Fuzzy Decision-theoretic Rough Sets Research Articles

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

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

Research on multi-granularity sequential three-way decisions based on the fuzzy T-equivalence relation

The fuzzy decision-theoretic rough set (FDTRS) is a data processing method based on the fuzzy theory designed to handle decision problems with uncertainty and fuzziness. It simplifies the complexity of decision-making and provides decision strategies by integrating multiple sources of information. This approach makes the decision process more scientific and rational. The mainstream FDTRS model breaks the over restrictive limits of classical decision-theoretic rough sets, computes the fuzzy similarity relation between two objects utilizing the Gaussian kernel function, which is another major breakthrough and innovation in the field of decision-theoretic rough sets. However, this model suffers from the problems of insufficient decision information, single perspective and high decision-making cost when dealing with dynamic, complex and uncertain problems. Emerging in recent years, sequential three-way decisions not only provides a flexible mechanism to implement the idea of progressive computation, but also deals with dynamic, complex and uncertain problems. To this end, this paper proposes a sequential three-way decision model based on the fuzzy T-equivalence relation (FTE-based sequential three-way decision model) from the perspective of sequential three-way decisions, and gives relevant definitions and examples to effectively solve the problem of insufficient information. Then in order to solve the single-view problem, we extend the sequential three-way decisions to the case of multi-granularity, and propose FTE-based multi-granularity sequential three-way decisions in four aggregation strategies with the corresponding properties and algorithms. In addition, the rationality of models are tentatively analyzed through specific examples. Finally, six sets of UCI standard datasets are used to validate the proposed models, which demonstrate their good performance. These models contribute to the field of fuzzy decision-theoretic rough sets and sequential three-way decisions.

An Improved Intuitionistic Fuzzy Decision-Theoretic Rough Set Model and Its Application

The Decision-Theoretic Rough Set model stands as a compelling advancement in the realm of rough sets, offering a broader scope of applicability. This approach, deeply rooted in Bayesian theory, contributes significantly to delineating regions of minimal risk. Within the Decision-Theoretic Rough Set paradigm, the universal set undergoes a tripartite division, where distinct regions emerge and losses are intelligently distributed through the utilization of membership functions. This research endeavors to present an enhanced and more encompassing iteration of the Decision-Theoretic Rough Set framework. Our work culminates in the creation of the Generalized Intuitionistic Decision-Theoretic Rough Set (GI-DTRS), a fusion that melds the principles of Decision-Theoretic Rough Sets and intuitionistic fuzzy sets. Notably, this synthesis bridges the gaps that exist within the conventional approach. The innovation lies in the incorporation of an error function tailored to the hesitancy grade inherent in intuitionistic fuzzy sets. This integration harmonizes seamlessly with the contours of the membership function. Furthermore, our methodology deviates from established norms by constructing similarity classes based on similarity measures, as opposed to relying on equivalence classes. This shift holds particular relevance in the context of aggregating information systems, effectively circumventing the challenges associated with the process. To demonstrate the practical efficacy of our proposed approach, we delve into a concrete experiment within the information technology domain. Through this empirical exploration, the real-world utility of our approach becomes vividly apparent. Additionally, a comprehensive comparative analysis is undertaken, juxtaposing our approach against existing techniques for aggregation and decision modeling. The culmination of our efforts is a well-rounded article, punctuated by the insights, recommendations, and future directions delineated by the authors.

Probabilistic Hesitant Fuzzy Decision-Theoretic Rough Set Model and Its Application in Supervision of Shared Parking

A sophisticated three-way decision model utilizing a multi-granularity probabilistic hesitant fuzzy rough set is introduced to mitigate the issue of information loss arising from hesitant fuzzy sets when characterizing decision information. Initially, the properties of probabilistic hesitant fuzzy sets are examined, subsequently proposing a distance measure and loss function tailored to these sets. Following this, a multi-attribute group decision-making model incorporating probabilistic hesitant fuzzy information is established, and pertinent decision rules that satisfy minimal risk criteria are presented. Building on this foundation, a series of critical steps for resolving a category of multi-attribute group decision-making problems that involve probabilistic hesitant fuzzy information is proposed. Lastly, the multi-attribute group decision-making model with probabilistic hesitant fuzzy information is applied to the supervision of urban shared parking platforms. The results indicate that the decision-making process based on probabilistic hesitant fuzzy sets is more reliable, and the decision-making outcome aligns with the actual situation, thus providing valuable decision-making references for managers.

