Fuzzy Model Research Articles

Enchanting dynamics: Juvenile and adult predators with prey model in an intuitionistic fuzzy environment

This study represents an interaction model including juvenile and adult predators along with prey, involving key characteristics like the inability of juvenile predators to reproduce, the impact of adult predators on juvenile growth rates and the transformation of some juveniles to adulthood. Furthermore, it is supposed that adult predators intake prey for sustenance, and the logistic growth of prey is assumed in the non-appearance of adult predators. Intra-species competition among adult predators, together with predation of juveniles and chasing, is conveyed. To tackle the imprecise biological parameters, most parametric values are considered as triangular intuitionistic fuzzy numbers. The model is further processed into an intuitionistic fuzzy model using the Hukuhara derivative and Yager’s ranking method is implemented to make the model crispified. Non-negativity and boundedness of the model are explored, after that, an investigation of possible equilibrium points is discussed. Local and global stability analyses close to these points are supervised. The study accentuates the significant influence of uncertain model parameters on the solution. Especially, uncertain estimates of intra-species competition among adult predators remarkably regulate the model’s stability. Extended uncertainty in intra-species competition for prey, although, is discovered to stabilize the system. In addition, increased consumption of juvenile predators by adult predators is observed to provide the system’s instability.

Identifying Key Factors of Reputational Risk in Finance Sector Using a Linguistic Fuzzy Modeling Approach

Management of reputational risk is crucial for financial institutions to establish a solid foundation for strategic decisions, gain customer trust, and enhance resilience against environmental adversities, as they largely operate on digital platforms. Since this becomes even more significant as online transactions and digital interactions amplify the visibility and potential impact of reputational issues in the context of electronic commerce, it is essential to thoroughly investigate environmental factors to achieve a comprehensive understanding of reputational risk. However, measuring and evaluating their influence on reputational risk is challenging due to their inherent connection to human perception. This study aims to explore the factors influencing reputational risk of financial organizations to mitigate potential reputational losses by addressing uncertainties associated with concepts such as vagueness. The employed methodology integrates the Decision-Making Trial and Evaluation Laboratory and Fuzzy Cognitive Map techniques using linguistic fuzzy terms. This approach focuses on both the direct effects of factors on reputational risk and the indirect effects arising from interdependencies between factors. Linguistic fuzzy variables enable us to consider the hesitation of the experts and the vagueness of human judgment. To validate the results, factors are also weighted using the fuzzy Stepwise Weight Assessment Ratio Analysis (SWARA) method. The most influential factors identified by both methods are market value, revenue, risk culture, shareholder value, firm performance, reputation awareness, and return on equity. Additionally, factors affecting other factors include firm performance, revenue, and growth opportunities.

Compressive strength of nano concrete materials under elevated temperatures using machine learning

In this study, four Artificial intelligence (AI) - based machine learning models were developed to estimate the Residual compressive strength (RCS) value of concrete supported with nano additives of Nanocarbon tubes (NCTs) and Nano alumina (NAl), after exposure to elevated temperatures ranging from 200 to 800 degrees. These models were developed via adapting meta- heuristic models including the Water cycle algorithm (WCA), Genetic algorithm (GA), and classical AI models of Artificial neural networks (ANNs), Fuzzy logic models (FLM), in addition to the statistical method of Multiple linear regression (MLR). 156 post heating experimental results available as a literature data (represents four input parameters of temperature change, heat exposure duration, nanomaterial type, and replacement proportion) are used to achieve the study’s objective. Results of the developed models demonstrated that ANN and FLM have strong potential in predicting RCS. However, it is often infeasible to generate practical equations that relate input and output variables from these models. Upon analysing the results of the WCA and GA, it was found that WCA yielded the most accurate predictions based on all performance indicators. Furthermore, RCS prediction equations with superior accuracy were derived utilizing the meta-heuristic AI models of WCA and GA, with Mean absolute errors (MAEs) of 3.09 kg/cm² and 3.53 kg/cm² for the training, 1.91 kg/cm² and 2.72 kg/cm² for the validation, and 1.91 kg/cm² and 2.72 kg/cm² for the testing data sets, respectively. Additionally, sensitivity analysis via neural networks weights and SHAP investigation were performed to reveals the impact and relationship of the input variables with the output variables. Both techniques reveal that temperature degree and time of exposure had the highest positive impact on RCS value, followed by NAl and NCTs, in order.

