Three-way Decision Theory Research Articles

Three-way decision-based label integration for crowdsourcing

In crowdsourcing learning, label integration is often used to infer instances’ integrated labels from their multiple noisy labels. However, almost all existing label integration algorithms apply the same strategy to infer different instances’ integrated labels, which limits their performance. This paper argues that different instances should enjoy different label integration strategies alone. Thanks to the three-way decision theory, a three-way decision-based label integration (TDLI) algorithm is proposed. In TDLI, we at first evaluate the label qualities of each instance and its K-nearest neighbors, and then utilize them to divide the whole crowdsourced datasets into three disjoint subsets, called positive set, boundary set and negative set, respectively. For each instance in the positive set, we directly apply the simplest majority voting (MV) to infer its integrated label. For each instance in the boundary set, we absorb its K-nearest neighbors’ multiple noisy labels to infer its integrated label by the weighted MV. For each instance in the negative set, we merge the positive and boundary sets to train a classifier to infer its integrated label by fusing its own multiple noisy label distribution and the predicted label distribution. Extensive experiments demonstrate that TDLI distinctly outperforms all the other existing label integration algorithms used to compare.

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.

A new portfolio approach integrating three-way decision and Encoder–Decoder network

In the stock market, it can be challenging to predict stock trends and identify stocks with investment potential due to uncertainty and risk. Accurate predictive models and reliable asset preselection methods are essential for portfolio management. This paper proposes an integration of the deep learning model, the three-way decision (3WD) theory, and the Mean-Variance (MV) method for asset preselection and optimal asset allocation. In the initial stage, an attention-based Encoder–Decoder model is used to predict asset returns and calculate volatility. It outperforms other benchmark models regarding relative error, absolute error, and directional accuracy. The subsequent stage involves selecting stocks based on expected returns and volatility characteristics. The 3WD theory is then used to identify the delayed decision set for implementing additional investment strategies to hedge portfolio risk and enhance returns. Finally, the MV model is employed for investment portfolio optimization. The proposed model is validated using a substantial dataset from the A-share market’s SSE 50 Index from January 2010 to December 2022. Results indicate that the proposed model outperforms benchmark models in terms of daily average returns, annualized Information ratio, Sortino ratio, and other aspects under certain trading costs. However, further exploration is required to establish a mechanism that limits the quantity of preselected assets to ensure its broad applicability.

New approach for quality function development based on cooperative game-based consensus mechanism and three-way decision method

Quality function deployment (QFD) is a team-based product development approach for identifying critical engineering characteristics according to customer requirements to improve customer satisfaction. Nonetheless, there are some limitations in the current QFD methods when used in real-world situations. For example, most of them cannot handle experts’ conflict opinions regarding the correlation evaluations between customer requirements and engineering characteristics, and only focus on how to acquire a complete importance ranking of engineering characteristics which is unnecessary in many realistic cases. In this study, we aim to develop a new QFD approach by using the cooperative game consensus reaching process and three-way decision theory. First, the cooperative game-based consensus mechanism is applied to help experts reach a consensus on the correlation assessments between customer requirements and engineering characteristics. Then, an extended three-way decision method is adopted to obtain the importance classifications of engineering characteristics and identify the critical ones for product improvement. Finally, the proposed QFD approach is illustrated with a case study regarding renewable energy storage technology improvement, and its efficiency and advantages are verified via comparative analysis and simulation analysis.

A review of three-way decision: Triadic understanding, organization, and perspectives

