Three-way Decisions Research Articles

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.

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.

A three-way conflict analysis model with decision makers’ varying preferences

The preferences of decision makers (DMs) over conflicting states have a significant impact on the stability of the conflict system. However, the DM’s preferences over conflicting states are generally unclear and variable, as they are influenced by the unpredictability of future situations of nature and the psychological behavior of DMs. To deal with multi-issue conflict problems, since the interval grey number and three-way decisions can reveal the mechanism of DMs’ grey and varying preferences in uncertain natural situations, we exploit grey system theory, conflict analysis, and three-way decisions to establish a novel conflict analysis model with varying decision makers’ preferences, and a conflict case of industry-university-research innovation alliance verifies the efficacy and rationality of the model.

A three-way decision approach for dynamically expandable networks

Conventional deep learning models are designed to work on a single task. They are required to be trained from scratch each time new tasks are added. This leads to overhead in training time. Continual deep learning models with dynamically expandable network architecture aim to handle this issue. The key idea in these models is to find a balance between the properties of stability (preserving the learned information) and plasticity (updating and accommodating the new information) also sometimes referred to as the stability-plasticity dilemma. The stability and plasticity of the model critically depends on three-way division of nodes into freeze, partially regularize and duplicate nodes. Freezing more nodes result in high stability but typically low plasticity. On the other hand, duplicating more nodes result in high plasticity but may not have an effective stability. In this paper, we introduce an approach called three-way decisions based dynamically expandable networks or 3WDDEN and its memory-based version called 3WDDEN-replay. The proposed approaches use game-theoretic rough sets to determine effective thresholds for three-way division of nodes by considering a tradeoff game between stability and plasticity. Experimental results of 3WDDEN on MNIST variant datasets show an overall improvement of 3.8% in accuracy compared to standard dynamically expandable network approach or DEN. 3WDDEN-replay further adds to accuracy with additional memory cost.

Behavioural three-way decision making with Fermatean fuzzy Mahalanobis distance: Application to the supply chain management problems

Behavioural three-way decision making has superseded conventional two-way decision making as a result of a surge in risk and complexity of decision making. Additionally, uncertainty management is necessary for decision making issues. Thus, the goal of this study is to set up new three-way multi-attribute decision making (MADM) model, particularly targeting the following: (i) to properly deal with issues regarding ambiguity and interrelationship in MADM problems, (ii) to incorporate mindsets of decision maker in all possible aspects, (iii) to depict outcomes in terms of acceptance, suspension and rejection rather than just ranking when there are numerous elements present Firstly, the presence of ambiguity in assessment information is reflected by Fermatean fuzzy set. An advanced distance measure, the Fermatean fuzzy Mahalanobis distance, is devised in order to address the connectivity of attributes. Therefore, regret theory-based gain and loss scores are calculated to define the dominant and dominated relations. The conditional probability is then estimated using a new method based on the two relations discussed before. After that, the value functions associated to each object are derived based on closeness coefficient and prospect theory. Finally, prospect theory-based three-way decision rules are forwarded to classify and rank the objects. The application of the developed model is demonstrated through two case studies of supply chain management. Several experimental analyses are conducted under two substantial datasets taken from the KEEL database. The Spearman correlation coefficient (greater than 0.648) and hypothesis testing (p-value is less than 0.01) are employed to establish the validity and rationality of the proposed model. What is more, the error rate and modified error rate under two datasets are 6.71%, 16.85% and 6.35%, 20.65%, respectively, indicate that the proposed model is superior to other available models.

