Search Results (31)

Variable precision fuzzy rough sets (VPFRSs) and multi-granulation fuzzy rough sets (MGFRSs) are both significant extensions of rough sets. However, existing variable precision models generally lack the inclusion property, which poses potential risks in applications. Meanwhile, multi-granulation models tend to emphasize either optimistic or pessimistic scenarios but overlook compromise situations. A generalized fuzzy remote neighborhood system is a symmetric union-fuzzified form of the neighborhood system, which can extend the fuzzy rough set model to a more general framework. Moreover, semi-grouping functions eliminate the left-continuity required for grouping functions and the associativity in t-conorms, making them more suitable for information aggregation. Therefore, to overcome the limitations of existing models, we propose an optimistic (OP), pessimistic (PE), and compromise (CO) variable precision fuzzy rough set (OPCAPFRS) based on generalized fuzzy remote neighborhood systems. The semi-grouping function and its residual minus are employed in the OPCAPFRS. We discuss the basic properties of the OPCAPFRS and prove that it satisfies the generalized inclusion property (GIP). This partially addresses the issue that a VPFRS cannot fulfill the inclusion property. A novel methodology for addressing multi-attribute decision-making (MADM) problems is developed through the fusion of the proposed OPCAPFRS framework and the VIKOR technique. The proposed method is applied to the problem of selecting an optimal CPU. Subsequently, comparative experiments and a parameter analysis are conducted to validate the effectiveness and stability of the proposed method. Finally, three sets of experiments are performed to verify the reliability and robustness of the new approach. It should be noted that the new method performed ranking on a dataset containing nearly ten thousand samples, obtaining both the optimal solution and a complete ranking, thereby validating its scalability. Full article

A novel multiple attribute group decision-making (MAGDM) model is introduced in this study, utilizing a diversified hesitant fuzzy multi-granulation information system to address challenges in incomplete information settings. The analysis commences with an exploration of hesitant fuzzy sets and multi-granulation approximation. Subsequently, the integration of cumulative prospect theory into Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) within a hesitant fuzzy framework is discussed, emphasizing the incorporation of a risk preference coefficient in GDM to enhance individual assessments. The model proposes a systematic approach to address various MAGDM scenarios under hesitant fuzzy conditions. An illustrative case study on resource-sharing is provided to demonstrate the efficacy of the diversified MAGDM model, with evaluation outcomes expressed using hesitant fuzzy elements, offering valuable insights into group decision-making in hesitant fuzzy environments. Full article

Rough sets and fuzzy sets are two complementary approaches for modeling uncertainty and imprecision. Their integration enables a more comprehensive representation of complex, uncertain systems. However, existing rough fuzzy sets models lack the expressive power to fully capture the interactions among structural uncertainty, cognitive hesitation, and multi-level granular information. To address these limitations, we achieve the following: (1) We propose intuitionistic fuzzy covering rough membership and non-membership degrees based on maximal description and construct a new single-granulation model that more effectively captures both the structural relationships among elements and the semantics of fuzzy information. (2) We further extend the model to a multi-granulation framework by defining optimistic and pessimistic approximation operators and analyzing their properties. Additionally, we propose a neutral multi-granulation covering rough intuitionistic fuzzy sets based on aggregated membership and non-membership degrees. Compared with single-granulation models, the multi-granulation models integrate multiple levels of information, allowing for more fine-grained and robust representations of uncertainty. Finally, a case study on real estate investment was conducted to validate the effectiveness of the proposed models. The results show that our models can more precisely represent uncertainty and granularity in complex data, providing a flexible tool for knowledge representation in decision-making scenarios. Full article

The rapid advancement of artificial intelligence is transforming agriculture by enabling data-driven plant disease monitoring and decision support. Soil-borne mosaic wheat virus (SBWMV) is a soil-transmitted virus disease that poses a serious threat to wheat production across multiple ecological zones. Due to the regional variability in environmental conditions and symptom expressions, accurately evaluating the severity of wheat soil-borne mosaic (WSBM) infections remains a persistent challenge. To address this, the problem is formulated as large-scale group decision-making process (LSGDM), where each planting plot is treated as an independent virtual decision maker, providing its own severity assessments. This modeling approach reflects the spatial heterogeneity of the disease and enables a structured mechanism to reconcile divergent evaluations. First, for each site, field observation of infection symptoms are recorded and represented using intuitionistic fuzzy numbers (IFNs) to capture uncertainty in detection. Second, a Bayesian graph convolutional networks model (Bayesian-GCN) is used to construct a spatial trust propagation mechanism, inferring missing trust values and preserving regional dependencies. Third, an enhanced spectral clustering method is employed to group plots with similar symptoms and assessment behaviors. Fourth, a feedback mechanism is introduced to iteratively adjust plot-level evaluations based on a set of defined agricultural decision indicators sets using a multi-granulation rough set (ADISs-MGRS). Once consensus is reached, final rankings of candidate plots are generated from indicators, providing an interpretable and evidence-based foundation for targeted prevention strategies. By using the WSBM dataset collected in 2017–2018 from Walla Walla Valley, Oregon/Washington State border, the United States of America, and performing data augmentation for validation, along with comparative experiments and sensitivity analysis, this study demonstrates that the AI-driven LSGDM model integrating enhanced spectral clustering and ADISs-MGRS feedback mechanisms outperforms traditional models in terms of consensus efficiency and decision robustness. This provides valuable support for multi-party decision making in complex agricultural contexts. Full article

