Three-way Decisions Research Articles

Fuzzy-Granular Concept-Cognitive Learning via Three-Way Decision: Performance Evaluation on Dynamic Knowledge Discovery

Fuzzy-Granular Concept-Cognitive Learning via Three-Way Decision: Performance Evaluation on Dynamic Knowledge Discovery

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 New Multi-Target Three-Way Threat Assessment Method with Heterogeneous Information and Attribute Relevance

Target threat assessment provides support for combat decision making. The multi-target threat assessment method based on a three-way decision can obtain threat classification while receiving threat ranking, thus avoiding the limitation of traditional two-way decisions. However, the heterogeneous situation information, attribute relevance, and adaptive information processing needs in complex battlefield environment bring challenges to existing methods. Therefore, this paper proposes a new multi-target three-way threat assessment method with heterogeneous information and attribute relevance. Firstly, dynamic assessment information is represented by heterogeneous information, and attribute weights are calculated by heterogeneous Criteria Importance Through Intercriteria Correlation (CRITIC). Then, the conditional probability is calculated by the heterogeneous weighted Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), and the adaptive risk avoidance coefficients are constructed by calculating the uncertainty of the assessment value, and then the relative loss function matrices are constructed. Finally, the comprehensive loss function matrices are obtained by the weighted Heronian mean (HM) operator, and the comprehensive thresholds are calculated to obtain the three-way rules. The case study shows that compared with the existing methods, the proposed method can effectively handle the heterogeneous information and attribute relevance, and obtain the risk avoidance coefficients without presetting or field subjective settings, which is more suitable for the complex mission environment.

Three-phase multi-criteria ranking considering three-way decision framework and criterion fuzzy concept

The criterion fuzzy concept refers to a fuzzy set that represents the decision-maker's subjective preference for each criterion within the universe of criteria. Addressing the challenge of ranking all alternatives based on a given criterion fuzzy concept is a novel research direction in the field of fuzzy multi-criteria ranking issues. This paper proposes a three-phase approach for multi-criteria ranking in fuzzy environments, which combines the criterion fuzzy concept and three-way decision thinking. The proposed approach not only analyzes the decision-making characteristics of all alternatives but also facilitates their ranking. During the first phase, a qualitative classification method based on the criterion fuzzy concept and ideal solutions is defined, which divides all alternatives into three independent decision sub-regions. During the second phase, by analyzing the priority relationships among the alternatives within every sub-region, three local ranking rules for alternatives are proposed to determine the ranking of alternatives in each classification region. During the third phase, the semantic relations among three classification regions are considered to give an overall ranking of all alternatives. Finally, combined with two existing quantitative ranking indicators, multiple data sets are employed to verify the feasibility and superiority of the proposed three-phase multi-criteria ranking approach.

Three-teaching: A three-way decision framework to handle noisy labels

Learning with noisy labels represents a prevalent weakly supervised learning paradigm. Uncertain knowledge resulting from noisy labels poses significant challenges for knowledge analysis. Given the memorization effect observed in deep neural networks, training on instances with minimal loss holds promise for effectively handling noisy labels. “Co-teaching”, which is the state-of-the-art training method in this field, is characterized by the simultaneous training of two deep neural networks using instances with low loss. While this approach has demonstrated promising performance, its effectiveness heavily relies on the predictive capabilities of two neural networks. If these networks fail to provide reliable predictions, the overall learning performance may be unsatisfactory. In order to solve this problem and inspired by three-way decision, we propose a powerful learning paradigm named “Three-teaching”, which employs the “voting mechanism” to guarantee the prediction quality incrementally. In this approach, both neural networks make predictions for all the data. However, only the data that exhibits consistent prediction results and has a low loss is retained to feed into the third neural network for updating its parameters. The learning process will proceed by alternating these three neural networks’ roles. The experimental results obtained from benchmark datasets illustrate that “Three-teaching” surpasses numerous state-of-the-art methods.

