Three-way Decision Model Research Articles

Mining multigranularity decision rules of concept cognition for knowledge graphs based on three-way decision

Machine understanding and thinking require prior knowledge consisting of explicit and implicit knowledge. The current knowledge base contains various explicit knowledge but not implicit knowledge. As part of implicit knowledge, the typical characteristics of the things referred to by the concept are available by concept cognition for knowledge graphs. Therefore, this paper attempts to realize concept cognition for knowledge graphs from the perspective of mining multigranularity decision rules. Specifically, (1) we propose a novel multigranularity three-way decision model that merges the ideas of multigranularity (i.e., from coarse granularity to fine granularity) and three-way decision (i.e., acceptance, rejection, and deferred decision). (2) Based on the multigranularity three-way decision model, an algorithm for mining multigranularity decision rules is proposed. (3) The monotonicity of positive or negative granule space ensured that the positive (or negative) granule space from coarser granularity does not need to participate in the three-classification process at a finer granularity, which accelerates the process of mining multigranularity decision rules. Moreover, the experimental results show that the multigranularity decision rule is better than the two-way decision rule, frequent decision rule and single granularity decision rule, and the monotonicity of positive or negative granule space can accelerate the process of mining multigranularity decision rules.

An Interval-Valued Three-Way Decision Model Based on Cumulative Prospect Theory

In interval-valued three-way decision, the reflection of decision-makers’ preference under the full consideration of interval-valued characteristics is particularly important. In this paper, we propose an interval-valued three-way decision model based on the cumulative prospect theory. First, by means of the interval distance measurement method, the loss function and the gain function are constructed to reflect the differences of interval radius and expectation simultaneously. Second, combined with the reference point, the prospect value function is utilized to reflect decision-makers’ different risk preferences for gains and losses. Third, the calculation method of cumulative prospect value for taking action is given through the transformation of the prospect value function and cumulative weight function. Then, the new decision rules are deduced based on the principle of maximizing the cumulative prospect value. Finally, in order to verify the effectiveness and feasibility of the algorithm, the prospect value for decision-making and threshold changes are analyzed under different risk attitudes and different radii of the interval-valued decision model. In addition, compared with the interval-valued decision rough set model, our method in this paper has better decision prospects.

An ensemble face recognition mechanism based on three-way decisions

The explainable human–computer interaction (HCI) is about designing approaches capable of using cognitive characteristics like humans. One such characteristic is human vision and its accuracy. The accuracy measures the trust in that system. Therefore, improving accuracy in the authorization with identification process is a primary concern for a visual-based explainable human–computer interaction system. In this article, we propose a three-way decision based ensembled face recognition mechanism called E3FRM. The E3FRM uses a three-way approach to determine the match cases and the respective worth of the captured image with the match cases. Features are extracted using PCA/FLD, and the ensembled face recognition algorithms utilize the extracted features to process the image. Ensemble Face recognition approaches find the match cases based on a given threshold. Finally, the three-way decision model evaluates the suitability of the captured image for acceptance, rejection, or deferred cases with a dual verification mechanism. Experimental results on well-known eighteen datasets suggest improvements in commonly used metrics of F1, Accuracy and Recall by up to 0.8% to 12.8%, 1% to 9.6% and 1.2% to 13.9%, respectively, in comparison to the state-of-the-art methods available, including SPCA +, ML-EM, FLDA-SVD, DMMA, Fast-DMMA, LU, LPP, TDL, KCFT, RBF + DT, and NMF. Furthermore, the proposed approach is comparatively analyzed with ensembled face recognition methods that result in an outperformed F1, Accuracy and Recall by up to 1.1% to 10.3%, 0.1% to 7.3% and 0.9% to 10.5%, respectively. These results suggest that the proposed model may improve face recognition accuracy and the resulting trust in the machines.

A three-way decision model on incomplete single-valued neutrosophic information tables

In this paper, we focus on the three-way decision model on incomplete single-valued neutrosophic information tables. Firstly, we define the minimum and maximum similarity measures between single-valued neutrosophic numbers (SVNNs) which may contain unknown values. On this basis, the notion of θ-weak similarity measure is given. Then, we introduce the conception of an incomplete single-valued neutrosophic information table (ISVNIT). For an incomplete single-valued neutrosophic information table, a new similarity relation is proposed based on the θ-weak similarity measure. Some properties are also studied. By using Bayesian decision theory and this similarity relation, we construct a three-way decision model on an ISVNIT. Finally, an example of choosing product service providers is explored to illustrate the rationality and feasibility of the proposed model. We also discuss the influence of parameters in the model on decision results.

