Decision-making (DM) problems in real-world environments are frequently described by ambiguity, expert hesitation, linguistic assessments, and incomplete information, which limit the effectiveness of traditional fuzzy set (FS) and intuitionistic fuzzy set (IFS) frameworks. To deal with such problems, this paper demonstrates an innovative and more expressive model, called linguistic cubic interval-valued intuitionistic fuzzy sets (LCuIVIFSs), which combines interval-valued intuitionistic fuzzy uncertainty, linguistic information, and cubic structures into a single framework. Some traditional operations of the newly defined LCuIVIFS model, such as union, intersection, and complement, are systematically introduced to ensure operational consistency and mathematical soundness. Within the framework of LCuIVIFSs, several aggregation operators (AOs), including arithmetic AO, geometric AO, weighted arithmetic AO, and weighted geometric AO, is presented to significantly combine complex and uncertain information. The key features of the proposed AOs are investigated. Moreover, a novel multi-criteria decision-making (MCDM) technique is developed using the newly defined AOs. To discuss the significance of the proposed approach, it is implemented to a case study of supplier selection problem in smart manufacturing, where both quantitative and qualitative criteria under uncertainty are considered. The final results ensure that the newly defined approach contributes reliable, flexible, and robust decision outcomes compared with existing FS-based models. The proposed study thus provides a valuable decision-support framework for complex DM problems under linguistic and cubic uncertainty.

Interactive Multi-Attribute Decision-Making in Construction Land Reduction: An Intuitionistic Fuzzy Mahalanobis–Taguchi Approach

Real-world environments are usually characterized by uncertainty, hesitation, and time-dependent information in decision-making problems. The current fuzzy and intuitionistic fuzzy models have the limitation that they cannot adequately model multidimensional and dynamic uncertainty without loss of information. To overcome this shortcoming, this paper develops a new dynamic multi-attribute decision-making model using complex intuitionistic fuzzy sets. A more powerful score function is initially suggested to address the comparison ambiguity that is inherent in traditional complex intuitionistic fuzzy ranking approaches. Based on this enhancement, two dynamic Dombi aggregation operators, i.e., the complex intuitionistic fuzzy dynamic Dombi weighted averaging and complex intuitionistic fuzzy dynamic Dombi weighted geometric operators, are proposed to effectively aggregate time-dependent decision information. The structural properties of the proposed operators, including closure, idempotency, monotonicity, and boundedness, are rigorously established. A systematic decision-making algorithm is then constructed under the proposed framework. The practicality and effectiveness of the approach are demonstrated through a case study involving the selection of an optimal Internet of Things platform. Comparative and sensitivity analyses confirm that the proposed methods provide stable, reliable, and more discriminative results than existing approaches. The developed framework offers a flexible and robust tool for dynamic decision-making problems in complex and uncertain environments.

This paper introduces a single Privacy-Preserving Data Mining (PPDM) framework that attempts to balance the privacy-utility dilemma between privacy and utility of the data. This methodology will combine a stringent preprocessing pipeline, which uses k-NN imputation and Tomek Link SMOTE to balance the classes and a multi-regularized approach to feature selection (L1, L2, and Elastic Net) to boost the significance of the attributes. As an extensive multi-noise injection layer is required to offer strong privacy assurances, Laplace, Cauchy, t-distribution, intuitionistic fuzzy, exponential, speckle, and Gaussian perturbations are adopted. Studying is carried out through a hybrid 1D CNN-LSTM system, which was designed to identify patterns in perturbed high-dimensional data. Comparison between the Breast Cancer, Adult, and Customer Churn datasets demonstrate that the framework has high predictive accuracy and Kappa scores with a minimum variance in the data utility. Experimental findings show that such multi-layered construction has a better defence-in-depth mechanism than traditional PPDM pipelines, which are capable of ensuring strong performance in sensitive analytical conditions.

This paper introduces a novel framework for bounded intuitionistic fuzzy sets using lower and upper threshold parameters. Unlike classical cut-set approaches, the proposed method preserves membership and non-membership degrees while restricting the universe. Fundamental algebraic properties and set-theoretic operations are investigated, and applications to intuitionistic fuzzy subgroup theory are presented. The results show that subgroup properties are retained within the bounded structure. This framework provides a flexible and effective tool for analyzing intuitionistic fuzzy systems.