A theory of three-way decision is about thinking, problem-solving, and computing in threes or through triads. In this paper, we review fifteen years of research on three-way decision by using the philosophy-theory-application triad and the who-what-when triad. First, we discuss the philosophy, theory, and application of three-way decision. At the philosophy level, we delve into the philosophical roots and fundamental nature of three-way decision to reveal the underlying philosophical thinking. At the theory level, we provide an insightful analysis of the theory and methodology of three-way decision. At the application level, we examine the integration of three-way decision with other theories and their applications and effectiveness in real-world scenarios. Second, we focus on bibliometrics analytics by using the who-what-when triad, which attempts to answer a fundamental question of “who did what when”. We propose a 3×3 model by applying the 3×3 method of three-way decision. The first 3 is the author-topic-time triad. The second 3 represents a three-level analysis for each of the first three: (1) categorizing authors into the three levels of prolific authors, frequent authors, and occasional authors, (2) classifying topics into the three levels of the core topics, emerging topics, and to-be-explored topics, and (3) dividing articles into the three levels of initial investigations, further developments, and most recent studies. Finally, we perform a bibliometrics analysis of three-way decision articles by using the 3×3 model of three-way decision. The results not only reveal the current status and trend of three-way decision research but also provide a road map for future research.

An ordinal–cardinal consensus model for three-way large-scale group decision-making considering co-opetition relations

In large-scale group decision-making (LSGDM), the complexity of the decision-making environment highlights the significance of co-opetition in reaching a consensus among decision-makers (DMs) with diverse knowledge. Thus, this paper proposes an ordinal–cardinal consensus model for three-way LSGDM that considers co-opetition relationships among DMs. Specifically, we first improve the ordinal consensus measure and propose the ordinal–cardinal consensus measure by analyzing the co-opetition relationships. Then, utilizing the constructed trust consensus network, DMs are categorized into subgroups, and spokespersons are selected from each subgroup. Further, we establish the consensus identification rule using the three-way decision (TWD) theory and design a personalized feedback regulation mechanism for distinct relationships among subgroup representatives based on ordinal consensus. Also, an example of economic revitalization is employed to illustrate the feasibility of the proposed approach. Finally, the benefits and values of the proposed method are highlighted by simulation and comparative analysis.

Three-way decision in machine learning tasks: a systematic review

In this article, we survey the applications of Three-way decision theory (TWD) in machine learning (ML), focusing in particular on four tasks: weakly supervised learning and multi-source data management, missing data management, uncertainty quantification in classification, and uncertainty quantification in clustering. For each of these four tasks we present the results of a systematic review of the literature, by which we report on the main characteristics of the current state of the art, as well as on the quality of reporting and reproducibility level of the works found in the literature. To this aim, we discuss the main benefits, limitations and issues found in the reviewed articles, and we give clear indications and directions for quality improvement that are informed by validation, reporting, and reproducibility standards, guidelines and best practice that have recently emerged in the ML field. Finally, we discuss about the more promising and relevant directions for future research in regard to TWD.

Three-way decision-based Takagi–Sugeno–Kang fuzzy classifier for partially labeled data

The salient features of Takagi–Sugeno–Kang (TSK) fuzzy classifiers are their superior nonlinear fitting capability and better interpretability, rendering them widely applicable in the domains of data mining and machine learning. However, using TSK fuzzy classifiers for partially labeled data has received little attention. Based on the three-way decision (TWD) theory, this study proposed a TSK fuzzy model to learn from partially labeled data. First, an adaptive sample weight strategy is introduced for the fuzzy partition of the antecedent part and the cross-entropy loss of the consequent part, respectively. Subsequently, a prototype-based firing strength loss mechanism is proposed to constrain the optimization of the model in the fuzzy representation space. It employs a TWD strategy based on the entropy criterion to classify samples as useful, useless, and uncertain, where the proposed model enhances the performance by iteratively utilizing a certain number of useful pseudo-labeled samples. Finally, the validity of the model is theoretically analyzed based on the principle of noise learning. The experimental results on UCI datasets demonstrate that the proposed model exhibits superior performance compared with classical semi-supervised methods, even attaining a performance comparable to that of the model trained on all data with ground-truth labels.