Approximating technology innovation performance with fuzzy approach

Purpose This study aims to construct a framework to evaluate technology innovation performance (TIP) of manufacturing organizations by adopting a fuzzy-based approach. In very short time, the world’s economic order has been reformed by economic globalization, thereby bringing new challenges as well as opportunities for the manufacturing industries. Policy makers encounter different decisions that require the use of various types of data in their decision-making process. These challenges raised the necessity of measuring innovation capability, which is critical issue for decision makers in today’s competitive world. The research results reveal the complexity of the path to technology innovation evaluation, constituting a novel contribution to the literature. Design/methodology/approach It is difficult for decision makers to make appropriate and effective decisions without knowing the innovation capability of companies in a particular sector or a region. As a result, not only on a macro but also on a micro level, an integrated and complete technique of measuring, estimating and even projecting innovation performance is necessary. In light of above mentioned facts, the present study proposes a technology innovation performance evaluation system of manufacturing organizations using fuzzy logic. Findings A model has been developed to be beneficial for any kind of organization where TIP evaluation is important consideration for enhancing manufacturing performance. Fuzzy control is used to determine the overall performance index by combining results of the TIP in selected criteria, which will certainly ensure suitability of the concerned organizations during performance rating calculations. Originality/value This study elaborates a fuzzy model to predict TIP with fuzzy rules. This is the first time a TIP evaluation model is developed using fuzzy approach that will be applicable for any kind of manufacturing industry where TIP evaluation is considered to be significantly important for cooperation’s to sustain competitiveness in the dynamic landscape.

Metamorphosing forex: advancements in volatility forecasting using a modified fuzzy time series framework

The interplay of exchange rates among nations significantly influences both international and domestic trade, underscoring the pivotal role of the foreign exchange market (Forex) in a country's economic landscape. Forex fluctuations have a significant impact on the everyday lives of both government agencies and the public population, directly influencing a country's prosperity or misfortune. This work proposes an advanced fuzzy time series model that incorporates domain universe sub-partitioning, parameter adjustment optimization methodologies, and interval forecasting methods. We utilized this model to examine annual exchange rate patterns between the Pakistani rupee (PKR) and the US dollar (US$), comparing its forecast accuracy to that of other models. Our proposed methodology outperformed existing methodologies in terms of forecasting precision, providing stakeholders with valuable insights for making informed, data-driven business decisions that benefit both individual firms and the country overall.

Development of a fuzzy analytic hierarchy process model, sensitivity analysis, and addressing barriers to additive manufacturing implementation in small- and medium-sized enterprises (SMEs)

Additive manufacturing (AM) is gaining popularity worldwide due to its potential to revolutionize manufacturing processes, improve product customization, and reduce waste. Nevertheless, small- and medium-sized enterprises (SMEs) encounter major challenges when implementing AM technologies. The objective of this research is to utilize the fuzzy analytic hierarchy process (FAHP) to identify and prioritize the critical challenges that impede the implementation of AM for SMEs. The study employs a two-stage methodology. First, a thorough literature review and expert discussions identify 15 major barriers to AM adoption. Second, a systematic model is proposed to establish a ranking of these barriers, which is based on the FAHP. The results are validated using sensitivity analysis to ensure the robustness of the findings. Additionally, potential solutions to overcome these barriers are discussed. The research indicates that the two most significant barriers for SMEs are the high costs of equipment and the scarcity of skilled designers. The model that has been presented is a valuable resource for SME managers and practitioners, as it allows them to make strategic and informed decisions that facilitate the efficient implementation of AM. This research is groundbreaking in its comprehensive analysis of the prioritization and ranking of AM implementation barriers, with a particular emphasis on SMEs. It offers essential insights for future research and practical applications.

Reliable Finite‐Time Control for Nonlinear Chaotic Semi‐Markov Jump Systems With Incomplete Transition Rates

ABSTRACTThis article studies the finite‐time control problem for a class of nonlinear chaotic semi‐Markov jump systems with incomplete transition rates described by the T‐S fuzzy model approach. As a means to depict the dynamical properties pertaining to the examined system, parametric uncertainties, faults, external disturbances and input saturation are taken into consideration. The foremost objective of this study is to come up with a composite control mechanism that effectively rejects and attenuates the repercussions of faults and disturbances. In particular, we primarily built a disturbance observer in order to obtain a precise estimation of the external disturbances. After which, the fault diagnosis observer is designated to effectively estimate the faults. Specifically, a composite reliable control mechanism is developed by fusing the output of the constructed observers with the mode‐dependent fuzzy‐rule based state feedback controller. By employing suitable Lyapunov functions in conjunction with the linear matrix inequality technique, a set of mode‐dependent conditions is derived to ensure the finite‐time stochastic boundedness of the underlying closed‐loop and estimation error systems. Following this, the anticipated controller and observer gain matrices are elicited by resolving the established linear matrix inequalities. Thereafter, intending to ascertain the efficacy and usefulness of accrued theoretical findings, simulation results performed on Chua's circuit system is endowed.