In this paper, a novel tool for decision-making problems, namely the distance measure between intuitionistic fuzzy sets (IFSs) is being forwarded. Classically, the previous distance measures did not consider the impact of the hesitancy parameter, which produces counterintuitive outcomes when measuring distance. The proposed distance measure fully considers the influence of hesitation degree on distance measurement. Simultaneously, it is not only consistent with the four properties of distance measure, but also has nonlinear characteristics. The incorporation of the logarithmic transformation introduces nonlinear characteristics in the distance computation, which allows the measure to capture subtle variations between intuitionistic fuzzy elements more effectively. This nonlinear behavior improves the discrimination capability of the distance measure when comparing IFSs. Several examples were analyzed to demonstrate that the suggested distance measure produces preponderance outcomes. In addition, the applicability of the suggested distance measure was displayed by a series of applications in pattern recognition.

In the rapidly changing world of banking systems, intelligent banking has emerged as a revolutionary force in the rapidly growing financial technology world. Smart banking provides a seamless, personalized experience, leveraging intelligent systems that apply technologies such as artificial intelligence (AI), blockchain, and big data to deliver mobile financial services. However, the risks of such innovations can also be confusing, such as cyber threats, data breaches, and vulnerabilities in work, and these aspects require strict assessment and control. This article presents a systematic multi-criteria group decision-making (MCGDM) model for risk assessment in intelligent banking, which incorporates the Circular Intuitionistic Fuzzy Bonferroni Mean (CIFBM) to assess the state of expert judgments and effectively manage uncertainty and ambiguity. Moreover, important theorems and properties, such as idempotency, monotonicity, and boundedness, have ensured its efficiency and reliability in risk assessment. A case study shows that the proposed approach has real-world applicability and can be used to prioritize risks, make decisions, and improve the security, efficiency, and flexibility of banking operations. This work provides a new, practical framework for addressing emerging risks in intelligent banking systems. It makes a valuable contribution to researchers and practitioners in the field of financial technology by combining rigorous theoretical development with practical implementation.

Transportation problems constitute a fundamental class of optimization models; however, real-world applications involve uncertainty, hesitation, and expert disagreement that cannot be adequately captured by deterministic or classical fuzzy approaches. This paper proposes a three-dimensional circular intuitionistic fuzzy potential method (3D–CIFMODI), which extends the classical MODI framework to Circular Intuitionistic Fuzzy Triples (C-IFTs) through radius-aware operations and indexed matrix representations. Unlike existing circular intuitionistic fuzzy transportation methods, which are primarily feasibility-driven, the proposed approach introduces a dual-based optimality framework based on circular reduced costs, preserving the full structure of uncertainty without reducing it to crisp equivalents. The method retains polynomial-time computational complexity O(mn(m+n)), i.e., O(n3) for square problems, with only a constant computational overhead due to circular operations. A numerical case study demonstrates the effectiveness and robustness of the proposed framework. Furthermore, a comparative analysis between classical intuitionistic fuzzy (IFS) and circular intuitionistic fuzzy (C-IFS) representations shows that incorporating the radius parameter significantly improves discrimination capability, solution stability, and interpretability. The results confirm that the proposed method provides a unified, interpretable, and computationally efficient framework for solving multi-layer transportation problems under circular intuitionistic fuzzy uncertainty.

Equitable prioritization of public investments is increasingly critical as municipalities face constrained budgets, heterogeneous neighborhood needs, and demands for transparent decisions. This paper proposes a fairness-aware group multi-criteria decision-making (MCDM) framework for ranking municipal infrastructure investments when budgets are constrained, and neighborhood needs differ. Six alternatives are assessed in the Istanbul case study: flood risk mitigation, inclusive public realm and cooling, smart and energy-efficient municipal assets, walking and cycling infrastructure, healthcare access improvements, and seismic retrofitting of public buildings. The criteria system combines efficiency, implementability, socio-environmental performance, and equity-oriented priorities through five main dimensions and 23 sub-criteria. In addition to cost, feasibility, and service effectiveness, the framework incorporates fairness-related criteria such as baseline need and deficit severity, vulnerability-targeting effectiveness, minimum service guarantee for the worst-off, and priority for low-accessibility centers. Public acceptance and environmental performance are also included. Stakeholder panels provide expert judgments using intuitionistic fuzzy sets, capturing membership, non-membership, and hesitation to reflect uncertainty. Criteria weights are derived with Intuitionistic Fuzzy Step-wise Weight Assessment Ratio Analysis (IF-SWARA), enabling importance elicitation and group aggregation without forcing crisp consensus. Alternatives are then ranked using Intuitionistic Fuzzy Combined Compromise Solution (IF-CoCoSo), which blends additive and multiplicative compromise solutions to balance overall performance with equity objectives. Robustness is assessed through sensitivity analysis by varying the γ parameter within the IF-CoCoSo procedure. A municipal case study demonstrates that healthcare access improvements achieve the highest compromise performance, followed by flood risk mitigation and seismic retrofitting of public buildings, while smart and energy-efficient municipal assets rank last. The findings confirm that explicitly embedding fairness criteria can shift municipal priorities toward alternatives that more directly reduce deprivation, risk, and spatial inequality. The main contribution of this study is not merely empirical application, but the development of a fairness-aware group MCDM framework that operationalizes distributive justice in municipal investment prioritization through a structured set of criteria.