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.

MTTEGDM: A Moving Target Evolutionary Game Defense Model Based on Three-Way Decisions

Aiming at the fact that the moving target defense game model fails to accurately portray attack and defense gains, resulting in bias in attack and defense games and the inability to select effective defense strategies, we construct the moving target three-way evolutionary game defense model (MTTEGDM). Firstly, the model is defined and analyzed theoretically under the premise of uncertainty and irrationality. Then, combined with the three-way decisions, the attack intention is introduced into the target network loss calculation, and a dynamic weight adjustment algorithm based on the three-way decisions is proposed to accurately characterize the attack and defense gains from a multi-attribute perspective. Finally, the evolutionary game model is used to analyze the evolution trend of the multi-stage defense strategy, so as to carry out feasible and effective defense behavior. The simulation results show that the model can accurately predict the optimal defense strategy of moving targets in different stages. Through a Monte Carlo simulation experiment, the proposed algorithm is compared with the traditional evolutionary game model, and the effectiveness and security of the proposed algorithm are verified.

Optimized third-generation prospect theory-based three-way decision approach for conflict analysis in multi-scale Z-number information systems

There has been limited research on considering decision-makers psychological factors and risk attitudes in the early three-way decision theory and methods. Behavioral three-way decision models can better describe and analyze decision-makers risk preferences and behaviors, with prospect theory being prominent. This paper introduces a third-generation prospect theory-based three-way decision model. It characterizes uncertain reference points for decision-maker preferences through positive/negative ideal points and medians. Due to nonlinear weighting functions in prospect theory, closed-form solutions for three-way decision thresholds are absent. The paper introduces α-model and β-model optimizations for numerical threshold solutions, simplifying three-way decision rules. Additionally, the proposed optimized three-way decision model is applied to conflict analysis, considering multi-scale and Z-number information's impact on conflict evaluation. Effective methods for deriving three-way conflict analysis rules and outcomes from multi-scale Z-number information systems are studied. Audit team conflict analysis examples validate the validity and feasibility of the proposed models and methods. Finally, several experimental results with data sets confirm overall performance.

Three-way decisions in generalized intuitionistic fuzzy environments: survey and challenges

Enhancing decision-making under risks is crucial in various fields, and three-way decision (3WD) methods have been extensively utilized and proven to be effective in numerous scenarios. However, traditional methods may not be sufficient when addressing intricate decision-making scenarios characterized by uncertain and ambiguous information. In response to this challenge, the generalized intuitionistic fuzzy set (IFS) theory extends the conventional fuzzy set theory by introducing two pivotal concepts, i.e., membership degrees and non-membership degrees. These concepts offer a more comprehensive means of portraying the relationship between elements and fuzzy concepts, thereby boosting the ability to model complex problems. The generalized IFS theory brings about heightened flexibility and precision in problem-solving, allowing for a more thorough and accurate description of intricate phenomena. Consequently, the generalized IFS theory emerges as a more refined tool for articulating fuzzy phenomena. The paper offers a thorough review of the research advancements made in 3WD methods within the context of generalized intuitionistic fuzzy (IF) environments. First, the paper summarizes fundamental aspects of 3WD methods and the IFS theory. Second, the paper discusses the latest development trends, including the application of these methods in new fields and the development of new hybrid methods. Furthermore, the paper analyzes the strengths and weaknesses of research methods employed in recent years. While these methods have yielded impressive outcomes in decision-making, there are still some limitations and challenges that need to be addressed. Finally, the paper proposes key challenges and future research directions. Overall, the paper offers a comprehensive and insightful review of the latest research progress on 3WD methods in generalized IF environments, which can provide guidance for scholars and engineers in the intelligent decision-making field with situations characterized by various uncertainties.

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.