Security Enhancement Scheduling Model for IoT‐Based Smart Cities Through Machine Learning Method

ABSTRACTThe Internet of Things (IoT) is rapidly evolving, and this has supported the adoption of a new computing paradigm that moves processing power to the network's edge. The job must be assigned to the computer nodes, where their associated data is available, to minimize overheads generated by data transmissions in the network, because the edge nodes have limited processing power and are vulnerable to security. Hence, the paper introduces a novel security‐enhanced scheduling model for IoT‐based smart cities utilizing machine learning techniques. Initially, nodes are initialized using the LHK‐Means algorithm. Subsequently, tasks, representing requests from multiple users to access IoT data, are scheduled. Anomaly detection tasks are then identified using an L2‐Norm‐based fuzzy model. Normal tasks are processed by the BN‐CNN model, which schedules data collection tasks through the initialized IoT device nodes. Comparative analysis with existing models illustrates the effectiveness of the proposed approach in terms of accuracy, precision, recall, sensitivity, specificity, and f‐measure.

Approach Based on the Ordered Fuzzy Decision Making System Dedicated to Supplier Evaluation in Supply Chain Management.

The selection of suppliers represents a pivotal aspect of supply chain management and has a considerable impact on the success and competitiveness of the organization in question. The selection of a suitable supplier is a multi-criteria decision making (MCDM) problem based on a number of qualitative, quantitative, and even conflicting criteria. The aim of this paper is to propose a novel MCDM approach dedicated to the supplier evaluation problem using an ordered fuzzy decision making system. This study uses a fuzzy inference system based on IF-THEN rules with ordered fuzzy numbers (OFNs). The approach employs the concept of OFNs to account for potential uncertainty and subjectivity in the decision making process, and it also takes into account the trends of changes in assessment values and entropy in the final supplier evaluation. This paper's principal contribution is the development of a knowledge base and the demonstration of its application in an ordered fuzzy expert system for multi-criteria supplier evaluation in a dynamic and uncertain environment. The proposed system takes into account the dynamic changes in the value of assessment parameters in the overall supplier assessment, allowing for the differentiation of suppliers based on current and historical data. The utilization of OFNs in a fuzzy model then allows for a reduction in the complexity of the knowledge base in comparison to a classical fuzzy system and makes it more accessible to users, as it requires only basic arithmetic operations in the inference process. This paper presents a comprehensive framework for the assessment of suppliers against a range of criteria, including local hiring, completeness, and defect factors. Furthermore, the potential to integrate sustainability and ESG (environmental, social, and corporate governance) criteria in the assessment process adds value to the decision making framework by adapting to current trends in supply chain management.

Dual Method for Comprehensive Evaluation of Sustainable Water Resources’ Utilization Capacity in Huangshui River in Yellow River Basin, China

The evaluation of sustainable water resources’ utilization capacity in the Huangshui Basin is essential for effective management and development in the water-scarce regions of northwest China. This research provides valuable insights into the basin’s potential capacity for sustainable water resource use by developing a comprehensive evaluation index that addresses the following three critical aspects: climate factors, water resource systems, and socio-economic conditions. The evaluation is conducted using a dual method, as follows: the fuzzy comprehensive evaluation model and the ELECTRE III evaluation method. The results indicate that the Huangshui Basin’s water resources, as a whole, exhibit a medium sustainable utilization capacity. Climatic factors and socio-economic characteristics are the main factors affecting the sustainable utilization of water resources in the Huangshui Basin. Remarkably, both methods yield consistent results, indicating that the overall sustainable utilization capacity of the Huangshui Basin’s water resources is medium. Climatic factors and socio-economic characteristics are identified as the primary aspects influencing the sustainable utilization of water resources in the basin. Based on these findings, recommendations such as enhancing the introduction of external water resources, improving water resources’ management, and implementing comprehensive remediation efforts can help to elevate the level of sustainable water use. This research not only contributes to a deeper understanding of the basin’s water resources’ dynamics, but also serves as an important reference for informed decision making regarding sustainable utilization in the Huangshui Basin.