Three-way conflict analysis and resolution based on q-rung orthopair fuzzy information

In solving some complex conflict problems, compared with intuitionistic fuzzy sets (IFSs) and Pythagorean fuzzy sets (PFSs), q-rung orthopair fuzzy sets (q-ROFSs) can better express and model imprecise information. In addition, three-way decisions (TWDs), an emerging theory of simulating human decision-making behavior, play an increasingly important role in the study of conflict problems. In order to solve conflict problems under q-rung orthopair fuzzy information (q-ROFI), we propose a three-way conflict analysis and resolution model based on TWDs and decision-theoretic rough sets (DTRSs) theory, which provides another answer for Deja's fundamental questions about Pawlak's conflict model, namely, “what are the inherent causes of conflict?” and “how can a viable strategy be found?” different from the existing ones. To be specific, firstly, we define new conflict distances and conflict function for q-ROFI system using aggregation functions and weight determination method, and prove some of their properties. On this basis, the concepts of three-level of contention set and agent set, a trisection of conflict set under individual contention and contention set, and maximum doughty coalition of q-ROFI are introduced. Secondly, after introducing the rough approximation threshold calculation method on the basis of standard evaluation set, to find the optimal viable strategy under the given q-ROFI, we calculate and sort the score function by the upper and lower approximation operators in the proposed q-rung orthopair fuzzy decision-theoretic rough sets (q-ROFDTRSs) model. Thirdly, we use the proposed model to study a land-use conflict case in a metropolitan area to verify the feasibility. Finally, from sensitivity and comparative analysis, we verify the stability and validity of the q-ROFDTRSs model.

On three perspectives for deriving three-way decision with linguistic intuitionistic fuzzy information

The determination of both thresholds in decision-theoretic rough sets is an important problem of study that has aroused widespread attention in recent years. Although many related methods have been proposed, they may need a substantial amount of computation in model solving even not capture the thresholds in some cases. In this paper, we introduce linguistic intuitionistic fuzzy numbers (LIFNs) into loss functions due to LIFNs integrating the advantages of linguistic terms and intuitionistic fuzzy numbers, and propose a single optimization model-based, threshold-determined method to derive three-way decision. First, we define a novel measure for ranking LIFNs, verify its properties, analyze the relationships between loss functions with LIFNs and establish linguistic intuitionistic fuzzy decision-theoretic rough sets with a novel measure for LIFNs. Second, we investigate linguistic intuitionistic fuzzy, three-way decision methods from three perspectives, especially from the third perspective. We construct a single optimization model for capturing the thresholds that can overcome the shortcomings of the methods from two other perspectives, and the uniqueness of the optimal solution of this model is proven with the aid of the Karush-Kuhn-Tucker (KKT) condition. Third, a single model-based perspective method and its corresponding algorithm are designed to determine the thresholds for linguistic intuitionistic fuzzy information. Last, an illustrative example and simulated experiments are conducted to show the validity of our method.

A Fuzzy Decision-Theoretic Rough Set Approach for Type-2 Fuzzy Conditional Information Systems and Its Application in Decision-Making

A Fuzzy Decision-Theoretic Rough Set Approach for Type-2 Fuzzy Conditional Information Systems and Its Application in Decision-Making

Redefined fuzzy rough set models in fuzzy β-covering group approximation spaces

The research purpose of this paper is to explore some new fuzzy rough set models in the fuzzy β-covering group approximation space (FβCGAS) and study the related properties, thereby provide new thinking directions for the theoretical development and application expansion of fuzzy rough set models. Firstly, in the fuzzy β-covering approximation space (FβCAS), in light of some existing fuzzy covering rough set (FCRS) models which do not satisfy the inclusion relations between the fuzzy upper and lower approximations, we define the concepts of parameterized fuzzy β-neighborhoods and parameterized fuzzy complementary β-neighborhoods to eliminate part of the noise data and establish four types of parameterized FCRS models that satisfy the inclusion relationship between the fuzzy lower and upper approximations. Meanwhile, the properties of the models are discussed. Further, in the FβCGAS, we define the concepts of the parameterized pessimistic (optimistic) fuzzy β-fitting neighborhoods and the parameterized pessimistic (optimistic) fuzzy complementary β-fitting neighborhoods and construct the parameterized pessimistic and optimistic FCRS models that satisfy the inclusion relationship between the fuzzy lower and upper approximations. At the same time, we likewise explore the properties of the models. Besides, we further use the newly proposed parameterized fuzzy neighborhoods to study the variable precision multi-granulation fuzzy decision-theoretic rough set models in the FβCGAS. Finally, for all the models mentioned above, we recommend them for solving the criteria weight determination problem, ranking problem, optimal selection problem and qualitative classification problem in multi-criteria decision-making. Meanwhile, we complete the relationships of all the new models mentioned in this paper and discuss them.