The global climate crisis, which has severely damaged economies and led to migration of millions of people worldwide as a result of typhoons, tsunamis and others environmental changes and disasters, requires increased urban sustainability in decision-making and preparedness for various human mobility strategies. Despite extensive research in the field of emergency evacuation, few publications are devoted to fuzzy conditions. However, many of the attributes inherent in emergency modeling are fuzzy and uncertain by nature. Thus, we account for the necessity of evacuation as a human mobility strategy under intuitionistic fuzzy conditions, which allow experts to express hesitation when evaluating criteria. We have developed a hybrid intuitionistic fuzzy method to find the best evacuation strategy in an uncertain environment. To verify the results, we applied our method to one of the eastern regions of China, Jiangxi Province, in the event of Typhoon Maria to define the necessity of evacuation based on seven criteria. Necessity of evacuation is expressed by five response alternatives: no evacuation, alertness, recommended evacuation, mild evacuation, urgent evacuation. According to the algorithm the most desirable strategy in this situation is alertness, which means preparedness for evacuation. The results obtained demonstrate superiority of the proposed hybrid method in comparison with other intuitionistic fuzzy approaches.

Analyzing conflicts between multiple objects within fuzzy information systems (ISs) and providing effective conflict resolution are challenging tasks due to the complexity and uncertainty of the real world. This article proposes a three-way conflict analysis and resolution model for intuitionistic fuzzy ISs (IFISs) based on three-way concept analysis (3WCA). First, the straight and vertical distances between intuitionistic fuzzy values (IFVs) are defined to obtain an intuitionistic fuzzy probability-credibility distribution. Second, intuitionistic fuzzy optimistic and pessimistic formal contexts are proposed based on two novel binary relations of intuitionistic fuzzy information. Afterward, two intuitionistic fuzzy concept lattices are obtained to analyze the marginal conflict degrees among multiple objects via consistency, inconsistency, and uncertainty attribute sets. By introducing three pairs of thresholds, the trisections of object pairs, objects, and attributes are derived through the three-way decision (3WD) process. Specifically, the maximal alliance unit, minimal conflict unit, and feasible strategy set are identified according to the three-way conflict analysis results. Subsequently, the consistency measure extracted from the intuitionistic fuzzy distance matrix is utilized to rank all feasible strategies. Finally, the experimental results are conducted to verify the effectiveness, superiority, and feasibility of the proposed model.

Rapid population growth, technological developments, and rising living standards have steadily increased global energy demand. Despite the growing interest in battery energy storage systems (BESSs), limited research has addressed their site selection under uncertainty using a comprehensive, uncertainty-aware framework. This study aims to select the most suitable location for BESS deployment by integrating technical, economic, environmental, and resilience-related criteria within a structured decision-making process. A novel hybrid approach combining Intuitionistic Fuzzy Step-Wise Weight Assessment Ratio Analysis (IF-SWARA) and Intuitionistic Fuzzy VlseKriterijumska Optimizacija I Kompromisno Resenje (IF-VIKOR) is employed to handle expert-based evaluations and rank candidate locations in Türkiye's Black Sea region. This hybrid structure offers an advanced and structured solution to complex location selection problems. The findings indicate that renewable energy potential and technical suitability are the most influential factors. A sensitivity analysis further confirms the robustness of this result across varying weights for the criteria. The proposed model not only contributes to the literature but also provides an applied tool to support energy planners and policymakers in making knowledgeable BESS investment decisions. This study contributes a replicable methodology for decision-makers aiming to integrate renewable energy and storage solutions, and it offers a structured path forward for future research in energy infrastructure planning under uncertainty. • A hybrid MCDM model supports BESS site selection under renewable uncertainty. • IF-SWARA and IF-VIKOR are integrated within an intuitionistic fuzzy framework. • Renewable potential and technical suitability rank highest among main criteria. • Grid proximity is identified as the most critical sub-criterion. • The model offers a transferable approach for sustainable energy planning.