A Novel Method for the Fuzzy Survival and Fuzzy Hazard Models of the Corticosterone Effect

To ascertain the significance of corticosterone release scores, theoretical research was conducted. We offer formulas for fuzzy Two-Parameter Weibull distributions, fuzzy Survival and Hazard functions, and related alpha-cut sets. We showed that, using fuzzy survival and hazard models based on two-parameter Weibull distributions, the smaller fuzzy survival model for the impact of corticosterone release increases and the higher fuzzy hazard model for the impact of corticosterone release decreases as the experiment termination alpha value increases. When the alpha value of the test's termination grows, the greater fuzzy survival scenario for the effect of corticosterone release decreases while the smaller fuzzy hazard models with the same effect increase.

Forecasting Non-stationary Time Series Using Deep Learning in a Fuzzy Time Series Framework and its Application to Stock Markets

Non-stationary time series prediction is challenging due to its dynamic and complex nature. Fuzzy time series models offer a promising solution for forecasting such data, but a key challenge lies in partitioning the universe of discourse, which significantly impacts forecasting accuracy. Traditional fuzzy time series models often use equal-length interval partitioning, which is more suited for stationary data and limits their adaptability to non-stationary time series. This paper introduces a novel variable-length interval partitioning method designed specifically for non-stationary time series. The developed method combines a Long Short-Term Memory (LSTM) Autoencoder with K-means clustering, enabling dynamic, data-driven partitioning that adapts to the changing characteristics of the data. The LSTM Autoencoder encodes the time series, which is clustered using K-means, and intervals are defined based on cluster centers. Furthermore, the Variable Length Interval Partitioning-based Fuzzy Time Series model (VLIFTS) is developed by incorporating this partitioning method and the concepts of Markov chain and transition probability matrix. In this model, fuzzy sets are viewed as states of a Markov chain, and transition probabilities are used in the forecasting phase. The model is validated on stock market indices Nifty 50, NASDAQ, S&P 500, and Dow Jones. Stationarity and heteroscedasticity are tested using Augmented Dickey-Fuller (ADF) and Levene's tests respectively. Statistical forecast accuracy metrics Root Mean Squared Error (RMSE) and Mean Absolute Percent Error (MAPE) show that VLIFTS significantly improves forecasting accuracy over traditional models. This hybrid approach enhances fuzzy time series modelling and can be applied to various non-stationary time series forecasting problems.

A comparative analysis of machine learning methods for display characterization

This paper explores the application of various machine-learning methods for characterizing displays of technologies LCD, OLED, and QLED to achieve accurate color reproduction. These models are formed from input (device-dependent RGB data) and output (device-independent XYZ coordinates) data obtained from three different displays. Training and test datasets are built using RGB data measured directly from the displays and corresponding XYZ coordinates measured with a high-precision colorimeter. A key aspect of this research is the application fuzzy inference systems for building interpretable models. These models offer the advantage of not only achieving good performance in color reproduction, but also providing physical insights into the relationships between the RGB inputs and the resulting XYZ outputs. This interpretability allows for a deeper understanding of the display’s behavior. Furthermore, we compare the performance of fuzzy models with other popular machine-learning approaches, including those based on neural networks and decision trees. By evaluating the strengths and weaknesses of each method, we aim to identify the most effective approach for display characterization. The effectiveness of each method is assessed by its ability to accurately reproduce and display colors, as measured by the ΔE00 visual error metric. Our findings indicate that the Fuzzy Modeling and Identification (FMID) method is particularly effective, allowing for an optimal balance between high accuracy and interpretability. Its competitive performance across all display types, combined with its valuable interpretability, provides insights for potential future calibration and optimization strategies. The results will shed light on whether machine learning methods offer an advantage over traditional physical models, particularly in scenarios with limited data. Additionally, the study will contribute to the understanding of the interpretability benefits offered by fuzzy inference systems in the context of LCD display characterization.