Attitude preference plays an important role in multigranulation data mining and decision-making. That is, different attitude preferences lead to different results. At present, both optimistic and pessimistic multigranulation rough sets have been studied independently and thoroughly. But, sometimes, a decision-maker’s attitude may vary, which may shift either from an optimistic to pessimistic view of decision-making or from a pessimistic to optimistic view of decision-making. In this paper, we propose a novel multigranulation rough set model, which synthesizes optimistic and pessimistic attitude preferences. Specifically, we put forward methods to evaluate the attitude preferences in four types of decision systems. Two main issues are addressed with regard to attitude preference dependency. The first is concerned with the common attitude preference, while the other relates to the sequence-dependent attitude preference. Finally, we present three types of multigranulation rough set models from the perspective of the different connection methods between optimistic and pessimistic attitude preferences. Full article

The complexity of large-scale group decision-making (LSGDM) in the digital society is becoming increasingly prominent. How to achieve efficient consensus through social networks (SNs) has become a core challenge in improving the decision quality. First, conventional clustering methods often rely on a single-distance metric, neglecting both numerical assessments and preference rankings. Second, ensuring the decision authenticity requires considering diverse behaviors, such as trust propagations, risk preferences, and minority opinion expressions, for scientific decision-making in SNs. To address these challenges, a consensus-reaching process (CRP) method based on an enhanced K-means++ clustering is proposed. The above method not only focuses on minority opinion handling (MOH), but also incorporates decision indicator sets (DISs) to analyze the degree of opinion divergences within groups. First, the Hamacher aggregation operator with a decay factor completes trust matrices, improving the trust representation. Second, a personalized distance metric that combines cardinal distances with ordinal distances is incorporated into the enhanced K-means++ clustering, enabling more precise clustering. Third, weights for decision-makers (DMs) and subgroups are determined based on trust levels and degree centrality indices. Fourth, minority opinions are appropriately handled via considering the diverse backgrounds and expertise of DMs, leveraging a difference-oriented DIS to detect and adjust these opinions via weight modifications until a consensus is reached. Fifth, the alternative ranking is objectively generated via DIS scores derived from multigranulation rough approximations. Finally, the feasibility of the proposed method is validated via a case study on unmanned aerial vehicle (UAV) selection using online reviews, supported by a sensitivity analysis and comparative experiments demonstrating superior performances over existing methods. The result shows that the proposed model can enhance clustering accuracies with hybrid distances, objectively measure the consensus via DISs, handle minority opinions effectively, and improve LSGDM’s overall efficiencies. Full article

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. Full article

In this article, we introduce two new rough set models based on the concept of double fuzzy relations. These models are called optimistic and pessimistic multi-granulation double fuzzy rough sets. We discuss their properties and explore the relationship between these new models and double fuzzy rough sets. Our study focuses on the lower and upper approximations of these models, which generalize the conventional rough set model. In addition, we suggest that the development of the multi-granulation double fuzzy rough set model is significant for the generalization of the rough set model. Full article

Air pollution (AP) is a significant environmental issue that poses a potential threat to human health. Its adverse effects on human health are diverse, ranging from sensory discomfort to acute physiological reactions. As such, air quality evaluation (AQE) serves as a crucial process that involves the collection of samples from the environment and their analysis to measure AP levels. With the proliferation of Internet of Things (IoT) devices and sensors, real-time and continuous measurement of air pollutants in urban environments has become possible. However, the data obtained from multiple sources of IoT sensors can be uncertain and inaccurate, posing challenges in effectively utilizing and fusing this data. Meanwhile, differences in opinions among decision-makers regarding AQE can affect the outcome of the final decision. To tackle these challenges, this paper systematically investigates a novel multi-attribute group decision-making (MAGDM) approach based on hesitant trapezoidal fuzzy (HTrF) information and discusses its application to AQE. First, by combining HTrF sets (HTrFSs) with multi-granulation rough sets (MGRSs), a new rough set model, named HTrF MGRSs, on a two-universe model is proposed. Second, the definition and property of the presented model are studied. Third, a decision-making approach based on the background of AQE is constructed via utilizing decision-making index sets (DMISs). Lastly, the validity and feasibility of the constructed approach are demonstrated via a case study conducted in the AQE setting using experimental and comparative analyses. The outcomes of the experiment demonstrate that the presented architecture owns the ability to handle multi-source IoT sensor data (MSIoTSD), providing a sensible conclusion for AQE. In summary, the MAGDM method presented in this article is a promising scheme for solving decision-making problems, where HTrFSs possess excellent information description capabilities and can adequately describe indecision and uncertainty information. Meanwhile, MGRSs serve as an outstanding information fusion tool that can improve the quality and level of decision-making. DMISs are better able to analyze and evaluate information and reduce the impact of disagreement on decision outcomes. The proposed architecture, therefore, provides a viable solution for MSIoTSD facing uncertainty or hesitancy in the AQE environment. Full article