Crowdfunding project evaluation based on Fermatean fuzzy SAHARA three-way decision method

Crowdfunding project evaluation based on Fermatean fuzzy SAHARA three-way decision method

Three-way decisions based multi-attribute decision-making with utility and loss functions

The traditional multi-attribute decision-making (MADM) methods are based on two-way decisions (2WD), i.e., acceptance and rejection. In contrast, three-way decisions (3WD) add a deferred decision to effectively handle MADM problems by reducing decision risks. In the past 3WD models have been broadly explored considering losses and utilities associated with the decisions, but none of the studies considered loss and utility together. Also, the existing studies lack the influence of decision-makers on outcomes. Accordingly, this paper presents a novel 3WD model based on a similarity measure, integrating the hybrid information of MADM matrix, utility and loss values along with the influence of decision-makers. First, the two states are formed by the fuzzy c-mean clustering algorithm. Second, the similarity class for each alternative is constructed based on the Jaccard index. With reference to the equivalence classes formed, conditional probabilities are further calculated and 3WD decision rules are studied. Finally, considering both expected utility and losses associated with the alternatives we propose a novel 3WD model for solving MADM problems. The effectiveness of the proposed approach is demonstrated with the help of an illustrative example. The proposed 3WD-MADM model is further verified from different perceptions through comparative and experimental analysis.

Conflict Analysis Triggered by Three-Way Decision and Pythagorean Fuzzy Rough Set

Conflict is ubiquitous in human society and has a profound impact on various fields such as the economy, politics, law, and military. Many scholars have focused on exploring the internal mechanisms and potential solutions to conflicts. Notably, describing agents’ attitudes is an effective way to construct a conflict model. However, in decision-making, agents’ attitudes on issues are often vague and ambiguous. Pythagorean fuzzy set can deal with fuzzy information more accurately than intuitionistic fuzzy set. On the basis of this understanding, we investigate the conflicts from the perspective of Pythagorean fuzzy set. Firstly, we use Pythagorean fuzzy numbers to express the attitudes of agents on issues, and subsequently establish a Pythagorean fuzzy conflict information system. Secondly, we classify agents into three categories by a pair of thresholds to establish a trisected agent set model with risk preference. Thirdly, we construct a three-way conflict analysis model based on multi-granulation Pythagorean fuzzy decision-theoretic rough set and discuss both global and local conflicts by combining conflict analysis with multi-granulation decision-theoretic rough set. Finally, we discuss the relationships and properties of the proposed conflict analysis models.

A preference group consensus method with three-way decisions and regret theory under multi-scale information systems

The foundation of intelligent computing and expert systems relies on the data processing conducted within the realm of multi-scale information systems (MSISs). Data processing within MSISs caters to diverse analytical needs, where the preference hierarchy among various factors plays a vital role in the consensus reaching process (CRP). Additionally, the three-way decisions (TWD) theory serves as an efficient tool, while regret theory (RT) quantifies decision-makers' risk inclinations associated with various psychological behaviors. Thus, the paper aims to introduce an innovative approach known as the CRP-TWD-RT-MSIS method. The study draws inspiration from spatial geometry, incorporating concepts like points, lines, surfaces, and bodies to create MSISs. This process generates a matrix of fuzzy preference relations (FPRs) among distinct decision-makers through data preprocessing. In addition, the paper explores feedback mechanisms based on identification and directional rules, as well as those rooted in minimal adjustments or cost considerations. Simultaneously, it takes negotiation and discussion time into account, culminating in the development of a personalized adjustment optimization model that focuses on minimizing time costs. In the end, the method's effectiveness and superiority are validated through a case study and a comparative analysis of real data from the Chinese Weather and Meteorological Bureau's website.

