way decisions have become a representative of trisecting-and-acting model for uncertainty data analysis. With granular computing point of view, a more reasonable decision-making model should process data from multiview and multilevel. Classical sequential three-way decisions are based on a granular structure with a single threshold under multiple levels of granularity, which make the traditional models incapable of adapting to the case of multiview granular structures with multiple thresholds. To overcome this disadvantage, we propose a generalized multigranulation sequential three-way decision model based on multiple different thresholds. By controlling the number of multiview granular structures satisfying the corresponding two tolerance thresholds, we further adopt the optimistic, pessimistic, variable, weighted and weighted arithmetic mean aggregation strategies to construct five kinds of multigranulation sequential three-way decision models from the quantitative point of view. The corresponding relationships and the uncertainty measures of these multigranulation sequential three-way decisions are discussed. Finally, the experimental results demonstrate that different multigranulation sequential three-way decisions can solve the problem under multiple granular structures and have more flexible fault tolerance under different levels of granularity. This study will enrich and prompt the development of the multigranulation three-way decisions.