An Integrated Interval-Valued Intuitionistic Fuzzy Transportation–PERT Model for Cost–Time Optimization under Uncertainty

A Novel Algorithm for Intuitionistic Fuzzy Group Decision-Making with Application to Cultural Tourism Competitiveness Evaluation in the Context of Rural Revitalization

Inclusion and preference relations are fundamental comparison tools in intuitionistic fuzzy set (IFS) theory and play an important role in decision analysis under uncertainty. In IFS representations, the hesitation degree reflects information that is not captured by membership and non-membership values alone. This study investigates the structural relationship between hesitation and the inclusion and preference relations of IFSs. A proposed interpretation of membership and non-membership degrees is employed to provide a geometric perspective on hesitation. Within this framework, analytical relations between hesitation inequalities and preference conditions are derived. In particular, it is shown that the hesitation inequality constitutes a necessary condition for preference, whereas inclusion relations remain compatible with a wider range of hesitation configurations. The theoretical observations are illustrated using electoral datasets from the 2002 South Korean presidential election and the 2000 United States presidential election in Florida. Regional vote shares are transformed into intuitionistic fuzzy representations to analyze the distribution of hesitation across regions. The examples demonstrate how hesitation may influence the stability of preference relations while inclusion relations remain structurally preserved.

An intuitionistic fuzzy set is a generalisation of the notion of a fuzzy set. An intuitionistic fuzzy graph is a kind of fuzzy graph which explains the degree of membership and non-membership of vertices and edges. In this paper closed neighbourhood and total degree-based first, second Zagreb indices, forgotten index, Randic index and harmonic index of intuitionistic fuzzy graphs are studied.

This study presents the development and systematic evaluation of novel aluminum-based metal matrix composites (AMMCs) reinforced with silicon carbide (SiC), graphite, and peanut shell ash (PSA), alloyed with copper (Cu) and magnesium (Mg), to enhance machinability, mechanical performance, and sustainability. Two hybrid composites were fabricated using stir casting: Sample A (Al-82%, SiC-5%, Cu-2%, Mg-1%, PSA-10%) and Sample B (Al-80%, SiC-10%, Cu-3%, Mg-2%, PSA-5%). The composites were characterized through microstructural analysis, tensile testing, hardness, FTIR (Fourier-Transform Infrared Spectroscopy), DSC (Differential Scanning Calorimetry), UV-Vis (Ultraviolet-Visible Spectroscopy), and XRD (X-Ray Diffraction). Machining trials were conducted under conventional and ultrasonic-assisted conditions, with machining parameters including cutting speed (A) ranging from 11 to 42mm/min (mean: 26.51mm/min, standard deviation: 13.22), feed rate (B) ranging from 0.05 to 0.15mm/rev (mean: 0.098mm/rev, standard deviation: 0.037), and depth of cut (C) varying from 0.5 to 0.95mm (mean: 0.698mm, standard deviation: 0.168), all treated as continuous numeric variables. Optimization was performed using Response Surface Methodology (D-optimal, reduced quadratic model) integrated with Fuzzy AHP and Intuitionistic Fuzzy MARCOS. Results indicated that Sample A exhibited superior ductility, energy absorption, and thermal stability due to the presence of bio-carbon phases, while Sample B demonstrated higher hardness, strength, and thermal conductivity attributed to refined SiC-Cu reinforcements. FTIR confirmed organic phases in Sample A and stronger inorganic bonding in Sample B, whereas XRD revealed crystalline SiC/Cu peaks in Sample B and amorphous bio-carbon in Sample A. Among machining runs, optimum performance was achieved in Run 7 (cutting speed: 42mm/min, feed rate: 0.05mm/rev, depth of cut: 0.85mm, Sample B), with low surface roughness (1.118µm), minimal tool wear (2.94µm), high material removal rate (10.764 cm3/min), and moderate power consumption (218.05 W). ANOVA and confirmation tests validated model accuracy with less than 5% error. Overall, Sample A is recommended for lightweight, ductile applications, while Sample B is better suited for high-strength, wear-resistant components. Sample A suits lightweight autosmotive and aerospace panels, while Sample B fits wear-resistant structural parts. Future work will examine durability, corrosion, PSA chemistry, and industrial scale-up.