Elasticity unleashed: Fine-grained cloud scaling through distributed three-way decision fusion with multi-head attention

With the proliferation of cloud computing, elastic resource scaling has emerged as a critical challenge. Cloud platforms must efficiently allocate resources to match dynamic workloads. This study addresses the key trade-off between responsiveness and prudence in scaling a novel distributed three-way decision fusion approach. Distributed three-way decisions of immediate, delayed, or no scaling are made at coarse and fine-time granularity levels. Subsequently, a multi-head attention mechanism intelligently fuses these decisions, weighing the relevance of the different granularities to synthesize an integrated scaling strategy. The reactiveness of sudden workload changes are balanced during fusion by considering long-term trends. Comprehensive experiments on real-world data demonstrated that the proposed fusion strategy substantially improves resource efficiency and adherence to service-level agreements compared to existing methods. Multi-head attention imparts autonomy in adapting to diverse operating conditions. The proposed principled methodology and attention-based decision aggregation hold significance for efficient, adaptive, and interpretable cloud scaling mechanisms.

Selection of landslide treatment alternatives based on LSGDM method of TWD and IFS

The disaster caused by landslide is huge. To prevent the spread of the disaster to the maximum extent, it is particularly important to carry out landslide disaster treatment work. The selection of landslide disaster treatment alternative is a large scale group decision-making (LSGDM) problem. Because of the wide application of social media, a large number of experts and the public can participate in decision-making process, which is conducive to improving the efficiency and correctness of decision-making. A IF-TW-LSGDM method based on three-way decision (TWD) and intuitionistic fuzzy set (IFS) is proposed and applied to the selection of landslide treatment alternatives. First of all, considering that experts and the public participate in the evaluation of LSGDM events, respectively, the method of obtaining and handling the public evaluation information is given, and the information fusion approach of the public and experts evaluation information is given. Second, evaluation values represented by fuzzy numbers are converted into intuitionistic fuzzy numbers (IFNs), and the intuitionistic fuzzy evaluation decision matrix described by IFNs is obtained. Then, a new LSGDM method of alternatives classification and ranking based on IFS and TWD is proposed, the calculation steps and algorithm description are given. In this process, we first cluster the experts, then consider the identification and management of non-cooperative behavior of expert groups. This work provides an effective method based on LSGDM for the selection of landslide treatment alternatives. Finally, the sensitivity of parameters is analyzed, and the feasibility and effectiveness of this method are compared and verified.

Weighted continuous triangular fuzzy conflict analysis and its three-way decision method1

In the existing conflict analysis models, they used a triangular fuzzy number on [0, 1] to describe the range of an agent’s attitude towards an issue, but there are still some shortcomings in describing the specific attitude and degree of conflict represented by the triangular fuzzy number. In this paper, the conflict analysis model is extended, improved and perfected. Firstly, the expectation of triangular fuzzy number is used in the [-1, 1] triangular fuzzy information system to reasonably express the specific attitudes represented by a triangular fuzzy number. Secondly, the weights of each issue are obtained by using the Sugeno measure, which determines the total attitude of the agent towards all issues. Thirdly, the relationship between agents is obtained with the help of the weighted distance of triangular fuzzy numbers. Finally, the thresholds α and β are calculated by means of triangular fuzzy decision theory rough sets.

Dynamic three-way multi-criteria decision making with basic uncertain linguistic information: A case study in product ranking

The concept of basic uncertain linguistic information (BULI) is proposed as an extension of basic uncertain information to enhance the measurement of data quality in decision-making processes by allowing for more flexible utilization of degrees of certainty. This paper seeks to investigate a new model of dynamic three-way decisions and develop an integrated framework for BULI-based multi-criteria decision-making using decision-theoretic rough sets (DTRSs). Firstly, we present the BULI-input dynamic ELECTRE-I method, which is capable of establishing an outranking relation. Then, a novel model of BULI decision-theoretic rough sets (BULIDTRSs) is proposed. The BULI similarity measure is employed to accurately estimate the conditional probability. Following this, we propose four potential approaches for combining loss functions by introducing the BULI ordered weighted averaging operator, which incorporates the consideration of decision risk. The derivation of the three-way decision rules is based on the comparison of BULI and the application of operational laws. In addition, the resolution of various issues such as the determination of criteria weights, identification of ideal solutions, and conversion of ratings to BULI is achieved through the development of a multi-criteria keyword frequency statistical method and a user credibility model. Subsequently, the algorithm for the dynamic three-way multi-criteria decision-making method, aimed at resolving product ranking issues, is presented. Eventually, we elaborate on the utilization of the proposed methodology through the illustration of a case study involving the ranking of passenger cars.