Three-way decision for probabilistic linguistic conflict analysis via compounded risk preference

Three-way decision, an essential granular computing research tool, provides an efficient solution to complex and uncertain problems. Behavioral decision theory can analyze the risk preferences of decision-makers effectively. Scholars have conducted preliminary exploration on the fusion of these two theories, but it is still challenging to describe the different types of risk preferences of decision-makers. This paper combines prospect theory with regret theory and studies the compound risk preference modeling of three-way decision to address this issue. Because three attitudes of conflicts coincide with three-way decision, many scholars have conducted multi-dimensional research on three-way conflict analysis and accomplished remarkable results. However, few relevant studies consider psychological factors and risk attitudes of decision-makers, and it is more appropriate to describe agents' attitudes on issues using linguistic terms. This paper applies the proposed three-way decision model based on compounded risk preference and probabilistic linguistic term sets to the conflict analysis problem. We utilize examples to explain the decision-making process of the proposed model and three-way conflict analysis method with the influence of the compounded risk preference under the action of reference point and regret avoidance coefficient. The illustrative example illustrates that the proposed three-way decision model can effectively solve the software development conflict analysis problem for different decision-makers and the comparative analysis shows the advantages of the proposed model and method compared with the two existing methods. Finally, we verify the performance of the three-way decision model based on compounded risk preference by UCI data sets in parameter experiments. The changes of the reference point from 10 to 0 and regret avoidance coefficient in 0, 0.15 and 0.3 respectively demonstrate the trend rule of the model's thresholds and delay-decision rate index.

Novel variable precision fuzzy rough sets and three-way decision model with three strategies

Variable precision (fuzzy) rough sets are interesting generalizations of Pawlak rough sets and can handle uncertain and imprecise information well due to their error tolerance capability. The comparable property (CP for short), i.e., the lower approximation is included in the upper approximation, is fundamental in Pawlak rough sets since many theories and applications rely on this property. However, the CP is lost in many existing variable precision (fuzzy) rough sets. Therefore, a novel variable precision fuzzy rough set model with CP is proposed and an associated three-way decision model is developed. Firstly, a pair of variable precision fuzzy upper and lower approximation operators are defined and studied through fuzzy implication and co-implication operators. We show that this pair of approximation operators satisfy various properties (including CP) that the existing variable precision fuzzy approximation operators do not possess. Secondly, new methods for constructing loss functions and conditional probabilities are given by using CP, and then a new three-way decision model with three strategies (optimistic, pessimistic, and compromise strategies) is established. Finally, an explanatory example is provided to examine validity, stability and sensitivity of the proposed three-way decision model.

Multi-criteria fuzzy portfolio selection based on three-way decisions and cumulative prospect theory

Portfolio selection is one of the hottest issue in decision-making and management engineering. But due to the capital market natural complexity and investors’ irrational behaviors, it is not easy for investors to achieve their predefined goals. In this study, we propose a novel three-way decisions model based on cumulative prospect theory and outranking relations. Compared with traditional two-way decisions, the introduction of a boundary region into the three-way decisions theory makes it possible to reduce decision risk. By constructing an outranked set for each alternative and a hybrid multi-criteria decision-making matrix, three strategies are proposed by us to design the three-way decisions model. In order to test the effectiveness of the proposed model, we introduce it into a fuzzy multi-period portfolio selection case and design an improved particle swarm optimization as the solution algorithm. Finally, the effectiveness of the algorithm is validated by some test functions. And an experiment based on real market data validates the proposed multi-period portfolio selection model outperforms other compared models in terms of return, risk and risk-adjusted criteria.

Mixed-attitude three-way decision model for aerial targets: Threat assessment based on IF-VIKOR-GRA method.