A novel approach to three-way conflict analysis and resolution with Pythagorean fuzzy information

As a universal phenomenon, conflicts exist widely in various walks of life, such as politics, economic lives, military operations, and cultural exchanges. In order to sove more complex and uncertain-conflict problems than what is possible within the confinement of current knowledge, this paper proposes a three-way conflict analysis model and conflict-degree based decision-theoretic rough set model for conflict resolution under Pythagorean fuzzy information. Firstly, we define a novel conflict distance and conflict function with Pythagorean fuzzy information from the perspective of absolute and relative conflict. We examine respectively a trisection of the conflict relation between a pair of agents, that among agents, that among disputes, and that among alliances. We also introduce the concepts of maximal strong alliances and maximal weak alliances. All of these efforts are then used to explain the reason for the emergence of conflicts. Secondly, to find an optimal feasible strategy for a given conflict situation, we propose a Pythagorean fuzzy decision-theoretic rough set model based on conflict functions and define the score function for each feasible strategy. Finally, for verifying our proposed model, a three-way conflict analysis and resolution are employed to address a governance issue of a local government.

A novel approach of three-way decisions with information interaction strategy for intelligent decision making under uncertainty

As an effective tool to deal with uncertain decision-making, three-way decisions (TWD) have gained wide attention in many applications. Decision-theoretic rough sets (DTRSs) as a classic model of TWD contain two key elements, i.e., conditional probability and loss functions. In this paper, we study the determination of these two elements in depth via the information interaction and modification strategy, and further propose a novel model of TWD. First, fuzzy c-means (FCM) is used to cluster the condition attribute information and loss function information, respectively. Considering the interaction of two types of information, we design the corresponding fusion tactic of these clustering results to get equivalent classes and develop a new calculation method of conditional probability. Then, we use probabilistic hesitant fuzzy sets (P-HFSs) to aggregate the loss functions of different members of the same equivalence class and get the probabilistic hesitant fuzzy elements (P-HFEs) loss functions. In this case, P-HFSs not only reflect the hesitant situation of decision-makers, but also depict the proportion of different opinions. Regarding P-HFEs loss functions, we also investigate the modification methods of its outliers in detail. Moreover, based on the P-HFEs loss functions, we propose TWD with probabilistic hesitant fuzzy decision-theoretic rough sets (P-HFDTRSs). Finally, in order to verify the effectiveness of our proposed method, we develop a series of comparative experiments and discuss the decision results on six UCI datasets.

Conflict analysis based on three-way decision for triangular fuzzy information systems

Triangular fuzzy numbers (TFNs) can not only provide the range of fuzzy points, but contain the three most representative fuzzy points, which play an essential role in describing fuzzy information. Combining with conflict situations, the agents' caution in the decision-making process can be well depicted by TFNs. However, little effort has been paid to conflict analysis on triangular fuzzy information systems (TFISs). In this paper, we study three-way conflict analysis based on TFISs. First, we propose the concept of TFISs and then establish a TFIS for conflict analysis. Further, relative area ΔS is defined to describe concrete attitudes of agents about issues. Second, since the importance of the same issue may vary for agents, we attach fuzzy weights to issues according to triangular fuzzy symmetric judgment matrices (TFSJMs) of agents. Third, we determine the total attitude of each agent to all issues. Then we illustrate how to compute thresholds α and β using the theory of triangular fuzzy decision-theoretic rough sets. Finally, a tri-partition of agents is obtained based on the thresholds.

