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Öğe A comprehensive systematic review on machine learning application in the 5G-RAN architecture: Issues, challenges, and future directions(Academic Press, 2025) Talal, Mohammed; Garfan, Salem; Qays, Rami; Pamucar, Dragan; Delen, Dursun; Pedrycz, Witold; Alamleh, Amneh; Alamoodi, Abdullah; Zaidan, B.B.; Simic, VladimirThe fifth-generation (5G) network is considered a game-changing technology that promises advanced connectivity for businesses and growth opportunities. To gain a comprehensive understanding of this research domain, it is essential to scrutinize past research to investigate 5G-radio access network (RAN) architecture components and their interaction with computing tasks. This systematic literature review focuses on articles related to the past decade, specifically on machine learning models integrated with 5G-RAN architecture. The review disregards service types like the Internet of Medical Things, Internet of Things, and others provided by 5G-RAN. The review utilizes major databases such as IEEE Xplore, ScienceDirect, and Web of Science to locate highly cited peer-reviewed studies among 785 articles. After implementing a two-phase article filtration process, 143 articles are categorized into review articles (15/143) and learning-based development articles (128/143) based on the type of machine learning used in development. Motivational topics are highlighted, and recommendations are provided to facilitate and expedite the development of 5G-RAN. This review offers a learning-based mapping, delineating the current state of 5G-RAN architectures (e.g., O-RAN, C-RAN, HCRAN, and F-RAN, among others) in terms of computing capabilities and resource availability. Additionally, the article identifies the current concepts of ML prediction (categorical vs. value) that are implemented and discusses areas for future enhancements regarding the goal of network intelligence. © 2024 Elsevier LtdÖğe A Design of Fuzzy Rule-Based Classifier for Multiclass Classification and Its Realization in Horizontal Federated Learning(Institute of Electrical and Electronics Engineers Inc., 2024) Hu, Xingchen; Zhu, Xiubin; Yang, Lan; Pedrycz, Witold; Li, ZhiwuPattern recognition plays an important role in the process of knowledge discovery. The construction of easily describable and interpretable classification rules is of vital importance in pattern recognition. In this study, we propose a development of fuzzy rule-based classifier for multiclass classification problems and elaborate on a privacy-preserving realization of the proposed methodology in the presence of decentralized datasets. Fuzzy rule-based models provide an effective and efficient alternative for characterizing the complex relationship between the input variables and target classes. An overall design process of the proposed classifier consists of two main phases: (a) formation of information granules (clusters) to reveal the underlying structure of the training data, and (b) construction of local classification rules whose outputs reflect the probability distribution of the input data over all the classes. The constructed information granules form a backbone of the architecture of the classifier while the optimization of the parameters of local rules is carried out through using a gradient descent method with the guidance of the cross-entropy loss function. Furthermore, a federated gradient-based optimization mechanism is utilized to construct fuzzy classifier in a privacy-preserving approach. The originalities of the proposed methodology are twofold: first, a design of fuzzy classifier through the synergy of cluster-centric architecture and the cross-entropy loss function is presented. Second, we augment the proposed fuzzy classifier based on the concept of federated learning such that it can learn from distributed data without sacrificing data security and confidentiality. Experiments are carried out on a two-dimensional synthetic dataset and a number of real-world datasets. Experimental results show the excellent classification capability of the proposed classifier realized in the centralized way and in the federated learning environment. © 1993-2012 IEEE.Öğe A Design of Fuzzy Rule-Based Classifier for Multiclass Classification and Its Realization in Horizontal Federated Learning(Institute of Electrical and Electronics Engineers Inc., 2024) Hu, Xingchen; Zhu, Xiubin; Yang, Lan; Pedrycz, Witold; Li, ZhiwuPattern recognition plays an important role in the process of knowledge discovery. The construction of easily describable and interpretable classification rules is of vital importance in pattern recognition. In this study, we propose a development of fuzzy rule-based classifier for multiclass classification problems and elaborate on a privacy-preserving realization of the proposed methodology in the presence of decentralized datasets. Fuzzy rule-based models provide an effective and efficient alternative for characterizing the complex relationship between the input variables and target classes. An overall design process of the proposed classifier consists of two main phases: (a) formation of information granules (clusters) to reveal the underlying structure of the training data, and (b) construction of local classification rules whose outputs reflect the probability distribution of the input data over all the classes. The constructed information granules form a backbone of the architecture of the classifier while the optimization of the parameters of local rules is carried out through using a gradient descent method with the guidance of the cross-entropy loss function. Furthermore, a federated gradient-based optimization mechanism is utilized to construct fuzzy classifier in a privacy-preserving approach. The originalities of the proposed methodology are twofold: first, a design of fuzzy classifier through the synergy of cluster-centric architecture and the cross-entropy loss function is presented. Second, we augment the proposed fuzzy classifier based on the concept of federated learning such that it can learn from distributed data without sacrificing data security and confidentiality. Experiments are carried out on a two-dimensional synthetic dataset and a number of real-world datasets. Experimental results show the excellent classification capability of the proposed classifier realized in the centralized way and in the federated learning environment. © 1993-2012 IEEE.Öğe A Development of Fuzzy-Rule-Based Regression Models Through Using Decision Trees(Institute of Electrical and Electronics Engineers Inc., 2024) Zhu, Xiubin; Hu, Xingchen; Yang, Lan; Pedrycz, Witold; Li, ZhiwuThis article presents a design and realization of fuzzy rule-based regression models based on standard decision trees. A two-phase design of rule-based model is offered in this study to provide a good alternative to cope with high dimensional data. We first build a standard decision tree on the basis of variables in order to discover homogeneous subsets of the data. Subsequently, a collection of fuzzy rules is induced by the decision tree with the aim of reflecting the underlying phenomenon. The calculation of membership degrees and the refinement of fuzzy rules on the basis of data located in each partition exhibit a substantial level of originality and innovation. The introduction of fuzziness into decision rules helps to characterize and quantify the continuous change of output values near the boundary areas. The constructed fuzzy rules could efficiently handle the ambiguity and vagueness in the experimental evidence and offer an accurate characterization of the nonlinearities of the input-output relationships. The developed fuzzy models could achieve much higher prediction accuracy in comparison with traditional decision trees of the same size and fuzzy rule-based models with the same number of rules. Another advantage of the proposed methodology comes with the evident readability of the formed fuzzy rules. A series of experiments is reported to demonstrate the superiority of the proposed architecture of fuzzy rule-based models over traditional fuzzy rule-based models and decision trees. © 1993-2012 IEEE.Öğe A distributed algorithm with network-independent step-size and event-triggered mechanism for economic dispatch problem(John Wiley and Sons Ltd, 2024) Chen, Baitong; Yang, Jianhua; Lu, Wei; Pedrycz, Witold; Sun, ChanghaiThe economic dispatch problem (EDP) poses a significant challenge in energy management for modern power systems, particularly as these systems undergo expansion. This growth escalates the demand for communication resources and increases the risk of communication failures. To address this challenge, we propose a distributed algorithm with network-independent step sizes and an event-triggered mechanism, which reduces communication requirements and enhances adaptability. Unlike traditional methods, our algorithm uses network-independent step sizes derived from each agent's local cost functions, thus eliminating the need for detailed network topology knowledge. The theoretical derivation identifies a range of step size values that depend solely on the objective function's strong convexity and the gradient's Lipschitz continuity. Furthermore, the proposed algorithm is shown to achieve a linear convergence rate, assuming the event triggering threshold criteria are met for linear convergence. Numerical experiments further validate the effectiveness and advantages of our proposed distributed algorithm by demonstrating its ability to maintain good convergence characteristics while reducing communication frequency. © 2024 John Wiley & Sons Ltd.Öğe A Generalized f-Divergence With Applications in Pattern Classification(IEEE Computer Society, 2025) Xiao, Fuyuan; Ding, Weiping; Pedrycz, WitoldIn multisource information fusion (MSIF), Dempster-Shafer evidence (DSE) theory offers a useful framework for reasoning under uncertainty. However, measuring the divergence between belief functions within this theory remains an unresolved challenge, particularly in managing conflicts in MSIF, which is crucial for enhancing decision-making level. In this paper, several divergence and distance functions are proposed to quantitatively measure discrimination between belief functions in DSE theory, including the reverse evidential KullbackLeibler (REKL) divergence, evidential Jeffrey's (EJ) divergence, evidential JensenShannon (EJS) divergence, evidential χ2(Eχ2) divergence, evidential symmetric χ2 (ESχ2) divergence, evidential triangular (ET) discrimination, evidential Hellinger (EH) distance, and evidential total variation (ETV) distance. On this basis, a generalized f-divergence, also called the evidential f-divergence (Ef divergence), is proposed. Depending on different kernel functions, the Ef divergence degrades into several specific classes: EKL, REKL, EJ, EJS, Eχ2 and ESχ2 divergences, ET discrimination, and EH and ETV distances. Notably, when basic belief assignments (BBAs) are transformed into probability distributions, these classes of Ef divergence revert to their classical counterparts in statistics and information theory. In addition, several Ef-MSIF algorithms are proposed for pattern classification based on the classes of Ef divergence. These Ef-MSIF algorithms are evaluated on real-world datasets to demonstrate their practical effectiveness in solving classification problems. In summary, this work represents the first attempt to extend classical f-divergence within the DSE framework, capitalizing on the distinct properties of BBA functions. Experimental results show that the proposed Ef-MSIF algorithms improve classification accuracy, with the best-performing Ef-MSIF algorithm achieving an overall performance difference approximately 1.22 times smaller than the suboptimal method and 14.12 times smaller than the worst-performing method. © 1989-2012 IEEE.Öğe A Granular Aggregation of Multifaceted Gaussian Process Models(Institute of Electrical and Electronics Engineers Inc., 2024) Yang, Lan; Zhu, Xiubin; Pedrycz, Witold; Li, Zhiwu; Hu, XingchenThis study focuses on the construction of granular Gaussian process models completed at different levels of granularity and the emergence of higher-type granular outputs through aggregating the individual prediction results. Each Gaussian process model is instantiated utilizing granular data (or information granules) to enhance algorithmic efficiency and can be tailored to specific levels of precision (granularity). The overall design methodology emphasizes human centricity in system modeling by focusing on both the interpretability and accuracy of the resulting models. First, clustering algorithms are applied to construct information granules that provide a comprehensive overview of the experimental evidence. As the number of information granules grows, the existing knowledge imbedded within data could be perceived and described at increased levels of details. Information granules are built in an augmented feature space constructed by concatenating the input and output variables. Next, Gaussian process models are constructed on a basis of the information granules formed at different levels of abstraction. Subsequently, the confidence intervals are transformed to intervals and the reconciliation of the predictions produced by individual models, which offer different perspectives on the system, leads to the emergence of more abstract entities (such as type-2 intervals/fuzzy sets, etc.) rather than plain numbers. The efficacy of the comprehensive model is measured by the coverage and specificity criteria of the granular outputs. Experimental studies conducted on a synthetic dataset and a number of real-world datasets validated the effectiveness and adaptability of the proposed methodology. © 1993-2012 IEEE.Öğe A large-scale supplier evaluation approach for circular economy in the presence of circular criteria interactions and weight consistency(Elsevier ltd, 2025) Wang, Jiali; Jiang, Wenqi; Huang, Ting; Pedrycz, WitoldCircular economy (CE) is an economic model in which we achieve sustainable development through resource recovery, reuse, and remanufacturing. Large-scale supplier evaluation is crucial for ensuring the sustainability of the CE supply chain and efficient utilization of resources. Especially, criterion interaction and consistency of criterion weights are two key factors of large suppliers' evaluation in CE. However, current research often overlooks these key factors, this study proposes a large-scale supplier evaluation approach in CE to address these issues. The novel aspects of the proposed approach come with considering the interaction between circular and non-circular criteria, as well as eliminating the impact of large-scale complex information on the consistency of criterion weights. Firstly, large-scale hesitant evaluation information is fused by evidence reasoning, and interaction rules between circular and non-circular criteria are established. Then, the interaction weights of the criteria are obtained based on the interaction of circular criteria, and the comprehensive criteria weights are determined by an improved best-worst method. Next, the decision makers' weights are generated by the utility value of the circular criterion. Finally, the results of numerical example and analysis show that 86% of the supplier ranking results are stable, and the consistency of the proposed approach is 0.9757, indicating that the proposed approach exhibits high validity and reliability. It emphasizes the significance of the supplier's circular ability in CE and reduces the interference of large-scale complex information on the consistency of evaluation results.