Assessing potential threats typically necessitates the use of a robust mathematical model, a comprehensive evaluation method and universal decision rules. A novel approach is utilized in this study to optimize existing threat assessment (TA) algorithms and three-way decision models (3WDMs) are leveraged that incorporate decision-theoretic rough sets (DTRSs) within dynamic intuitionistic fuzzy (IF) environments to create a mixed-attitude 3WDM based on the IF-VIKOR-GRA method in the context of aviation warfare. The primary objectives of this study include determining conditional probabilities for IF three-way decisions (3WDs) and establishing mixed-attitude decision thresholds. Both the target attribute and loss function are expressed in the form of intuitionistic fuzzy numbers (IFNs). To calculate these conditional probabilities, an IF technique is used to combine the multi-attribute decision-making (MADM) method VIKOR and the grey relational analysis (GRA) method, while also taking into account the risk-related preferences of decision-makers (DMs). Optimistic and pessimistic 3WDMs are developed from the perspectives of membership degree and non-membership degree, then subsequently integrated into the comprehensive mixed-attitude 3WDM. The feasibility and effectiveness of this methodology are demonstrated through a numerical example and by comparison to other existing approaches.

Regret Theory-Based Three-Way Decision Model in Hesitant Fuzzy Environments and Its Application to Medical Decision

In real world, a typical decision-making problem in the medical field can be seen as an uncertain hesitant fuzzy multiattribute decision-making problem when existing experiences of decision-makers are insufficient. A three-way decision model is an effective tool to deal with uncertain decision-making problems, which can realize the classification of objects. However, different psychological behaviors of decision-makers are likely to affect decision-making results in actual decision-making processes. In order to address this challenge, we first propose a regret-theory-based three-way decision model in hesitant fuzzy environments, which mainly combines regret theory with hesitant fuzzy sets to calculate the perceived utility value of objects. Second, since one of the core ingredients for regret theory is the regret–rejoice function, we put forward a new regret–rejoice function that preserves the original indecisive uncertainty in hesitant fuzzy environments. In addition, according to the inherent relationship of the used data, this article provides a three-way classification method based on the preference ranking organization method for enrichment evaluations I method. Finally, the practicability, rationality, and superiority of the proposed method are shown via the case analysis and comparative analysis in the medical field.

A Three-Way Decision Approach for Water Resources System Resilience Evaluation and Its Application

Resilience is a significant uncertainty thought of water resources system security. Compared with risk analysis, resilience pays more attention to the ability of water resources system itself to deal with adverse events. However, a standard system of water resources system resilience’s concept and evaluation have not yet formed. In view of this, this study had attempted to decompose the process of resisting interference of water resources system and analyzed the characteristics and influencing factors of three sub processes of resistance, recovery and adaptation. Furtherly, a new resilience evaluation index system of water resources system was explored and a three-way dicision approach for water resources system resilience analysis based on variable fuzzy sets and partial connection number was developed. Specifically, a multi-grade quantitative evaluation of water resources resilience was carried out based on variable fuzzy sets method, and then the quantitative evaluation results were transformed into qualitative decision-making results using a new three-way decision model based on partial connection number of set pair analysis. Finally, a case study of China’s Yangtze River Economic Belt (YEB) in 2008–2017 was performed and the results show that the resilience of water resources system in the YEB does not show an obvious improvement trend, or even almost stagnant. Of the 110 samples, 83.6% were at the medium level. Only 6.4% are barely at the excellent level, but they are basically in Shanghai.

A three-way decision method with tolerance dominance relations in decision information systems.

In recent years, various medical diagnosis problems have been addressed from the perspective of multi-attribute decision making. Among them, the three-way decision theory can provide a novel scheme to solve medical diagnosis issues under the framework of multi-attribute decision making via considering transforming relationships between loss functions and decision matrices. In this paper, we primarily explore a three-way decision method with tolerance dominance relations in ordered decision information systems. In existing three-way decision models, all objects can be divided into two states, we utilize decision attributes to obtain the set of two states in ordered decision information systems. Then, in order to improve the accuracy of patient classifications, the paper simultaneously considers the influence of loss and gain functions for each object, and uses loss and gain functions to obtain net profit functions as new measurement functions. Meanwhile, a class of three-way decisions in terms of multi-attribute decision making rules based on a tolerance dominance relation is established. In light of the proposed three-way decision method, we further construct a multi-attribute decision making method by using tolerance dominance relations and the constructed method is applied to a medical diagnosis issue of Lymphography. Finally, a comparison analysis and an experimental evaluation are performed to illustrate the feasibility and effectiveness of the presented methodology.