Novel three-way decision model in medical diagnosis based on inexact reasoning

According to the clinical symptoms, a patient exhibits and medical domain knowledge, determining the type of disease the patient has is essential for medical diagnosis. Uncertainty is the nature of medical diagnosis. The intuitionistic fuzzy set (IFS) is one of the effective tools to deal with uncertainty problems. In recent years, IFS has been widely used to deal with medical diagnosis problems. The existing mainstream approach is to rank the underlying diseases and then assign the first-ranked disease to the patient. These methods cannot deal with situations where patients have multiple diseases at the same time or no disease at all. In addition, these methods may generate unreasonable diagnostic results in some cases. Consider clinical symptoms as evidence that a patient has or does not have the disease. With the increase in clinical symptoms, physicians will increase their belief or disbelief that the patient has the disease. Therefore, based on the method of inexact reasoning, this paper proposed an inexact reasoning model in medical diagnosis, namely IRM-MD, which can rank the underlying diseases and avoid generating unreasonable diagnostic results. Furthermore, a three-way decision model for medical diagnosis based on IRM-MD, namely 3WDM-IRM, is proposed. This model can effectively deal with cases where patients have multiple conditions at the same time or none at all, and prevent missed diagnoses and misdiagnoses. Finally, the numerical experiment results show that (a)the results generated by the IRM-MD model are similar to those of other existing models, and (b)the 3WDM-IRM model can effectively identify whether a patient has a disease or not, and identify multiple diseases that the patient has at the same time.

Three-way group decisions using evidence theory under hesitant fuzzy linguistic environment

In the actual decision-making process, there will be situations where decision-makers with hesitant attitudes have difficulties in evaluating alternatives numerically, and hesitant fuzzy linguistic term sets can provide decision-makers with an effective way to describe hesitancy in linguistic terms. In multi-attribute group decision-making, each decision maker typically holds different preferences. If the variation in decision makers’ assessment weights across evaluations of each attribute for every alternative is not adequately accounted for, it can result in a problem of coarse-grained calculations, leading to information loss. Additionally, the three-way decision model faces significant challenges in information fusion within the context of the hesitant fuzzy linguistic environment. Therefore, we propose a new three-way decision-making model under the hesitant fuzzy linguistic environment. The model obtains the confidence of different decision makers in attribute evaluations through the fusion of D-S evidence theory, and can perform more fine-grained fusion calculations on the evaluation information of different decision makers. In addition, the model considers the cost function of each alternative in different decision-making actions under hesitant fuzzy linguistic environment, calculates the two thresholds of each alternative in the three-way decision model, and derives the decision rules. The effectiveness of the model is verified through a numerical example and two comparative experiments, therefore, the model can be applied in intelligent classification or recommendation systems of hesitant fuzzy linguistic information systems.

Three-way decision: a unification of two-universe models of rough sets

Three-way decision: a unification of two-universe models of rough sets

Three-way clustering: Foundations, survey and challenges

Clustering, as an unsupervised data mining technique, allows us to classify similar objects into the same cluster according to certain criteria. It helps us identify patterns between objects, reveal the associations between objects, and discover hidden structures. Traditional two-way clustering (2W clustering) algorithms represent one cluster by one set and only two types of relationships are considered between a sample and a cluster, namely, belonging to and not belonging to. Two-way decision is not always feasible especially in situations that are characterized by uncertainty and lack of information. Guided by the principle of three-way decision (3WD) as thinking in threes, three-way clustering (3W clustering) addresses the information uncertainty problem using core and the fringe regions to character a cluster. The universe is split into three sections by these two sets, which capture three kinds of relationships between objects and a cluster, namely, belonging to, partially belonging to, and not belonging-to. Compared with 2W clustering methods, 3W clustering incorporates the fringe region to describe the uncertain relationship between objects and clusters, which provides more information about the clustering structure. This survey points out the historical developments of three-way clustering and makes an overview of the achievements in the field of three-way clustering. In addition, to reap a clearer grasp of the development and research significance of three-way clustering, we divide the existing three-way clustering approaches into two categories and present the bibliometric analysis of related approaches. Finally, we point out some challenges and future research topics in three-way clustering. It is hoped that this review can serve as a reference and provide convenience for scholars and practitioners in the field of three-way clustering.

Analysis of core attribute and approximate reduct based on the three-way decision

Attribute reduction plays an important role in pattern recognition and machine learning, and the theory of rough sets has become a commonly used model for attribute reduction since its superiority in describing and quantifying vagueness and uncertainty. However, little attention has been paid to analyzing the importance of core attributes in different circumstances, and core attributes are generally all selected into the reduct without considering their differences. In this study, the role of core attributes is analyzed in terms of their impacts on classification ability, and the three-way partition of attributes is proposed to distinguish different core attributes and condition attributes. Then, a unified approximate attribute reduction framework based on the three-way decision is introduced to keep the quality and resulting classification performance of the reduct. Moreover, a general forward-adding and back-deleting heuristic algorithm is developed to effectively select important attributes and also eliminate unimportant core and condition attributes in the boundary region. Comprehensive comparative experiments and statistical significance analysis are conducted on UCI data sets. The experimental results show that our method achieves a better attribute reduction rate and classification performance and also verify that core attributes are not always indispensable.