As nonassociative fuzzy logic connectives, it is important to study fuzzy rough set models using overlap functions that replace the role of t-norms. Overlap functions and t-norms are logical operators with symmetry. Recently, intuitionistic fuzzy rough set and multi-granulation fuzzy rough set models have been proposed based on overlap functions. However, some results (that contain five propositions, two definitions, six examples and a proof) must be improved. In this work, we improved the existing results. Moreover, to extend the existing fuzzy rough sets, a new fuzzy covering rough set model was constructed by using the generalized overlap function, and it was applied to the diagnosis of medical diseases. First, we improve some existing results. Then, in order to overcome the limitations of the fuzzy covering rough set model based on overlap functions, a fuzzy $\beta$-covering rough set model based on generalized overlap functions was established. Third, some properties of the fuzzy $\beta$-covering rough set model based on generalized overlap functions are discussed. Finally, a multi-criteria decision-making (MCDM) method of the fuzzy $\beta$-covering rough set based on generalized overlap functions was proposed. Taking medical disease diagnosis as an example, the comparison with other methods shows that the proposed method is feasible and effective. Full article

A multigranulation rough set (MGRS) model is an expansion of the Pawlak rough set, in which the uncertain concept is characterized by optimistic and pessimistic upper/lower approximate boundaries, respectively. However, there is a lack of approximate descriptions of uncertain concepts by existing information granules in MGRS. The approximation sets of rough sets presented by Zhang provide a way to approximately describe knowledge by using existing information granules. Based on the approximation set theory, this paper proposes the cost-sensitive multigranulation approximation of rough sets, i.e., optimistic approximation and pessimistic approximation. Their related properties were further analyzed. Furthermore, a cost-sensitive selection algorithm to optimize the multigranulation approximation was performed. The experimental results show that when multigranulation approximation sets and upper/lower approximation sets are applied to decision-making environments, multigranulation approximation produces the least misclassification costs on each dataset. In particular, misclassification costs are reduced by more than 50% at each granularity on some datasets. Full article

In multigranulation environments, variable precision multigranulation rough set (VPMGRS) is a useful framework that has a tolerance for errors. Approximations are basic concepts for knowledge acquisition and attribute reductions. Accelerating update of approximations can enhance the efficiency of acquiring decision rules by utilizing previously saved information. In this study, we focus on exploiting update mechanisms of approximations in VPMGRS with the addition of granular structures. By analyzing the basic changing trends of approximations in VPMGRS, we develop accelerating update mechanisms for acquiring approximations. In addition, an incremental algorithm to update variable precision multigranulation approximations is proposed when adding multiple granular structures. Finally, extensive comparisons elaborate the efficiency of the incremental algorithm. Full article

Qian presented multigranulation rough set (MGRS) models based on Pawlak’s rough set (RS) model. There are two types of MGRS models, named optimistic MGRS and pessimistic MGRS. Recently, Shabir et al. presented an optimistic multigranulation intuitionistic fuzzy rough set (OMGIFRS) based on soft binary relations. This paper explores the pessimistic multigranulation intuitionistic fuzzy rough set (PMGIFRS) based on soft relations combined with a soft set (SS) over two universes. The resulting two sets are lower approximations and upper approximations with respect to the aftersets and foresets. Some basic properties of this established model are studied. Similarly, the MGRS of an IFS based on multiple soft relations is presented and some algebraic properties are discussed. Finally, an example is presented that illustrates the importance of the proposed decision-making algorithm. Full article

The rough set model for dual universes and multi granulation over dual universes is an interesting generalization of the Pawlak rough set model. In this paper, we present a pessimistic multigranulation roughness of a fuzzy set based on soft binary relations over dual universes. Firstly, we approximate fuzzy set w.r.t aftersets and foresets of the finite number of soft binary relations. As a result, we obtained two sets of fuzzy soft sets known as the pessimistic lower approximation of a fuzzy set and the pessimistic upper approximation of a fuzzy set—the w.r.t aftersets and the w.r.t foresets. The pessimistic lower and pessimistic upper approximations of the newly proposed multigranulation rough set model are then investigated for several interesting properties. This article also addresses accuracy measures and measures of roughness. Finally, we give a decision-making algorithm as well as examples from the perspective of application. Full article

Multigranulation rough set (MGRS) based on soft relations is a very useful technique to describe the objectives of problem solving. This MGRS over two universes provides the combination of multiple granulation knowledge in a multigranulation space. This paper extends the concept of fuzzy set Shabir and Jamal in terms of an intuitionistic fuzzy set (IFS) based on multi-soft binary relations. This paper presents the multigranulation roughness of an IFS based on two soft relations over two universes with respect to the aftersets and foresets. As a result, two sets of IF soft sets with respect to the aftersets and foresets are obtained. These resulting sets are called lower approximations and upper approximations with respect to the aftersets and with respect to the foresets. Some properties of this model are studied. In a similar way, we approximate an IFS based on multi-soft relations and discuss their some algebraic properties. Finally, a decision-making algorithm has been presented with a suitable example. Full article