The intuitionistic fuzzy concept-oriented three-way decision model

Recently, some researchers have explored three-way decision models in the fuzzy multi-criteria environments from the perspective of criterion fuzzy concept. The main characteristics of these models include the subjective preference of decision-maker for criteria and the evaluation value information system provided by decision-maker. However, the criterion fuzzy concept only considers the decision-maker’s membership preference to each criterion, and ignores the decision-maker’s non-membership preference to each criterion. In view of this, this paper further proposes a new criterion fuzzy concept, namely the intuitionistic fuzzy concept, to express decision-maker’s preference for each criterion. At the same time, we build an intuitionistic fuzzy concept-oriented three-way decision model to solve the ranking and classification problem in the intuitionistic fuzzy multi-criteria environments with decision-maker’s preference. Firstly, based on the defined intuitionistic fuzzy concept, we construct a new intuitionistic fuzzy loss function model. Meanwhile, using intuitionistic fuzzy similarity, we propose a new conditional probability calculation method to express the correlation degree between the intuitionistic fuzzy concept and alternative’s evaluation values. Secondly, we introduce three decision-making perspectives from the membership degree and non-membership degree of expected loss to obtain the final three-way classification scheme. Moreover, by combining the thresholds of the positive and negative perspectives, we obtain the comprehensive thresholds of the comprehensive perspective, which can be used to rank all alternatives. Finally, a supplier selection problem is used to verify the feasibility and superiority of the model, and six data sets are used to verify the applicability of the model.

A three-way classification with fuzzy decision trees

This study is concerned with the design of a three-way classification mechanism realized through combing fuzzy decision trees and expressing uncertainty associated with classification results. The fuzzy decision tree used in this study is constructed through the generalization of the commonly used decision trees. The notion of three-way decision model first proposed for the interpretation of rules generated in rough set approximation has been widely used in many fields. This study proposes an efficient way to flag data with high level of uncertainty with the classification realized by fuzzy decision trees, which is the capability that commonly used fuzzy decision trees do not have. The data identified in this way are left to users’ judgments or more advanced classification techniques. The developed mechanism is formed as a two-stage construct where a fuzzy decision tree is built by generalizing the Boolean classification boundaries of a pre-constructed decision tree using fuzzy sets and then determining the level of uncertainty to identify instances to be rejected due to a lack of sufficient confidence in their belongingness. The rejected instances that are difficult to process are classified as non-commitment cases and left to some further analyses. The rejection quality of the developed three-way classifier is quantified in terms of the classification accuracy and rejection coefficient. We also elaborate on striking a sound tradeoff between these two performance indicators. Experimental studies demonstrate that the developed mechanism could effectively improve the classification accuracy at the cost of a small proportion of the rejected instances and achieve better performance in comparison with other three-way decision models when generating a three-way decision output.

A prospect-regret theory-based three-way decision model with intuitionistic fuzzy numbers under incomplete multi-scale decision information systems

As a new data representation in the big data era, a multi-scale decision information system (MSDIS) realizes “multi-level, multi-angle and multi-view” evaluations in various problems. However, most of existing multi-scale data analysis models are built for complete information systems (CISs), whereas the research on incomplete multi-scale decision information systems (I-MSDISs) is not perfect. Additionally, the irrational behavior of one decision-maker (DM) often has an impact on decision outcomes. On this basis, this paper develops a prospect-regret theory-based three-way decision (3WD) model with intuitionistic fuzzy numbers (IFNs) under an I-MSDIS, which is abbreviated as PR-3WD-I-MSDIS. Specifically, we first select the optimal scale combination of I-MSDISs by the matrix theory to complete the information extraction of incomplete optimal sub-systems. Then, we further propose an attribute weight evaluation strategy under the incomplete optimal subsystem, which fully considers the neighborhood information of each object. Subsequently, the concept and calculation method of aggregated weighted fuzzy conditional probabilities are constructed from the perspective of intuitionistic fuzzy sets. Furthermore, a prospect-regret theory-based relative profit function is proposed, which sufficiently takes into account the loss and utility in decision-making processes. Finally, a novel three-way classification and ranking method is developed for solving incomplete multi-scale problems. The experimental results on real-world datasets demonstrate that the PR-3WD-I-MSDIS model achieves excellent performance.

