Search Results (39)

The growing demand for hydrogen as a low-carbon energy carrier has renewed interest in coal, an abundant and globally available resource, making it crucial to assess its suitability for efficient hydrogen production via in situ pyrolysis. The main objective of this study is to propose a new and robust hesitant fuzzy Multi-Criteria Decision-Making (MCDM) framework to the literature to determine the coal alternative that will provide the most efficient hydrogen production. For this purpose, five different coals with the largest reserves in the United States (Wyoming, Illinois, West Virginia, Kentucky, and Pennsylvania) were examined under eight criteria. To manage uncertainties in determining the weights of the criteria, the hesitant fuzzy set-based step-wise weight assessment ratio analysis (SWARA) method was used. The coal alternatives were ranked using the Alternative Ranking Technique based on Adaptive Standardized Intervals (ARTASI). The proposed framework uses expert evaluations and performance criteria as input parameters to determine criterion weights and rank the alternatives. The output consists of the calculated criterion weights, utility values, and the final ranking of the liquid hydrogen rocket oxidizer systems. The robustness of the obtained results is further verified through parametric analyses of the w and Ψ parameters and comparative other MCDM methods validation. The findings consistently demonstrate that Wyoming coal is the most suitable alternative for hydrogen production via in situ pyrolysis. This study provides a systematic decision support framework for evaluating coal resources and offers valuable guidance for future hydrogen production strategies based on in situ coal pyrolysis. Full article

Decision-making problems often involve simultaneous sources of uncertainty: interval-valued hesitation in expert judgments, positive–neutral–negative assessments, parameter-dependent evaluations, and boundary-region indiscernibility. To address these combined forms of uncertainty, this paper develops an interval-valued spherical fuzzy soft rough set (IVSFSRS) framework. The model integrates interval-valued spherical fuzzy information, soft parameterization, and rough lower–upper approximations in a unified approximation space. In response to the need for a more explicit theoretical foundation, an IVSF soft relation is formally defined and its role in constructing the approximation operators is clarified. The paper also presents basic operations, Hamacher-type extensions for the lower and upper approximations, and proof sketches showing the validity of the proposed operators. Furthermore, an IVSFSRS-based multi-criterion group decision-making procedure is developed, and a TOPSIS-oriented formulation is outlined to improve practical applicability. A demonstrative location-selection example, comparative analysis with related models, and sensitivity discussion illustrate the expressive power, robustness, and limitations of the proposed approach. Full article

The problem of bilevel decision-making under multi-expert uncertain information is addressed in this paper. Traditional fuzzy bilevel models are unable to accurately quantify expert consensus and capture evaluation hesitation. To overcome these limitations, a fully hesitant fuzzy bilevel linear programming model is proposed, in which all coefficients and decision variables are characterized by hesitant fuzzy numbers. By virtue of $(\alpha ,k)$-cuts, the original model is equivalently transformed into an interval-valued bilevel programming problem and further decomposed into best–best and worst–worst sub-models to derive the upper and lower bounds of optimal solutions. Under the Slater constraint qualification, Karush–Kuhn–Tucker (KKT) conditions are adopted to convert the two sub-models into single-level mathematical programs with complementarity constraints (MPCCs), thereby enabling efficient model solving. The proposed method is applied to the resource allocation problem in quantum communication networks. The numerical results demonstrate that the optimal solution interval converges to a unique core value as the membership-level $\alpha$ increases, while a larger consensus parameter k reduces the fuzzy support set without altering the core solution. Full article

Probabilistic risk assessment of complex offshore oil and gas systems is often challenged by scarce statistical data and multiple uncertainties. Traditional point-value probability and standard Bayesian networks cannot fully represent and propagate these uncertainties, which may mislead high-risk security decision-making. To address this issue, this paper proposes a new hybrid risk assessment framework that combines interval-valued T-spherical fuzzy sets (IVTSFS) with credal networks (CN). First, IVTSFS is used to quantify the subjective risk perception of multiple experts, effectively capturing hesitancy, fuzziness, and group disagreement. An improved probability mapping mechanism is introduced to align linguistic evaluations with objective failure frequency spaces, thereby avoiding systemic transformation biases. Subsequently, the interval conditional probability table is constructed using the imprecise leakage noise-OR model, which alleviates the problem of parameter dimension explosion in complex causal structure and explicitly retains the parameter uncertainty. The 2U algorithm is then applied to perform accurate interval inference in CN. The feasibility and comparative advantages of the method are illustrated in the actual case of the single-point mooring system. The results clearly output the upper and lower bounds of the system failure risk, and identify the key vulnerable nodes through diagnostic reasoning and sensitivity analysis. This study has theoretical contributions in fuzzy decision-making and uncertainty modeling. By unifying advanced fuzzy cognitive quantification and imprecise probability propagation, it provides a structured uncertainty representation tool for expert-informed risk screening under data scarcity. Full article