Öğe A Linguistically Interpretable Deep Fuzzy Classification System With Feature Transformation and Reconstruction(Institute of Electrical and Electronics Engineers Inc., 2024) Zang, Zhen Sheng; Yin, Rui; Lu, Wei; Pedrycz, Witold; Zhang, Li-YongClassification tasks involving tabular data often require a balance between exceptional performance and heightened interpretability. To address this challenge, we propose a linguistically interpretable deep fuzzy classification system called FFT-FFR-RBFC. The system employs a fuzzy feature transformation (FFT) unit, formed by employing a stacked architecture of multiple Takagi-Sugeno-Kang fuzzy models with nonlinear conclusions, to distill high-level fuzzy features from the input data, a rule-based fuzzy classifier unit to perform classification using these features, while a fuzzy feature reconstruction unit in tandem with the FFT to enhance the system's linguistic interpretability by remapping the high-level features back to their original space. The proposed approach is optimized by minimizing a composite loss function that balances classification and reconstruction losses, ensuring a harmonious interplay between performance and interpretability. Comprehensive evaluation across 20 diverse datasets demonstrates that the system's is exceptionally promising, particularly for high-dimensional or large-scale tabular data classification tasks, achieving superior classification performance while maintaining a high degree of interpretability. © 1993-2012 IEEE.Öğe A New Neurodynamics-Based Model for Fuzzy Convex Optimization Problems with Fuzzy Coefficients and General Constraints(Institute of Electrical and Electronics Engineers Inc., 2024) Chen, Jiqiang; Ma, Litao; Pedrycz, WitoldFuzzy convex optimization problems with fuzzy coefficients (FCOPFCs) arise in many applications. Although many neurodynamics-based models have been proposed for solving FCOPFCs, most of them are designed for FCOPFCs with equality or inequality constraints only. However, in many applications, the FCOPFCs often come with both equality and inequality constraints (general constraints, for short), so most of the neurodynamics-based models no longer work in these situations. Therefore, this article aims to construct a new model for FCOPFCs with general constraints to extend the applications of neurodynamics-based models. First of all, based on fuzzy set theory, the original FCOPFCs with general constraints is transformed into a series of interval programming tasks and further transformed into crisp optimization problems with weights. Then, a novel continuous-time neurodynamics-based model with a single-layer structure is established to solve the crisp optimization problem with weights. Further, we discuss the global existence and prove the stability of state solutions. The theoretical results show that the state solutions reach the feasible region within finite time and converge to the optimal solution with the smallest 2-norm. Simulation results completed for three kinds of FCOPFCs show the validity of the approach, and the results in real-world applications demonstrate the excellent performance of the proposed model. © 2024 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.Öğe A Relative Projection-Based Multiattribute Group Decision-Making Model with Noncooperative Behavior Management and Application to NEV Supplier Selection(Institute of Electrical and Electronics Engineers Inc., 2024) Liu, Zulin; Liu, Fang; Tu, Huonian; Pedrycz, Witold; Yao, ZuofangThis article reports a novel consensus model where a group of internal and external experts evaluate alternatives under multiple attributes and provide mutual evaluations. First, different from previous studies, the cognitive and interest conflicts of internal and external experts are considered simultaneously. But interest conflict is emphasized for internal experts, and cognitive conflict is mainly considered for external experts. Second, we explore the categorization and management methods of noncooperative behaviors (NCBs) of experts. The relative projection-based indexes are proposed for the first time to measure the degrees of cognitive and interest conflicts by using multiattribute preference matrices (MAPMs) and the weight vectors of attributes. A group of experts are divided into three categories and the corresponding management strategies are developed. Third, we investigate the consensus mechanism among experts with cognitive and interest conflicts. For reaching an acceptable consensus level, an adjustment process is proposed to revise some local entries in MAPMs and mutual evaluation matrix (MEM). A penalty mechanism is further established to dynamically update the weights of experts. An algorithm is designed to capture the consensus reaching process in multiattribute group decision making, where internal and external experts are distinguished by proposing a parameter. Finally, the high-performance battery supplier selection of new energy vehicle is studied to illustrate the proposed model. The results reveal that the efficiency of reaching consensus can be enhanced by using the developed model with effective management of NCBs. © 2024 IEEE. Personal use is permitted, but republication/redistribution requires IEEE permission.