Robust Fault Estimation and Fault‐Tolerant Control for a Class of Fuzzy Singularly Perturbed Systems With State Time Delay Based on Learning Observer

ABSTRACTThis article studies the problem of fault estimation (FE) and dynamic output fault‐tolerant control (DOFTC) for a class of Takagi–Sugeno (T–S) fuzzy singularly perturbed systems (SPSs) which subject to time delay, external disturbance and actuator fault. A new fault estimation and fault‐tolerant control scheme was proposed and designed for the influence of the change of perturbation parameter on the singularly perturbed system. This scheme adopts the Takagi–Sugeno (T–S) fuzzy model, learning observer and dynamic output feedback fault‐tolerant mechanism, so that the system has multi‐time‐scale dynamic stability. The results show that this method has more accurate estimation effect, faster convergence speed, and very fast steady‐state response of fault‐tolerant control when faults occur. Furthermore, when constructing the Lyapunov function, the improved matrix was selected to ensure that the closed‐loop system is stable for all , and at the same time, the conservativeness of the results was reduced. Finally, the feasibility and correctness of the proposed design method were illustrated through two numerical examples.

Empowering decentralized identity systems for Web 3.0 in complex spherical fuzzy knowledge

The Web 3.0 network system, the next generation of the world wide web, incorporates new technologies and algorithms to enhance accessibility, decentralization, and security, mimicking human comprehension and enabling more personalized user interactions. The key component of this environment is decentralized identity management (DIM), embracing an identity and access management strategy that empowers computing devices and individuals to manage their digital personas. Aggregation operators (AOs) are valuable techniques that facilitate combining and summarizing a finite set of imprecise data. It is imperative to employ such operators to effectively address multicriteria decision-making (MCDM) issues. Yager operators have a significant extent of adaptability in managing operational environments and exhibit excellent effectiveness in addressing decision-making (DM) uncertainties. The complex spherical fuzzy (CSF) model is more effective in capturing and reflecting the known unpredictability in a DM application. This research endeavors to enhance the DM scenario of the Web 3.0 environment using Yager aggregation operators within the CSF environment. We present two innovative aggregation operators, namely complex spherical fuzzy Yager-ordered weighted averaging (CSFYOWA) and complex spherical fuzzy Yager-ordered weighted geometric (CSFYOWG) operators. We elucidate some structural characteristics of these operators and come up with an updated score function to rectify the drawbacks of the existing score function in the CSF framework. By utilizing newly proposed operators under CSF knowledge, we develop an algorithm for MCDM problems. In addition, we adeptly employ these strategies to handle the MCDM scenario, aiming to identify the optimal approach for ensuring the privacy of digital identity or data in the evolving landscape of the Web 3.0 era. Moreover, we undertake a comparative study to highlight the veracity and proficiency of the proposed techniques compared to the previously designed approaches.

A novel integrated soft sensing model for online cement clinker quality monitoring based on fuzzy fine-grained classification

The content of free calcium oxide (f-CaO) in cement clinker is an important index for cement quality. For the problems of multiple working conditions and unbalanced distribution of sample labels in cement clinker production, a soft sensing method of cement clinker f-CaO content based on fuzzy fine-grained classification (FF) is proposed. First, a divide-and-conquer strategy is used to divide the samples into high, medium, and low subsets according to cement clinker f-CaO and extract the fine-grained features under diverse types of multiple production conditions. Second, fuzzy classification based on the membership function is used in the FF model to solve the uncertainty of the sample categories. To ensure the rationality of the classification, the fuzzy membership rule is combined with a convolutional neural network to implement the fuzzy classification method. Finally, different feature extraction methods are proposed to be selected according to the data size of various categories of samples. After experimental validation, the evaluation metrics of RMSE decreased by 4.5 % and R2increased by 17.8 % for the direct classification model compared to the single model. The RMSE of the fuzzy classification model over the direct classification model was again reduced by 2.34 % and R2was again improved by 7.24 %, showing the effectiveness of the proposed soft measurement model.

A sustainable network design for municipal solid waste management considering waste-to-energy conversion under uncertainty

This research proposes a sustainable municipal solid waste management (MSWM) system to address population growth, consumerism, and resource scarcity. It introduces a two-phase decision structure combining multi-attribute decision-making (MADM) tools. Phase one develops a hybrid risk-oriented fuzzy MADM tool for selecting optimal waste-to-energy technologies, considering environmental and technological factors. Phase two uses a fuzzy bi-objective multi-period mixed-integer linear programming model to design the MSWM supply chain efficiently under uncertainty. A case study in North Tehran demonstrates the framework’s practical applicability and effectiveness in real-world scenarios, highlighting that effective source separation boosts recycling, reduces costs, and provides social benefits. Sensitivity analyses offer insights to enhance waste segregation practices. The study emphasizes integrating economic, environmental, and social sustainability in waste management decision-making. By offering a novel, holistic approach, this research addresses existing gaps in systematic decision-making processes and provides a robust tool for municipalities to optimize strategies under uncertainty.