With the increasing prevalence of AI-supported services, the assessment of service quality in the e-tourism sector has become a more complex and multidimensional process. This study aims to analyse the dimensions of AI-supported e-tourism service quality using an advanced fuzzy multi-criteria decision-making approach that takes into account uncertainty and hesitation in expert judgements. Within this scope, the relative importance levels of the criteria associated with the six fundamental dimensions defined within the AISAQUAL model were modelled using interval-valued q-rung orthopair fuzzy sets (IVq-ROFS), and a flexible and parametric integration process was applied via Hamacher operators. The analytical framework was structured using the CIMAS method, which directly reflects expert experience in the criterion weighting process; a multi-stage evaluation process was conducted by integrating decision-makers’ levels of experience into the weighting mechanism. In this process, linguistic evaluations were converted into fuzzy numbers, combined using the Hamacher product operator, and reduced to precise values via scoring functions to calculate criterion weights. The findings indicate that incorporating uncertainty and interactions between criteria into the model leads to variations in the relative importance ranking of service quality dimensions. Furthermore, it was determined that the proposed approach produces more consistent and discriminatory results compared to classical weighting methods. In conclusion, the study demonstrates that the use of advanced fuzzy decision-making methods in the evaluation of AI-supported service quality can yield more realistic and reliable results. Full article

Over the past few decades, extensive attention has been given by researchers and practitioners to the development and application of multi-criteria decision-making (MCDM) methods within intuitionistic fuzzy environments across a wide range of fields and disciplines. This challenging research area has emerged as one of the most prominent topics, and its importance and popularity are expected to continue growing in the future. The elliptic intuitionistic fuzzy set (EIFS) addresses complex, multidimensional, non-symmetrical vagueness and uncertainty more effectively than other traditional intuitionistic fuzzy sets (IFSs). Sustainable renewable energy source selection is a critical decision-making (DM) process aiming to identify the most suitable energy alternative. The process of selecting sustainable renewable energy sources necessitates a comprehensive assessment of numerous criteria, which encompass environmental ramifications, economic feasibility, and societal acceptance. Contemporary research suggests novel methodologies to enhance this selection process, highlighting the need for an MCDM framework that integrates a variety of factors. This study presents an innovative DM framework for sustainable renewable energy source selection based on EIFS and a newly developed aggregation operator, the Elliptic Intuitionistic Fuzzy Weighted Muirhead Mean Aggregation (EIFWMMA) operator. These mechanisms expand upon conventional intuitionistic fuzzy frameworks by employing an elliptical portrayal of membership and non-membership degrees, facilitating a more accurate and lifelike representation of uncertainty and hesitation in evaluations by experts. To enhance computational efficiency, the framework weaves together machine learning-driven dimensionality reduction and weight optimization strategies of principal component analysis (PCA) for DM. The suggested operators are employed in an MCDM scenario centered around the selection of sustainable renewable energy sources, where the hierarchy of alternatives is established through score values derived from EIFWMMA. A comparative exploration of Circular Intuitionistic Fuzzy Sets (C-IFSs) and Interval-Valued Intuitionistic Fuzzy Sets (IVIFSs) uncovers that the elliptical formulation yields consistently reliable, precise, and geometrically comprehensible results. The findings affirm that EIFS-based operators offer a resilient, adaptable, and broadly applicable strategy for tackling MCDM challenges amidst uncertainty. The Min–Max normalization method is employed to validate our proposed methodology for identifying alternatives within the MCDM paradigm. It also improves accuracy, stability, and scalability in comparison to conventional approaches. Full article

A novel sustainable supplier selection (SSS) method is proposed to address the interrelation among attributes and the psychological state and risk attitude of decision-makers (DMs). The method integrates proportional interval type-2 hesitant fuzzy sets (PIT2HFSs), a generalized Shapley-based aggregation operator, and a modified regret theory combined with a normalized bidirectional projection (NBP) measure. The aggregation operators handle the correlations among attributes, while the NBP and regret theory reflect DMs’ risk preferences by considering both the best and worst alternatives. An application case study in a manufacturing enterprise, along with sensitivity and comparative analyses, demonstrates the effectiveness and robustness of the proposed approach. The results indicate that the method outperforms existing approaches in handling attribute interdependencies, decision uncertainty, and human risk behavior, providing a comprehensive and practical framework for sustainable supplier selection in the manufacturing industry. Full article