A Novel Three-Way Investment Decisions Based on Decision-Theoretic Rough Sets with Hesitant Fuzzy Information

As a classic model of three-way decisions, the decision-theoretic rough sets (DTRSs) have been adopted to help make profit-based investment decisions. However, there is epistemic uncertainty in the assessment of investment projects, hence the hesitant fuzzy sets (HFSs) are appropriate tool for characterizing the revenue functions and cost functions. To get a more reasonable result in the three-way investment decisions, we introduce HFSs to DTRSs and explore a new three-way investment decision model. Firstly, we take into account the revenue and cost of DTRSs with hesitant fuzzy elements and propose a hesitant fuzzy decision-theoretic rough sets (HFDTRSs) model. Then, we calculate the revenue functions and cost functions by aggregating hesitant fuzzy elements with the Bayesian decision procedure. Considering the differences in the personalities and attitudes of decision-makers, we propose optimistic strategy and pessimistic strategy to aggregate revenue functions and cost functions. Finally, based on the score of profit maximization, we make three-way investment decisions. A case study of coal investment was used to demonstrate the proposed methods.

Three-way group decisions based on multigranulation hesitant fuzzy decision-theoretic rough set over two universes

Three-way group decisions based on multigranulation hesitant fuzzy decision-theoretic rough set over two universes

Note on “Fuzzy multi-granulation decision-theoretic rough sets based on fuzzy preference relation”

In this note, we point out that the transfer function for computing the fuzzy preference degree in Mandal and Ranadive (Soft Comput, 2018. https://doi.org/10.1007/s00500-018-3411-7 ) for the construction of upward/downward fuzzy relations is not additive consistent. Appropriate counterexample is given. Further, their modified versions are presented.

The Approach to Probabilistic Decision-Theoretic Rough Set in Intuitionistic Fuzzy Information Systems

For the moment, the representative and hot research is decision-theoretic rough set (DTRS) which provides a new viewpoint to deal with decision-making problems under risk and uncertainty, and has been applied in many fields. Based on rough set theory, Yao proposed the three-way decision theory which is a prolongation of the classical two-way decision approach. This paper investigates the probabilistic DTRS in the framework of intuitionistic fuzzy information system (IFIS). Firstly, based on IFIS, this paper constructs fuzzy approximate spaces and intuitionistic fuzzy (IF) approximate spaces by defining fuzzy equivalence relation and IF equivalence relation, respectively. And the fuzzy probabilistic spaces and IF probabilistic spaces are based on fuzzy approximate spaces and IF approximate spaces, respectively. Thus, the fuzzy probabilistic approximate spaces and the IF probabilistic approximate spaces are constructed, respectively. Then, based on the three-way decision theory, this paper structures DTRS approach model on fuzzy probabilistic approximate spaces and IF probabilistic approximate spaces, respectively. So, the fuzzy decision-theoretic rough set (FDTRS) model and the intuitionistic fuzzy decision-theoretic rough set (IFDTRS) model are constructed on fuzzy probabilistic approximate spaces and IF probabilistic approximate spaces, respectively. Finally, based on the above DTRS model, some illustrative examples about the risk investment of projects are introduced to make decision analysis. Furthermore, the effectiveness of this method is verified.

Optimal granulation selection for similarity measure-based multigranulation intuitionistic fuzzy decision-theoretic rough sets

Optimal granulation selection for similarity measure-based multigranulation intuitionistic fuzzy decision-theoretic rough sets

Multi-granulation Pythagorean fuzzy decision-theoretic rough sets based on inclusion measure and their application in incomplete multi-source information systems

Multi-granulation rough sets (MGRSs) and decision-theoretic rough sets (DTRSs) are two important and popular generalizations of classical rough sets. The combination of two generalized rough sets have been investigated by numerous researchers in different extensions of fuzzy settings such as interval-valued fuzzy sets (IVFSs), intuitionistic fuzzy sets (IFSs), bipolar-valued fuzzy sets (BVFSs), etc. Pythagorean fuzzy (PF) set is another extension of fuzzy set, which is more capable in comparison to IFS handle vagueness in real world. However, few studies have focused on the combination of the two rough sets in PF settings. In this study, we combine the two generalized rough sets in PF settings. First, we introduce a type of PF subset (of subset of the given universe) of the PF Set (of the given universe). Then we establish two basic models of multi-granulation PF DTRS (MG-PF-DTRS) of PF subset of the PF set based on PF inclusion measure within the framework of multi-granulation PF approximation space. One model is based on a combination of PF relations (PFRs) and the construction of approximations with respect to the combined PFR. By combining PFRs through intersection and union, respectively, we construct two models. The other model is based on the construction of approximations from PFRs and a combination of the approximations. By using intersection and union to combine the approximations, respectively, we again get two models. As a result, we have total four models. Further for different constraints on parameters, we obtain three kinds of each model of the MG-PF-DTRSs. Then, their principal structure, basic properties and uncertainty measure methods are investigated as well. Second, we give a way to compute PF similarity degrees between two objects and also give a way to compute PF decision-making objects from incomplete multi-source information systems (IMSISs). Then we design an algorithm for decision-making to IMSISs using MG-PFDTRSs and their uncertainty measure methods. Finally, an example about the mutual funds investment is included to show the feasibility and potential of the theoretic results obtained.