An integrated three-way decision methodology for sustainability of wastewater circularity in thermal power plants

The presence of multiple criteria for evaluating wastewater reuse applications indicates the potential usage of Multi-Criteria Decision-Making (MCDM) methods for this purpose. However, there is currently a scarcity of studies in the domain literature that utilize MCDM approaches in this application topic. This paper therefore advances the domain literature in two distinctive ways. Firstly, it analyzes and advances the reuse agenda of wastewater from thermal power plants, recognized as large-scale users of water, thus promoting greater water circularity. Secondly, it provides a methodological advance by integrating the notion of Three-Way Decision (3WD) into the computational structure of MCDM methods by introducing a middle reference point. Such an initiative results in a novel 3WD extension of the Measurement of Alternatives and Ranking according to COmpromise Solution (MARCOS) method. Additionally, this work provides a proof that the MARCOS method utilizes a compromise solution in identifying priority alternatives, along with the integration of a Weighted Aggregated Sum Product ASsessment (WASPAS) metric. An initial hypothetical example illustrates how the proposed approach augments the canonical MARCOS method, particularly in promoting the “thinking in threes” as a more natural information processing approach and the high degree of distinguishability of priorities between decision alternatives. An actual case study in a thermal power plant then demonstrates the contributions of this work. With the best-worst method used to determine the priorities of the decision attributes, the findings reveal that wastewater reuse applications achieving reduced costs for needed infrastructures, operational simplicity, technological compatibility, consumer safety and household savings are preferred by stakeholders. The 3WD-MARCOS approach identifies industrial and commercial use, municipal use, environmental restoration, and household use as the high-priority alternatives, with cooking and drinking as least preferred. These insights guide stakeholders in their design of initiatives that allocate resources for greater wastewater reuse. A comparative analysis yields high consistency of these findings with similar MCDM methods. In addition, the efficacy of the novel 3WD-MARCOS method highlights its potential in handling MCDM problems, including those promoting water circularity.

A novel interval-valued Fermatean fuzzy three-way decision making method with probability dominance relations

Interval-valued Fermatean fuzzy sets (IVFFSs) as an extension of Fermatean fuzzy sets (FFSs) are a new powerful mathematical tool that apply interval value to describe uncertainty. Compared to interval-valued intuitionistic fuzzy sets (IVIFSs) and interval-valued Pythagorean fuzzy sets (IVPFSs), IVFFSs can handle more uncertain information. This paper presents a novel fuzzy three-way multi-attribute decision-making approach with the probabilistic dominance relation, based on the model of IVFSSs. The proposed method firstly uses the probabilistic dominance relation to calculate the conditional probability of each alternative. Subsequently, it builds loss functions from the perspective of the ideal solution. Our suggested method is able to rank and classify the alternatives into the positive region, the boundary region, and the negative region while the existing MADM approaches under IVFSSs only sort them without classification. Additionally, the suggested solution involves a much lower error rate than the existing methods. And our method’s conditional probability may be determined objectively and takes the relation between attributes and interactions among alternatives into account, which reduce the risk associated with subjectivity in the decision-making process of existing approaches. The effectiveness and suitability of the suggested approach are illustrated by two real-world applications such as the photovoltaic poverty alleviation project selection and the hotel location evaluation and experimental findings.

Novel transformation methods from semi-three-way decision spaces to three-way decision spaces and their applications