To address high uncertainty, dynamic evolution, and limited information in emergency decision-making for major sudden disasters, this paper proposes a sliding-window game-theoretic method with four reference points for emergency response selection. Firstly, interval-valued T-spherical fuzzy sets are adopted to capture decision-makers’ uncertain and hesitant evaluations in interval form. Subsequently, a four-reference-point framework, including the external, internal, average development speed, and ideal proximity reference points, is established to reflect stage-dependent psychological baselines. Furthermore, criterion weights are updated by a sliding-window game-theoretic combination weighting scheme that integrates entropy, anti-entropy, criteria importance through intercriteria correlation, and the coefficient of variation, and performs rolling updates across stages. Prospect values are then computed relative to the four reference points and aggregated to rank alternatives at each stage. Finally, a case study of the 2024 Huludao extreme rainfall event applies the proposed method to evaluate four candidate schemes across six criteria over three decision stages. Results show that rescue cost has the highest weight in all stages, while the importance of rescue speed decreases and social impact increases as the response progresses. The proposed method identifies a comprehensive flood relief scheme led by the People’s Liberation Army and the People’s Armed Police Force as the best option in all stages, because it achieves the highest comprehensive prospect values among all alternatives. Comparative analyses indicate more consistent identification of the optimal scheme than existing approaches, supporting sustainable and resource-efficient disaster management. Full article

Investment decision-making is often characterized by uncertainty and the subjective weighting of criteria. This study aims to develop a more robust decision support framework by integrating the Generalized Interval-Valued Hesitant Intuitionistic Fuzzy Soft Set (GIVHIFSS) with the Analytic Hierarchy Process (AHP) to objectively weight criteria and handle multi-evaluator hesitancy. In the proposed GIVHIFSS-AHP model, the AHP is employed to derive mathematically consistent criterion weights, which are subsequently embedded into the GIVHIFSS structure to accommodate interval-valued and hesitant evaluations from multiple decision-makers. The model is applied to a numerical case study evaluating five investment alternatives. Its performance is assessed through a comparative analysis with standard GIVHIFSS and GIFSS models, as well as a sensitivity analysis. The results indicate that the model produces financially rational rankings, identifying blue-chip technology stocks as the optimal choice (score: +2.4). The comparative analysis confirms its superiority over existing models, which yielded less-stable rankings. Moreover, the sensitivity analysis demonstrates the robustness of the results against minor perturbations in criterion weights. This research introduces a novel and synergistic integration of the AHP and GIVHIFSS. The key advantage of this approach lies in its ability to address the long-standing issue of arbitrary criterion weighting in Fuzzy Soft Set models by embedding the AHP as a foundational mechanism for ensuring validation and objectivity. This integration results in mathematically derived, consistent weights, thereby yielding empirically validated, more reliable, and defensible decision outcomes compared with existing models. Full article

The reliability and safety of five-axis CNC abrasive water jet machining are critical for many industries. This study employs Failure Mode and Effects Analysis (FMEA) to identify and mitigate potential failures in this machining system. Traditional FMEA, which relies on crisp numerical values, often struggles with handling uncertainty in risk assessment. To address this limitation, this paper introduces an Interval-Valued Spherical Fuzzy FMEA (IVSF-FMEA) approach, which enhances risk evaluation by incorporating membership, non-membership, and hesitancy degrees. The IVSF-FMEA method leverages the inherent rotational symmetry of interval-valued spherical fuzzy sets and the permutation symmetry among severity, occurrence, and detectability criteria, resulting in a transformation-invariant and unbiased risk assessment framework. Applying IVSF-FMEA to seven periodic failure (PF) modes in five-axis CNC water jet machining achieves a more precise prioritization of risks, leading to improved decision-making and resource allocation. The findings highlight improper fixturing of the workpiece (PF6) as the most critical failure mode, with the highest RPN value of −0.54, followed by mechanical vibrations (PF2) and tool wear and breakage (PF1). This indicates that ensuring proper fixturing stability is essential for maintaining machining accuracy and preventing defects. Comparative analysis with traditional FMEA demonstrates the superiority of the proposed fuzzy-based approach in handling subjective assessments and reducing ambiguity. The findings highlight improper fixturing, mechanical vibrations, and tool wear as the most critical failure modes, necessitating targeted risk mitigation strategies. This research contributes to advancing risk assessment methodologies in complex manufacturing environments. Full article

As a non-associative connective in fuzzy logic, the analysis and research of overlap functions have been extended to many generalized cases, such as interval-valued and intuitionistic fuzzy overlap functions (IFOFs). However, overlap functions face challenges in the Pythagorean fuzzy (PF) environment. This paper first extends overlap functions to the PF domain by proposing PF overlap functions (PFOFs), discussing their representable forms, and providing a general construction method. It then introduces a new PF similarity measure which addresses issues in existing measures (e.g., the inability to measure the similarity of certain PF numbers) and demonstrates its effectiveness through comparisons with other methods, using several examples in fractional form. Based on the proposed PFOFs and their induced residual implication, new generalized PF rough sets (PFRSs) are constructed, which extend the PFRS models. The relevant properties of their approximation operators are explored, and they are generalized to the dual-domain case. Due to the introduction of hesitation in IF and PF sets, the approximate accuracy of classical rough sets is no longer applicable. Therefore, a new PFRS approximate accuracy is developed which generalizes the approximate accuracy of classical rough sets and remains applicable to the classical case. Finally, three multi-criteria decision-making (MCDM) algorithms based on PF information are proposed, and their effectiveness and rationality are validated through examples, making them more flexible for solving MCDM problems in the PF environment. Full article