Öğe A Vertical Federated Multi-View Fuzzy Clustering Method for Incomplete Data(Institute of Electrical and Electronics Engineers Inc., 2025) Li, Yan; Hu, Xingchen; Yu, Shengju; Ding, Weiping; Pedrycz, Witold; Kiat, Yeo Chai; Liu, ZhongMulti-view fuzzy clustering (MVFC) has gained widespread adoption owing to its inherent flexibility in handling ambiguous data. The proliferation of privatization devices has driven the emergence of new challenge in MVFC researches. Federated learning, a technique that can jointly train without directly using raw data, has gain significant attention in decentralized MVFC. However, their applicability depends on the assumptions of data integrity and independence between different views. In fact, while within distributed environments, data typically exhibits two challenging problems: (1) multiple views within a single client; (2) incomplete data. Existing methods exhibit limitations in effectively addressing these challenges. Hence, in this study, we aim at achieving the effective clustering for incomplete data by a novel vertical federated MVFC framework. Specifically, a unified clustering framework is designed to capture both local client learning and global server training. For the local client learning, the data reconstruction strategy and prototype alignment strategy are introduced to ensure the preservation of data structure and refinement of clustering relationships, which mitigates the impact of incomplete data. Meanwhile, the global training process implements aggregation based on client-specific information. The whole process is realized based on the unified fuzzy clustering framework, promoting collaborative learning between client-specific and server information. Theoretical analyses and extensive experiments are carefully conducted to validate the effectiveness and efficiency of the proposed method from multiple perspectives. © 1993-2012 IEEE.Öğe Accelerated Fuzzy C-Means Clustering Based on New Affinity Filtering and Membership Scaling(Ieee Computer Soc, 2023) Li, Dong; Zhou, Shuisheng; Pedrycz, WitoldFuzzy C-Means (FCM) is a widely used clustering method. However, FCM and its many accelerated variants have low efficiency in the mid-to-late stage of the clustering process. In this stage, all samples are involved in updating their non-affinity centers, and the membership grades of most samples, whose assignments remain unchanged, are still updated by calculating the sample-center distances. All these factors lead to the algorithms converging slowly. In this paper, a new affinity filtering technique is developed to recognize a complete set of non-affinity centers for each sample with low computations. Then, a new membership scaling technique is suggested to set the membership grades between each sample and its non-affinity centers to 0 and maintain the fuzzy membership grades for others. By integrating these two techniques, FCM based on new affinity filtering and membership scaling (AMFCM) is proposed to accelerate the whole convergence process of FCM. Numerous experimental results performed on synthetic and real-world data sets have shown the feasibility and efficiency of the proposed algorithm. Compared with state-of-the-art algorithms, AMFCM is significantly faster and more effective. For example, AMFCM reduces the number of FCM iterations by 80% on average.Öğe Accelerating the integration of the metaverse into urban transportation using fuzzy trigonometric based decision making(Pergamon-Elsevier Science Ltd, 2024) Deveci, Muhammet; Pamucar, Dragan; Gokasar, Ilgin; Martinez, Luis; Koppen, Mario; Pedrycz, WitoldMetaverse is defined as a fictional universe that could serve as a simulation environment of reality. Beginning in the past with games, it becomes increasingly integrated into human life as time passes. Metaverse usage is inevitable in every aspect of life. One of its potential application areas could be urban transportation. A novel fuzzy trigonometric based on the combination of the Full Consistency Method (FUCOM) and Combined Compromise Solution (CoCoSo) is proposed to rank three alternatives with twelve criteria under four major aspects: managerial, safety, user, and urban mobility. In the first stage, fuzzy FUCOM methods are used to calculate the weights of the criteria. In the second stage, the fuzzy trigonometric based CoCoSo method is applied to evaluate and rank the alternatives. The proposed model enables the nonlinear processing of complex and uncertain information using fuzzy trigonometric functions. The findings demonstrate focusing on a particular age group can make it easier to integrate the metaverse with urban transportation. The findings of this study have the potential to serve as a guide for decision-makers. The metaverse-based applications could be started by policymakers, which is a promising opportunity with potential boundaries beyond human comprehension making this statement weaker.