As a vital theoretical research of three-way decision (3WD), three-way decision space (3WDS) further enriches the theory on 3WD and enhances its application. In 3WDS, decision evaluation function (DEF) is an indispensable component and plays a crucial role in practical decision problems. But, a large number of valuable functions are the semi-decision evaluation functions (S-DEFs). For this problem, Hu gave many S-DEFs and presented a transformation method from S-DEFs to DEFs. Since then, it has led to a research hotspot that is the introduction of the usual aggregation functions (AFs) into the transformation method of Hu's form. This paper focuses on the new form of transformation methods from semi-three-way decision spaces (S-3WDSs) to 3WDSs and their applications. Firstly, we present a new form of transformation method with parameter σ from S-DEFs to DEFs. And, we verify both theoretically and experimentally that this introduced parameter σ provides a valid window to dynamically adjust 3WDSs by changing the parameter σ, respectively. Notably, this new form of transformation method covers all existing 3WDSs transformation methods except the representable uninorms-based methods. Secondly, we give a more general function named with F-function, which can be introduced to these construction methods in the same way as usual AFs. This enables decision-makers to select more suitable functions for solving practical problems. Thirdly, based on the new form, usual AFs and F-functions, we present some new construction methods of S-DEFs (resp. DEFs) related to fuzzy sets, interval-valued fuzzy sets and random sets. Finally, to make up for the application of the theory of 3WDSs in complex datasets, we select 7 complex datasets for experimenting and conduct comparative and sensitivity analysis to test the viability and efficacy of our methods. Notably, we also give an algorithm to calculate the thresholds α and β, which can adjust the optimal thresholds α and β according to different 3WDSs.

A TOPSIS method based on sequential three-way decision

A TOPSIS method based on sequential three-way decision

Three-way decisions based on bipolar-valued fuzzy sets over three-way decision spaces

The concept of bipolar-valued fuzzy set was introduced by Zhang. Can we discuss three-way decisions based on bipolar-valued fuzzy sets over three-way decision spaces? In response to this problem, firstly, the paper discusses partially orders on truth values of bipolar-valued fuzzy sets and three-way decision spaces on this basis. Secondly, this paper presents construction method of decision evaluation functions based on bipolar-valued fuzzy sets over three-way decision spaces. Thirdly, this paper makes three-way decisions based on bipolar-valued fuzzy sets over three-way decision spaces and uses an example on an evaluation problem of credit card applicants to illustrate some notions of the (semi-, quasi-)three-way decision spaces and benefits of constructing methods from semi-(quasi-)decision evaluation functions to decision evaluation functions. Finally, the conclusions are summed up.

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 imbalanced learning based on fuzzy twin SVM

Three-way decision (3WD) is a powerful tool for granular computing to deal with uncertain data, commonly used in information systems, decision-making, and medical care. Three-way decision gets much research in traditional rough set models. However, three-way decision is rarely combined with the currently popular field of machine learning to expand its research. In this paper, three-way decision is connected with SVM, a standard binary classification model in machine learning, for solving imbalanced classification problems that SVM needs to improve. A new three-way fuzzy membership function and a new fuzzy twin support vector machine with three-way membership (TWFTSVM) are proposed. The new three-way fuzzy membership function is defined to increase the certainty of uncertain data in both input space and feature space, which assigns higher fuzzy membership to minority samples compared with majority samples. To evaluate the effectiveness of the proposed model, comparative experiments are designed for forty-seven different datasets with varying imbalance ratios. In addition, datasets with different imbalance ratios are derived from the same dataset to further assess the proposed model’s performance. The results show that the proposed model significantly outperforms other traditional SVM-based methods.

A q-rung orthopair fuzzy multi-attribute group decision making model based on attribute reduction and evidential reasoning methodology

Multi-attribute group decision-making (MAGDM) is an analytical decision-making framework which gathers the views of multiple experts, and they often assess alternatives by degree adverbs in realistic scenarios. In order to treat expert opinions well, q-rung orthopair fuzzy sets (q-ROF) emerged as a data disposal tool, however, how to aggregate the information rationally remains a challenge. In this paper, q-ROF evidential reasoning methodology (q-ROF ERM) is proposed to guarantee the functionality in the case of conflicting, extreme information evaluations from experts and attributes. Second, the q-ROF attribute reduction (AR) framework is invented for attribute importance measurement. The flexibility and elegance of the model are boosted by the variation of the λ parameter and its lead to the elimination of redundant attributes. In addition to this, the q-ROF output three-way decision (TWD) framework is created to give the classification and ranking of alternatives. The relative output function derived from fuzzy distance measure and the adjustable utility pursuit coefficient τ afford both objectivity and subjectivity to the program selection, allowing the evaluation outcomes to be relevant to human cognition. Finally, the comparative experiments and sensitivity analyses of the two cases illustrate the scientificity and reliability of the presented framework in the MAGDM scenario.