Three-way decisions with decision-theoretic rough sets in multiset-valued information tables

The goal of three-way decisions is to divide a universe into three pair-wise disjoint regions and to act on some or all of these regions using appropriate strategies. The decision-theoretic rough set model, a typical three-way decision model, trisects a universe using a pair of thresholds computed from loss functions. Previous studies of decision-theoretic rough set models do not consider loss functions based on multiset values and are unable to deal with multiset-valued information tables. In this paper, two generalized decision-theoretic rough set models involving multiset-valued data are proposed, namely a multiset-decision-theoretic rough set model and a multiset-fuzzy-decision-theoretic rough set model. Two methods are introduced that compute expected costs from loss functions. The first method is based on the mutiset addition and a new normal-multiset multiplication. The second method is based on a new concept known as the p-length of finite normal multisets. These two methods offer different ways of building multiset-decision-theoretic rough set models. By integrating the multiset-decision-theoretic rough set model with the fuzzy decision-theoretic rough set model, a multiset-fuzzy-decision-theoretic rough set model is created, a model which considers fuzzy relations in multiset-valued information tables. An example that recommends different home options is given to illustrate these models.

Three-Way Decisions with Interval-Valued Intuitionistic Fuzzy Decision-Theoretic Rough Sets in Group Decision-Making

In this article, we demonstrate how interval-valued intuitionistic fuzzy sets (IVIFSs) can function as extended intuitionistic fuzzy sets (IFSs) using the interval-valued intuitionistic fuzzy numbers (IVIFNs) instead of precision numbers to describe the degree of membership and non-membership, which are more flexible and practical in dealing with ambiguity and uncertainty. By introducing IVIFSs into three-way decisions, we provide a new description of the loss function. Thus, we firstly propose a model of interval-valued intuitionistic fuzzy decision-theoretic rough sets (IVIFDTRSs). According to the basic framework of IVIFDTRSs, we design a strategy to address the IVIFNs and deduce three-way decisions. Then, we successfully extend the results of IVIFDTRSs from single-person decision-making to group decision-making. In this situation, we adopt a grey correlation accurate weighted determining method (GCAWD) to compute the weights of decision-makers, which integrates the advantages of the accurate weighted determining method and grey correlation analysis method. Moreover, we utilize the interval-valued intuitionistic fuzzy weighted averaging (IIFWA) operation to count the aggregated scores and the accuracies of the expected losses. By comparing these scores and accuracies, we design a simple and straightforward algorithm to deduce three-way decisions for group decision-making. Finally, we use an illustrative example to verify our results.

Multi-granulation fuzzy decision-theoretic rough sets and bipolar-valued fuzzy decision-theoretic rough sets and their applications

This paper investigates the decision-theoretic rough set (DTRS) approach in the frameworks of multi-granulation fuzzy and bipolar-valued fuzzy (BVF) probabilistic approximation spaces, respectively. By integrating fuzzy probability and BVF probability into the Bayesian decision procedure, we get four types of model of multi-granulation fuzzy decision-theoretic rough set (MG-FDTRS) approach and multi-granulation bipolar-valued fuzzy decision-theoretic rough set (MG-BVF-DTRS) approach. Our four types of model of the MG-FDTRS and the MG-BVF-DTRS approaches are mainly based on computation of the four different conditional probabilities within the frameworks of multi-granulation fuzzy and BVF probabilistic approximation spaces, respectively. The main contribution of this paper is twofold. One is to extend the fuzzy decision-theoretic rough set (FDTRS) approach to the MG-FDTRS and the MG-BVF-DTRS approaches. Another is to address its applicable ability as it is applied to deal with the multi-source fuzzy and BVF probabilistic decision systems. An example is included to show the feasibility and potential results obtained.