An Architecture of Enhanced Profiling Assurance for IoT Networks

Attacks launched from IoT networks can cause significant damage to critical network systems and services. IoT networks may contain a large volume of devices. Protecting these devices from being abused to launch traffic amplification attacks is critical. The manufacturer usage description (MUD) architecture uses pre-defined stateless access control rules to allow or block specific network traffic without stateful communication inspection. This can lead to false negative filtering of malicious traffic, as the MUD architecture does not include the monitoring of communication states to determine which connections to allow through. This study presents a novel solution, the enhanced profiling assurance (EPA) architecture. It incorporates both stateless and stateful communication inspection, a unique approach that enhances the detection effectiveness of the MUD architecture. EPA contains layered intrusion detection and prevention systems to monitor stateful and stateless communication. It adopts three-way decision theory with three outcomes: allow, deny, and uncertain. Packets that are marked as uncertain must be continuously monitored to determine access permission. Our analysis, conducted with two network scenarios, demonstrates the superiority of the EPA over the MUD architecture in detecting malicious activities.

Considering personalized individual semantics with ordinal and cardinal consensus reaching processes via three-way decision and regret theory

The seamless integration of computerized methodologies into industrial engineering problem-solving is pivotal for optimizing efficiency. In the specific domain of multi-attribute group decision-making (MAGDM) with probabilistic linguistic term sets (PLTSs), these methodologies offer systematic approaches to consensus building, ensuring effective decision processes in intricate scenarios. Within the realm of PLTSs, the consensus-reaching process (CRP) for MAGDM is gaining prominence. This paper addresses this evolving area by proposing ordinal and cardinal CRPs within the framework of PLTSs, specifically incorporating the regret theory (RT) of three-way decisions (TWD). The paper introduces an initial distance formula under PLTSs, providing a complementary approach to assess similarity relations among decision-makers (DMs). To account for diverse semantics across DMs, personalized individual semantics (PIS) is integrated into the CRP, recognizing variations in DMs’ alternatives and attributes. To enhance realism, the paper introduces the concepts of individual alternative sets and individual attribute sets. Additionally, the paper integrates ordinal and cardinal consensus, establishing a dynamic feedback adjustment mechanism grounded in the principles of RT and TWD. The method’s reasonableness is validated through a real case study, and a comparative analysis with the existing methods underscores the superiority of the approach presented in this paper.

Regret-based three-way decisions with set pair analysis in incomplete information systems

Set pair analysis is a valuable tool for managing uncertain systems and can effectively handle missing information in the decision-making process. In addition, regret theory can objectively describe the impact of decision-maker psychology on decision-making. However, traditional decision-making methods rarely combine set pair analysis and regret theory to discuss decision problems. Thus, this article aims to integrate regret theory into the three-way decision theory based on set pair analysis, presenting a novel approach to address multi-attribute decision-making problems in real life. Specifically, we first propose a data-driven approach based on set pair analysis to determine attribute weights. Then, a similarity relationship is established based on the weighted distance to calculate conditional probability. Meanwhile, the average value of regret and joy under each attribute is selected as a reference point to determine the relative utility function using regret theory. Subsequently, we develop a new three-way decision method in incomplete information systems and apply it to solve practical problems. Finally, the effectiveness and superiority of our method are demonstrated by case analysis and comparison. We also conduct sensitivity analysis to examine the stability of the new method.

Grey conflict analysis approach with constraints

PurposeWe attempt to construct a grey three-way conflict analysis model with constraints to deal with correlated conflict problems with uncertain information.Design/methodology/approachIn order to address these correlated conflict problems with uncertain information, considering the interactive influence and mutual restraints among agents and portraying their attitudes toward the conflict issues, we utilize grey numbers and three-way decisions to propose a grey three-way conflict analysis model with constraints. Firstly, based on the collected information, we introduced grey theory, calculated the degree of conflict between agents and then analyzed the conflict alliance based on the three-way decision theory. Finally, we designed a feedback mechanism to identify key agents and key conflict issues. A case verifies the effectiveness and practicability of the proposed model.FindingsThe results show that the proposed model can portray their attitudes toward conflict issues and effectively extract conflict-related information.Originality/valueBy employing this approach, we can provide the answers to Deja’s fundamental questions regarding Pawlak’s conflict analysis: “what are the underlying causes of conflict?” and “how can a viable consensus strategy be identified?”