Purpose This study bridges a critical literature gap by proposing a novel quality function deployment (QFD) framework that integrates the intuitionistic fuzzy Choquet integral (IFCI) with group decision-making (GDM) for the medical devices industry. The purpose is to develop an objective and robust decision-support tool that not only handles the uncertainty and hesitation inherent in linguistic assessments but also explicitly models the nonlinear interactions among technical criteria, which are often overlooked in traditional QFD. Design/methodology/approach The study proposes an IFCI approach for the QFD process with GDM. The proposed methodology is explained in detail, and a case study in the medical devices industry is presented. The proposed model establishes the theoretical framework, while the case study offers empirical validation in a real-world context. Findings By integrating the intuitionistic fuzzy integrated determination of objective criteria weights (IF-IDOCRIW) method and IFCI approach into QFD, the methodology effectively captures diverse perspectives and manages uncertainties in GDM. Unlike traditional QFD models that assume linear, additive relationships among criteria, the proposed method captures nonlinear interdependencies and synergy effects. A key finding was the proposed method's ability to reveal non-additive synergies between criteria, leading to a prioritization that diverges from what traditional linear models would produce. The results were validated through a sensitivity analysis, which confirmed the stability of the top-ranked characteristics while identifying others whose priority is highly dependent on decision-maker weights, providing crucial strategic insights for resource allocation and risk management. Originality/value This paper contributes to the literature by integrating the IF-IDOCRIW method and IFCI with QFD, extending traditional frameworks to better handle GDM under uncertainty. The approach introduces a decision-support tool that improves the accuracy of resource allocation and prioritization in quality management. By capturing both linear and nonlinear relationships among key criteria, it offers a more comprehensive and dynamic assessment method, enhancing strategic decision-making in complex settings like the medical devices industry.

ABSTRACT Studies of the Venture Capital (VC) screening process traditionally assume that VC criteria are independent of other criteria. However, these criteria may interact and influence each other in cause‐and‐effect relationships. Therefore, there is a need to understand the interdependence of VC screening criteria. In this study, a decision support framework is proposed for VC screening criteria, based on the Decision‐Making Trial and Evaluation Laboratory (DEMATEL) method and Intuitionistic Fuzzy Set (IFS) theory (IFS‐DEMATEL). Building on prior work on VC investors, we identify a holistic list of 20 evaluation criteria in seven categories (founding team, product or service, financial, market, environmental, social, and governance characteristics). The IFS‐DEMATEL method is used to identify the relative importance attached by VC investors to different criteria, pinpoint the most significant criteria, and explicate the cause‐and‐effect relationships between criteria. Finally, the proposed framework is used to empirically examine VC screening criteria based on a case study involving VC experts/investors from the UK and the US. We find that environmental protection, the team and working environment, and profitability are the most influential criteria; that is, they have the greatest impact on the other criteria. This study both enhances the VC screening literature and makes an important practical contribution by proposing and illustrating a decision support framework capable of addressing VC screening decisions in complex and imprecise real‐world scenarios.

College English course instruction mainly covers content that includes language knowledge and practical skills, and it is also a primary avenue for enhancing students' English learning strategies and intercultural communication competence. The college English teaching quality evaluation is a multi-attribute decision making (MADM). This paper approaches college English teaching quality assessment as a MADM process. Fundamental computational rules for interval-valued intuitionistic fuzzy sets are presented, including the Hamacher sum and product operations. A novel aggregation tool, termed the induced interval-valued intuitionistic fuzzy Hamacher interactive ordered weighted averaging operator, is developed and its desirable mathematical properties are thoroughly examined. The proposed operator is then applied to solve MADM problems within the framework of interval-valued intuitionistic fuzzy sets. To validate its practical utility, a detailed case study on evaluating college English teaching quality is conducted using this new methodology.