Öğe Adaptive Nonstationary Fuzzy Neural Network(Elsevier, 2024) Chang, Qin; Zhang, Zhen; Wei, Fanyue; Wang, Jian; Pedrycz, Witold; Pal, Nikhil R.Fuzzy neural network (FNN) plays an important role as an inference system in practical applications. To enhance its ability of handling uncertainty without invoking high computational cost, and to take variations in rules into consideration as well, we propose a new inference framework-nonstationary fuzzy neural network (NFNN). This NFNN is composed of a series of zero -order TSK FNNs with the same structure but using slightly perturbed fuzzy sets in the corresponding neurons, which is inspired from the non -stationary fuzzy sets and can mimic the variation in human's decision -making process. In order to obtain a concise and adaptive rule base for NFNN, a modified affinity propagation (MAP) clustering method is proposed. The MAP can determine the number of rules in an adaptive manner, and is used to initialize the rule parameters of NFNN, which we call Adaptive NFNN (ANFNN). Numerical experiments have been carried out over 17 classification datasets and three regression datasets. The experimental results demonstrate that ANFNN exhibits better accuracy, generalization ability, and fault -tolerance ability compared with the classical type -1 fuzzy neural network. In 15 of the 17 classification datasets, ANFNN achieves the same or better accuracy performance compared to interval type -2 FNNs with about half time consumed. This work confirms the feasibility of integrating simplestructured type -1 TSK FNNs to achieve the performance of interval type -2 FNNs, and proves that ANFNN can be a more accurate and reliable alternative to classical type -1 FNN.Öğe Advantage prioritization of digital carbon footprint awareness in optimized urban mobility using fuzzy Aczel Alsina based decision making(Elsevier, 2024) Deveci, Muhammet; Gokasar, Ilgin; Pamucar, Dragan; Zaidan, Aws Alaa; Wei, Wei; Pedrycz, WitoldCity governments prioritize mobility in urban planning and policy. Greater mobility in a city leads to happier citizens. Although enhanced urban mobility is helpful, it comes with costs, notably in terms of climate change. Transportation systems that enable urban mobility often emit greenhouse gases. Cities must prioritize digital carbon footprint awareness. Cities may reduce the environmental impact of urban mobility while keeping its benefits by close monitoring and reducing the carbon footprint of digital technologies like transportation applications, ride-sharing platforms, and smart traffic control systems. The aim is to advantage prioritize three alternatives, namely doing nothing, upgrading and optimizing data centers and networks, and using renewable energy sources for data centers and networks to minimize the digital carbon footprint using the proposed decision making tool. This study consists of two stages. In the first stage, fuzzy Aczel-Alsina functions (fuzzy Aczel-Alsina weighted assessment - ALWAS method) based Ordinal Priority Approach (OPA) is proposed to find the weights of criteria. Secondly, fuzzy ALWAS Combined Compromise Solution (CoCoSo) model improved to evaluate and choose the best alternative among the three alternatives. The improved ALWAS-CoCoSo model enables flexible nonlinear processing of uncertain information and simulation of different risk levels. Besides, we proposed the improved fuzzy OPA algorithm for processing uncertain and incomplete information. The case study is provided to the decision-makers to advantage prioritize the alternatives based twelve criteria organized into four aspects, including digital carbon footprint, externalities, technical capability, and economics. The ranking results reveal that A(3) = 2.445 is the best among the three alternative, while A(1) = 1.705 is the worst alternative. The results show that the best way to reduce the digital carbon footprint is to use renewable energy sources to power data centers and networks (A(3)).Öğe Aggregation of Basic Uncertain Information With Two-Step Aggregation Frame(Ieee-Inst Electrical Electronics Engineers Inc, 2024) Jin, Lesheng; Chen, Zhen-Song; Pedrycz, Witold; Senapati, Tapan; Yatsalo, Boris; Mesiar, Radko; Beliakov, GlebThere exist various categories of uncertain information, and their corresponding methods of aggregation may also vary. At present, there exists a dearth of specifically tailored techniques for aggregating basic uncertain information (BUI). The present study introduces a two-step aggregation frame that is applicable to inputs of both real-valued and BUI-valued inputs. In the process of constructing such a frame, several novel notions and definitions are introduced. These comprise of extended aggregation operators with respect to a finite set and to a collection of subsets of the set, some certainty independent BUI aggregation and some certainty dependent BUI aggregation, BUI merging operators and BUI aggregation operators, BUI-valued min operator, and BUI-valued Sugeno integral. Some corresponding deductions, necessary reasoning and numerical examples are presented.