BTWM-HF: A behavioral three-way multi-attribute decision-making method with hesitant fuzzy information

Three-way decision (TWD) theory offers a novel paradigm for solving hesitant fuzzy multi-attribute decision-making problems. However, many existing TWD approaches follow the principle of minimum risk, thereby overlooking the influence of the psychological factors of decision-makers (DMs) on decision outcomes when faced with losses and gains. To address this challenge, we propose a behavioral three-way multi-attribute decision-making method with hesitant fuzzy information via hesitant fuzzy TODIM. The proposed method encompasses two key features. One is that the relative utility functions based on the dominance degree are constructed, aiming to portray the psychological behaviors of DMs. The other is the development of an objective calculation of weighted conditional probabilities, achieved without relying on a state set and a binary relation. The feasibility of the proposed method is verified by two numerical examples, one on software selection and the other from the UCI database. The results of the multi-aspect comparative analysis demonstrate that the proposed method exhibits good performance in terms of ranking and classification. Moreover, the experimental results indicate the effectiveness and applicability of the presented method.

Systematic attribute reductions based on double granulation structures and three-view uncertainty measures in interval-set decision systems

Attribute reductions eliminate redundant information to become valuable in data reasoning. In the data context of interval-set decision systems (ISDSs), attribute reductions rely on granulation structures and uncertainty measures; however, the current structures and measures exhibit the singleness limitations, so their enrichments imply corresponding improvements of attribute reductions. Aiming at ISDSs, a fuzzy-equivalent granulation structure is proposed to improve the existing similar granulation structure, dependency degrees are proposed to enrich the existing condition entropy by using algebra-information fusion, so 3×2 attribute reductions are systematically formulated to contain both a basic reduction algorithm (called CAR) and five advanced reduction algorithms. At the granulation level, the similar granulation structure is improved to the fuzzy-equivalent granulation structure by removing the granular repeatability, and two knowledge structures emerge. At the measurement level, dependency degrees are proposed from the algebra perspective to supplement the condition entropy from the information perspective, and mixed measures are generated by fusing dependency degrees and condition entropies from the algebra-information viewpoint, so three-view and three-way uncertainty measures emerge to acquire granulation monotonicity/non-monotonicity. At the reduction level, the two granulation structures and three-view uncertainty measures two-dimensionally produce 3×2 heuristic reduction algorithms based on attribute significances, and thus five new algorithms emerge to improve an old algorithm (i.e., CAR). As finally shown by data experiments, 3×2-systematic construction measures and attribute reductions exhibit the effectiveness and development, comparative results validate the three-level improvements of granulation structures, uncertainty measures, and reduction algorithms on ISDSs. This study resorts to tri-level thinking to enrich the theory and application of three-way decision.

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.

Two novel three-way decision models based on fuzzy [formula omitted]-covering rough sets and prospect theory under q-rung orthopair fuzzy environments

Three-way decision (TWD) and prospect theory (PT) are efficacious theories for investigating uncertain problems. TWD can mitigate the risks associated with rapid decision-making in traditional decision-making. PT can describe the psychological behavior of decision-makers. Furthermore, q-rung orthopair fuzzy sets (q-ROFSs) exhibit wider-ranging applications since they generalize intuitive fuzzy sets and Pythagorean fuzzy sets and unify them under one framework. However, the acquisition of q-ROFSs is an important issue in practical problems. In light of these considerations, this paper develops two TWD models under q-rung orthopair fuzzy environments, employing the principles of PT. To begin, we introduce two novel fuzzy β-covering rough sets that meet the inclusion property. Subsequently, utilizing the proposed fuzzy rough set, we provide an objective methodology to acquire q-ROFSs. Following this, the relative utility function is given through a combination of the value function and EDAS method. Additionally, the weighting function is constructed using two distinct approaches: one that continues to incorporate the ideas of EDAS method, and the other that utilizes the probabilistic dominance α-neighborhood classes to calculate conditional probabilities. After that, classification rules and sorting rules are derived. Ultimately, we substantiate the validity and excellence of the proposed TWD models through comparative and experimental analysis.