Barrier function–based adaptive STSMC for steering feel feedback of SBW vehicle with uncertainty

As an essential component of human–computer interaction in steer-by-wire (SBW) vehicles, the steering feel feedback system provides drivers with accurate steering feel by precisely controlling the output torque of the steering feel motor. Meanwhile, the existence of uncertainties makes the accurate control of steering feel feedback torque become an acknowledged challenging issue. This article proposes an adaptive super-torque sliding mode control strategy based on barrier functions for the steering feel feedback system of SBW vehicles with highly complex dynamics in the presence of uncertainties. First, to achieve intelligent modeling under the influence of uncertainty factors, a dynamic system with unknown uncertainty based on adaptive fuzzy logic system (FLS) is proposed. In the framework of this model, the uncertainty factors introduced by unknown external disturbance, parameter uncertainty, and model couplings are considered as a lumped uncertainty function. Furthermore, the membership functions of the FLS are dynamically adjusted based on nearest neighbor clustering, aiming to enhance the modeling accuracy beyond traditional fuzzy modeling. To further offset the system uncertainty and FLS approximation error, an adaptive super-twisting sliding mode control (STSMC) method based on barrier function is proposed. This algorithm retains the advantages of traditional sliding mode control (SMC) methods in dealing with systems with uncertainty and eliminates the need for a priori knowledge of the upper bound of uncertainties by introducing the adaptive law based on barrier function, avoiding the use of complex identification algorithms. Moreover, it eliminates the gain of overestimation and significantly reduces chattering phenomenon in traditional sliding mode control. Finally, based on Lyapunov stability theory, this article proves the proposed system can achieve convergence within a finite time. Compared with STSMC, traditional SMC and proportional–integral–derivative (PID) control, the results verify the effectiveness of the proposed control method. The proposed strategy provides a new solution to reduce the steering feel feedback torque error under the influence of uncertain factors.

Identification methodology for MIMO Hammerstein nonlinear model with process noise

In this paper, we present a methodology for identifying the multi-input–multi-output (MIMO) Hammerstein nonlinear model under colored noise. The Hammerstein model presented comprises neural fuzzy models (NFMs) as its static nonlinear block and rational transfer functions (RTF) model as its dynamic linear block. The hybrid signals consisting of separable signals and random signals are utilized to deal with the MIMO Hammerstein model identification issue, and the separable signals to implement separation identification of MIMO Hammerstein model is introduced, that is, the two blocks are separately identified. First, parameters of the linear block are estimated applying correlation function-based least squares method in the presence of measurable input–output of Gaussian signals, which can efficiently weaken the process noise interference. Second, estimate of noise parameters vector is introduced to solve the unknown noise vector in the information matrix, then a recursive extended least squares method is developed for identifying parameters of nonlinear block and colored noise model based on available input–output of random signals. The validity and precision of the presented methodology are demonstrated applying a numerical simulation and a nonlinear process, and it is known from the research results that compared with existing identification techniques, the methodology utilized achieved higher identification accuracy.

Enhancing group decision-making: Maximum consensus aggregation for fuzzy cross-efficiency under hesitant fuzzy linguistic information

Group decision-making (GDM) is essential as it recognizes the inherent complexity of many decision scenarios, which frequently require the collective wisdom and knowledge of multiple decision-makers (DMs) to be effectively resolved. The proposed method aims to develop fuzzy data envelopment analysis (DEA) cross-efficiency models tailored to address GDM challenges, wherein attribute values are provided by DMs using hesitant fuzzy linguistic term sets (HFLTSs). For this purpose, we initially transform HFLTSs into their corresponding fuzzy envelopes, defined as trapezoidal fuzzy numbers (TrFNs). This conversion strategy effectively minimizes the loss in assessments based on HFLTSs while retaining the inherent ambiguity of the original information. Building upon this foundation, we develop fuzzy cross-efficiency models by leveraging the α-level sets of fuzzy envelopes. These models are designed to handle fuzzy input and output variables under various α-level sets, which are capable of considering all possible attribute values for each alternative. Following this, we implement a maximum consensus model using fuzzy cross-efficiency to assign weights to DMs. These weights facilitate the aggregation of individual fuzzy cross-efficiency intervals obtained from DMs’ assessments into collective ones, which serve to rank alternatives. Finally, we showcase the effectiveness and superiority of our proposal through numerical validation and comparative analysis.