Öğe An incremental preference elicitation-based approach to learning potentially non-monotonic preferences in multi-criteria sorting(Elsevier b.v., 2025) Li, Zhuolin; Zhang, Zhen; Pedrycz, WitoldLeveraging assignment example preference information, to determine the shape of marginal utility functions and category thresholds of the threshold-based multi-criteria sorting (MCS) model, has emerged as a focal point of current research within the realm of MCS. Most studies assume decision makers can provide all assignment example preference information in batch and that their preferences over criteria are monotonic, which may not align with practical MCS problems. This paper introduces a novel incremental preference elicitation- based approach to learning potentially non-monotonic preferences in MCS problems, enabling decision makers to progressively provide assignment example preference information. Specifically, we first construct a max- margin optimization-based model to model potentially non-monotonic preferences and inconsistent assignment example preference information in each iteration of the incremental preference elicitation process. Using the optimal objective function value of the max-margin optimization-based model, we devise information amount measurement methods and question selection strategies to pinpoint the most informative alternative in each iteration within the framework of uncertainty sampling inactive learning. Once the termination criterion is satisfied, the sorting result for non-reference alternatives can be determined through the use of two optimization models, i.e., the max-margin optimization-based model and the complexity controlling optimization model. Subsequently, two incremental preference elicitation-based algorithms are developed to learn potentially non-monotonic preferences, considering different termination criteria. Ultimately, we apply the proposed approach to a firm financial state rating problem to elucidate the detailed implementation steps, and perform computational experiments on both artificial and real-world data sets to compare the proposed question selection strategies with several benchmark strategies.Öğe An overall framework of modeling, clustering, and evaluation for trapezoidal information granules(IEEE-INST electrical electronics engineers, 2024) Tang, Yiming; Gao, Jianwei; Pedrycz, Witold; Xi, Lei; Ren, FujiIn existing granular clustering algorithms, the design of coverage and specificity does not fully capture the inherent structural characteristics of granular data together with the optimization issue, and the current weight setting for the granular data is not sufficient. To address these problems, in this study, the trapezoidal information granule, which is rarely studied before, is concentrated, and we come up with a novel granular clustering algorithm called the weighted possibilistic fuzzy c-means algorithm for trapezoidal granularity (WPFCM-T). First, under the acknowledged principle of justifiable granularity, novel functions of coverage and specificity are designed for trapezoidal information granules, considering the internal characteristics of such granules. The idea of particle swarm optimization (PSO) is exploited to upgrade the established granular data, and then the trapezoidal information granule construction (TIGC) method is proposed to realize granular modeling. Second, an exponential weight is constructed with regard to coverage and specificity, while a novel distance via $\alpha$-cuts is given. The possibilistic fuzzy c-means structure is introduced into granular clustering, in which the new weight and distance are integrated, resulting in the proposed WPFCM-T algorithm. Third, the RC is studied to evaluate granular clustering, and hence an overall framework including granular modeling, clustering, and evaluation is constructed. Finally, through experiments completed on artificial datasets, UCI datasets, large datasets, high-dimensional datasets, and noisy datasets, WPFCM-T has superior granular data reconstruction ability by contrast with other granular clustering algorithms, indicating that the granular clustering performance of WPFCM-T is better than the others.Öğe Analysis of power asymmetry conflict based on fuzzy options graph models(Elsevier, 2024) Chen, Lu; Pedrycz, Witold; Xu, HaiyanAsymmetric power conflicts occur frequently. Because of the complexity of the conflict as well as the vagueness of the decision makers' cognition, it becomes urgent and highly motivated to propose an appropriate method to solve power asymmetry conflict. In this study, we consider that decision makers provide option choices quantified by some degrees of membership. The choice of an option is determined by the thresholds of selection degree. At the same time, due to the influence of the power, the follower adjusts its degree of option choice to reach consensus with the leader. The computational rules determining fuzzy truth value are given, and a fuzzy truth value option prioritization method is proposed to calculate the ranking of the states, where the states ordering is related to the fuzzy degree of option selection. Different from the previous studies, this paper is the first one to study the asymmetric power conflict from the perspective of options, considering the psychological threshold of decision maker for option selection, and pointing out that the option choice is described with the fuzzy values rather than being treated as two-valued (Boolean). Furthermore, the introduced stability analysis also reflects the interaction of the options of different decision makers, which makes the proposal being more in rapport with real-world scenarios. Finally, a case study of carbon emission reduction power asymmetry conflict in supply chain is studied to demonstrate the performance of the proposed method.