To aid in the selection of generative artificial intelligence (GAI) chatbots, this paper introduces a fuzzy multi-attribute decision-making framework based on their key features and performance. The proposed framework includes a new modification of the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), adapted for an interval-valued hesitant Fermatean fuzzy (IVHFF) environment. This TOPSIS extension addresses the limitations of classical TOPSIS in handling complex and uncertain data capturing detailed membership degrees and representing hesitation more precisely. The framework is applicable for both static and dynamic evaluations of GAI chatbots in crisp or fuzzy assessments. Results from a practical example demonstrate the effectiveness of the proposed approach for comparing and ranking GAI chatbots. Finally, recommendations are provided for selecting and implementing these conversational agents in various applications. Full article

Effective franchise selection is crucial for global brands like Pizza Hut to maintain consistent quality and operational excellence amidst a competitive landscape. This paper introduces a novel confidence-interval circular intuitionistic fuzzy set (CIC-IFS) framework, designed to address the intricate challenges of master and sub-franchise selection in the European market. By integrating competence coefficients of decision-makers into the final evaluations, the model allows for a more accurate representation of expert judgments. Decision-makers can choose from various scenarios, ranging from super pessimistic to super optimistic, using ten forms of aggregation operations over index matrices. The proposed approach leverages confidence intervals within the circular intuitionistic fuzzy set paradigm to capture the uncertainty, vagueness, and hesitancy inherent in the decision-making process. A case study involving Pizza Hut’s European operations demonstrates the model’s efficacy in differentiating potential franchisees and identifying those best aligned with the brand’s values. The results indicate a significant improvement in selection accuracy compared to traditional methods and other fuzzy approaches, thereby enabling Pizza Hut to make more informed decisions and solidify its market position. Full article

The evaluation of the shrinkage–swelling characteristic of expansive clay is of great significance, but it is a complex problem since the evaluation process involves numerous uncertain factors, such as randomness, non-subordination, and hesitation uncertainties. Here, an intuitionistic connection cloud model has been proposed to address this issue. First, an evaluation index system is established. According to the reliability of interval-valued evaluation indexes, the corresponding cloud numerical characteristic parameters are specified based on the membership interval generated by the intuitionistic fuzzy principle. Moreover, the improved conditional information entropy based on rough set theory is utilized to assign the index weight. Subsequently, combined with the weight, the intuitionistic connection degree of the sample to the classification standard is determined to identify the shrinkage–swelling grade. Finally, a case study on the shrinkage–swelling grade of untreated and lime-treated expansive clays in Hefei Xinqiao International Airport was performed to illustrate the validity and reliability of the model. The results show that the proposed model is reasonable and feasible for the evaluation of the shrinkage–swelling grade of untreated and lime-treated expansive clays. Full article

Initially, fuzzy sets and intuitionistic fuzzy sets were used to address real-world problems with imprecise data. Eventually, the notion of the hesitant fuzzy set was formulated to handle decision makers’ reluctance to accept asymmetric information. However, in certain scenarios, asymmetric information is gathered in terms of a possible range of acceptance and nonacceptance by players rather than specific values. Furthermore, decision makers exhibit some hesitancy regarding this information. In such a situation, all the aforementioned expansions of fuzzy sets are unable to accurately represent the scenario. The purpose of this article is to present asymmetric information situations in which the range of choices takes into account the hesitancy of players in accepting or not accepting information. To illustrate these problems, we develop matrix games that consider the payoffs of interval-valued intuitionistic hesitant fuzzy elements (IIHFEs). Dealing with these types of fuzzy programming problems requires a significant amount of effort. To solve these matrix games, we formulate two interval-valued intuitionistic hesitant fuzzy programming problems. Preserving the hesitant nature of the payoffs to determine the optimal strategies, these two problems are transformed into two nonlinear programming problems. This transformation involves using mathematical operations for IIHFEs. Here, we construct a novel aggregation operator of IIHFEs, viz., min-max operators of IIHFEs. This operator is suitable for applying the developed methodology. The cogency and applicability of the proposed methodology are verified through a numerical example based on the situation of conflict between hackers and defenders to prevent damage to cybersecurity. To validate the superiority of the proposed model along with the computed results, we provide comparisons with the existing models. Full article