A bipolar three-way decision model and its application in analyzing incomplete data

The theory of three-way decision has contributed to data science in many topics, such as three-way classification, three-way clustering, and three-way feature selection. Most three-way decision models are formulated based on evaluation functions that commonly consider two opposite aspects of positive and negative, alliance and conflict, etc. This idea coincides with the concept of bipolarity, which studies the two opposite poles of positive and negative. However, the connections between bipolarity and three-way decision models have not been well investigated, despite the fact that they share many common features. Therefore, this work explores their relationships and proposes a new bipolar three-way decision model. Firstly, we examine the connections between the polarity theory, including the concepts of unipolarity and bipolarity, and decision models, including the two-way and three-way decision models. The examination suggests a lack of a three-way decision model corresponding to certain types of bipolarity. Thus, secondly, we propose a new bipolar three-way decision model 3WD-(ep,en)2, which considers a pair of a positive evaluation function ep and a negative evaluation function en and applies a pair of thresholds on each function. Finally, we illustrate the usefulness and effectiveness of 3WD-(ep,en)2 in data science through its application in analyzing incomplete data. In particular, we present a computational formulation based on similarity classes and a conceptual formulation based on a conjunctive description language. The two formulations together provide a multi-view understanding of the approach.

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.

Three-way decision approach for water ecological security evaluation and regulation coupled with VIKOR: A case study in Beijing-Tianjin-Hebei region

Owing to the great correlation between human survival and water ecological security (WES), the research on the evaluation and regulation of WES is of great significance. However, the evaluation thought of WES is not clear enough and most of the evaluation methods can only get ranking results subjectively, which are not suit to judge the grade, especially in the complex and uncertain decision environment. Thus, under the guidance of the resilience idea, it is proposed to build an evaluation indicator system of WES from three aspects: resistance, restorative and adaptability. Then the data were transformed into Pythagorean fuzzy number (PFN), and the resilience index was obtained based on VIKOR (VIseKriterijumska Optimizacija I Kompromisno Resenje) method to realize ranking; After that, the comprehensive thresholds were estimated by the resilience index, and a new three-way decision (3WD) model for the WES evaluation was constructed for grade evaluation; Finally, the model was applied to the evaluation of WES in Beijing-Tianjin-Hebei region (BTH) of China from 2006 to 2020. The results show that the WES in BTH has significant spatial-temporal differentiation; From 2006 to 2020, except Hebei, the WES level has not been significantly improved; Beijing, Tianjin and Hebei were respectively in grade III, V and I in 2016–2020; The resistance of WES is an urgent direction to be optimized in Beijing and Tianjin, while Tianjin and Hebei should strengthen the restorative of WES. The model framework constructed in this study is effective and has good generalizability, which can provide a new way for WES evaluation.

A three-way decision approach with S-shaped utility function under Pythagorean fuzzy information

Three-way decision, as opposed to conventional two-way decision-making, can more effectively reduce decision-making risks by adding a postponed decision-making. With respect to the three-way decision problem consisting of Pythagorean fuzzy information, considering the risk attitudes of decision makers(DMs), we exploit Pythagorean fuzzy sets (PFNs), S-shaped utility and three-way decision to establish a new Pythagorean three-way decision model. The model realizes the effective integration of Pythagorean fuzzy theory and three-way decision, and enriches three-way decision based on risk preference. Firstly, we define a new PFN score function and construct a new condition probability by using Pythagorean fuzzy similarity, which not only reflects the difference in distance but conforms to human cognitive habits. Subsequently, considering the impact of the changes in risk preferences on the measurement of decision risks, we define an action utility function and construct the risk measurement matrix function based on S-shaped utility function, calculate the thresholds by employing optimization formulation. According to key steps and algorithms, the Pythagorean fuzzy-three-way decision rules based on S-shaped utility function can be obtained. Finally, we utilize an example of selecting film projects to validate the interpretability and applicability of our proposed model.

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.