Exploring static rebalancing strategies for dockless bicycle sharing systems based on multi-granularity behavioral decision-making

In the continuously evolving context of urbanization, more people flock to cities for job opportunities and an improved quality of life, resulting in undeniable pressure on transportation networks. This leads to severe daily commuting challenges for residents. To mitigate this urban traffic pressure, most cities have adopted urban dockless bicycle sharing systems (UDBSS) as an effective measure. However, making accurate decisions regarding UDBSS demand in different city locations is crucial, as incorrect choices can worsen transportation problems, causing difficulties in finding bicycles or excessive deployments leading to disorderly accumulation. To address this decision-making challenge, it is essential to consider uncertain factors like daily weather, temperature, and workdays. To tackle this effectively, we construct an adjustable multi-granularity (MG) complex intuitionistic fuzzy (CIF) information system using complex intuitionistic fuzzy sets (CIFSs). This system objectively determines classification thresholds using an evaluation-based three-way decision (TWD) method, creating adjustable MG CIF probability rough sets (PRSs). Additionally, to recognize the irrationality of decision-makers (DMs), we propose a method that combines prospect theory (PT) with regret theory (RT), providing a more comprehensive understanding of the influence of DMs' psychological factors on decision outcomes. Building upon these foundations, we present static rebalancing strategies for UDBSS based on MG PRSs and prospect-regret theory (P-RT) within the CIF information system. Finally, using UDBSS data collected from various sensors, we conduct experimental analysis to verify its feasibility and stability. In summary, this approach considers residents’ daily usage preferences, including bicycles utilization and return, with the aim of minimizing unmet resident demands and predicting usage patterns for the next day. It effectively addresses the issue of UDBSS distribution inefficiencies and holds a significant advantage in prediction, making it suitable for broader applications in transportation systems and contributing to the establishment of more advanced modern intelligent transportation systems (MITSs) in the future.

Three-way decision-making methods with multi-intuitionistic β-neighborhood-based multiattribute group decision-making problems

Multiattribute group decision-making (MAGDM) is a decision analysis method used to address decision-making problems that have multiple attributes and multiple decision alternatives. It is generally believed that multigranulation rough sets (MGRSs) are a twofold scheme to solve MAGDM problems. Thus, in this paper, we aim to generalize MGRSs and decision-theoretic rough sets (DTRSs) to intuitionistic fuzzy β-covering (IFβC) information systems and propose a novel MAGDM method to handle decision-making problems, which not only deepens the cognition of the three-way decision (3WD) model but also expands its application in decision-making problems. The paper first introduces a novel conditional probability using the ideal positive degree of intuitionistic fuzzy numbers (IFNs) and then investigates its properties. Second, in the IFβC environment, we utilize the proposed conditional probabilities to construct two types of multigranulation decision-theoretic rough set (MGDTRS) models, an optimistic strategy and a pessimistic strategy, discuss their theoretical properties and explore the relationship between the two strategies. Third, a novel MAGDM method for multi-intuitionistic β-neighborhoods is established in accordance with the proposed MGDTRS model. We also establish an algorithm for the proposed MAGDM method. Fourth, we apply the proposed method to address several MAGDM problems. By conducting comparative analysis with existing methods, we demonstrate the effectiveness of the proposed method and discuss the advantages and limitations of the proposed method. Furthermore, we conduct extensive parameter experimentation analysis on the proposed method from different perspectives. The experimental results demonstrate the stability and effectiveness of our proposed method.