Three-way group consensus with experts' attitudes based on probabilistic linguistic preference relations

Intelligent decision-making collaborates with big data analytics to navigate the intricate landscape of the digital economy, orchestrating data-driven strategies to achieve the most favorable results. Through the integration of specific objectives and relevant data, intelligent decision-making involves the modeling, analysis, and realization of decisions. This comprehensive process seamlessly incorporates elements such as constraints, strategies, preferences, and uncertainty, ultimately leading to the autonomous achievement of optimal outcomes. In this context, the probabilistic linguistic preference relation (PLPR) serves as a recently introduced form of linguistic evaluations, offering adaptable expression of expert preference assessments. Within the domain of preferences, consistency emerges as a pivotal consideration. Extremes occur when calculating the additive consistency of PLPR using expectation values. To comprehensively address the trouble, this paper introduces an innovative planning model that employs deviation degrees. The establishment of a consistency threshold is approached objectively using the principle of minimum individual regret and maximum group delight. Once consistency is established, the process advances to consensus reaching process (CRP). During the consensus feedback phase, the infusion of the three-way decision (TWD) theory accounts for distinct expert modification attitudes, while ensuring consistency remains upheld throughout the modification procedure. For clarity, the proposed technique is referred to as the TWD-GC-EA method. Notably, the effectiveness of the designed approach is demonstrated through its application to a real-world scenario. Furthermore, a comparative assessment is conducted against several other consensus methods to validate its efficacy and superiority.

Three-way decisions with evaluative linguistic expressions

The theory of three-way decisions (3WD) requires dividing a finite, non-empty universe into three disjoint sets called positive, negative, and boundary regions. Three types of decisions are then made on the objects in each region: acceptance, rejection, and abstention (or non-commitment), respectively. Until today, a large number of 3WD extensions and applications have been proposed; some of the most recent ones also include aspects of linguistics. In this article, we first propose an innovative linguistic interpretation of three-way decisions, where the positive, negative, and boundary regions are constructed by means of the so-called evaluative linguistic expressions. These are expressions of natural language, such as small, medium, very short, quite roughly strong, extremely good, etc., and they are described within a logical theory based on the formal system of higher-order fuzzy logic. Furthermore, in line with our linguistic 3WD approach, we introduce the novel notion of linguistic rough sets, thus contributing to the development of Rough Set Theory. Finally, we connect the theory of linguistic three-way decisions with the standard 3WD model based on probabilistic rough sets, establishing conditions under which the two approaches coincide. Our results highlight connections between two different research areas: three-way decisions and the theory of evaluative linguistic expressions.

Preference-based regret three-way decision method on multiple decision information systems with linguistic Z-numbers

Three-way decision theory (3WD) provides a reasonable solution to solve multi-criteria decision-making (MCDM) problems and reduces more decision risks than two-way decision (2WD). However, the impact of preferences on decision results has not been reasonably considered in 3WD. Thus, this paper proposes a preference-based regret 3WD model on multiple decision information systems (MDISs) with linguistic Z-numbers (LZNs) to address the defect. First of all, a Z-LINMAP method is proposed by extending LINMAP method into the LZNs environment to derive criteria weights, Z-number ideal solutions and preference coefficients. On the basis of preference coefficients, the consistency-order and inconsistency-order are defined and further the consistency and inconsistency equivalence classes are presented to derive the conditional probabilities of alternatives. Then, the regret loss functions based on regret theory are presented and the regret 3WD rules of a single decision information system are designed. Furthermore, the weighted expected regret loss function and loss score function are defined to classify and rank all alternatives for MDISs. Finally, the proposed 3WD model is applied to the image recognition case with human-computer interaction to verify the effectiveness, and the comparative and sensitivity analyses are carried out to demonstrate the feasibility of our model.

Exploiting local label correlation from sample perspective for multi-label classification via three-way decision theory

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