Search Results (240)

Under the dual pressures of global climate change and energy structure transition, the offshore wind–solar–current energy coupling hydrogen production (OCWPHP) system has emerged as a promising integrated energy solution. However, its complex multi-energy structure and harsh marine environment introduce systemic risks that are challenging to assess comprehensively using traditional methods. To address this, we develop a novel risk assessment framework based on hesitant fuzzy sets (HFS), establishing a multidimensional risk criteria system covering economic, technical, social, political, and environmental aspects. A hybrid weighting method integrating AHP, entropy weighting, and consensus adjustment is proposed to determine expert weights while minimizing risk information loss. Two aggregation operators—AHFOWA and AHFOWG—are applied to enhance uncertainty modeling. A case study of an OCWPHP project in the East China Sea is conducted, with the overall risk level assessed as “Medium.” Comparative analysis with the classical Cumulative Prospect Theory (CPT) method shows that our approach yields a risk value of 0.4764, closely aligning with the CPT result of 0.4745, thereby confirming the feasibility and credibility of the proposed framework. This study provides both theoretical support and practical guidance for early-stage risk assessment of OCWPHP projects. Full article

In the digital context, how to achieve symmetrical integration between subjective evaluation and structural stability becomes the key to improving the design effect of iterative product optimization. In this paper, we propose an iterative design method for CIHFS-DEMATEL products that incorporates structural symmetry analysis. The method is based on online review mining and constructs a credibility-based interval hesitant fuzzy set (CIHFS) to symmetrically express the ambiguity and credibility differences in the decision-maker’s subjective evaluation. In turn, a novel exact score function called credibility interval hesitant fuzzy score function (CHFSF), incorporating information symmetric weights, is proposed to realize the bidirectional symmetric mapping between subjective fuzzy inputs and objective exact outputs. Subsequently, the CIHFS-DEMATEL model is introduced to identify the causal paths and a symmetric interaction structure between potential users’ demands. Finally, the demand module mapping matrix is constructed to realize the symmetric decision-making closure loop from demand to solution. Taking the “Intelligent Classified Trash Can” as a case study, we verify the superiority of the method in terms of recognition accuracy, rationality of weight allocation, and structural stability. This study emphasizes the structural symmetry between “input–evaluation–output”, which provides a theoretical foundation and practical framework for the optimal design of products with complex multi-source information. Full article

Consensus in group decision-making has become a hotspot to ensure the agreement opinions of decision makers (DMs). The irrational behaviors of DMs, such as confidence, will impact the consensus results, which should be considered. In addition, the existing self-confidence level directly given by DMs rather than exacted from evaluation information may generate malicious manipulation. Furthermore, double-hierarchy hesitant fuzzy linguistic term set (DHHFLTS) is an effective tool to express the complex evaluations of DMs. In this paper, the endo-confidence of DHHFLTS to reflect confidence of DMs from the perspective of evaluation information is defined. Then, we propose a novel consensus model with endo-confidence of DMs based on DHHFLTSs. First, some improved operators of DHHFLTSs are developed. Second, the weight is determined based on both entropy and endo-confidence. Due to the fact that the consensus threshold should decrease as the endo-confidence increases, we give a novel method to obtain the consensus threshold considering endo-confidence level. Moreover, the two-stage adjustment mechanism is presented for non-consensus DMs and the selection process is constructed. Finally, an illustrative example is carried out to demonstrate the feasibility of the proposed model, and a series of comparative analysis is used to show its stability. 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 concept of Multi Q-Fermatean hesitant fuzzy soft sets (MQFHFSS), derived from the integration of multi-Q fuzzy soft sets and Fermatean hesitant fuzzy sets, can be applied in practice to optimise the resolution of complex multi-criteria decision-making problems. The method exceeds traditional approaches such as Fermatean hesitant fuzzy sets, fuzzy soft sets, and Pythagorean fuzzy sets in enhancing the ability to capture higher levels of uncertainty, hesitation, and symmetry in multi-criteria evaluations, thereby supporting more balanced judgments in complex decision-making situations. In this study, we investigate the novel MQFHFSS concept along with the associated operations. The fundamental characteristics of aggregation operators derived from MQFHFSS have been examined to address some complex decision-making issues. Moreover, we discuss some key algebraic features and their different cases, emphasizing the role of symmetry under the influence of MQFHFSS. Finally, we illustrate some numerical examples and solve the real-world decision-making problem by using the proposed technique. Full article

Terminal forensics in large mobile networks is a vital activity for identifying compromised devices and analyzing malicious actions. In contrast, the study described here begins with the domain of terminal forensics as the primary focus, rather than the threat itself. This paper proposes a new multi-criteria decision-making (MCDM) model that integrates complex picture fuzzy sets (CPFS) with the combinative distance-based assessment (CODAS), referred to throughout as complex picture fuzzy CODAS (CPF-CODAS). The aim is to assist in forensic analysis for detecting mobile botnet command and control (C&C) systems. The CPF-CODAS model accounts for the uncertainty, hesitation, and complex numerical values involved in expert decision-making, using degrees of membership as positive, neutral, and negative values. An illustrative forensic case study is constructed where three mobile devices are evaluated by three cybersecurity professionals based on six key parameters related to botnet activity. The results demonstrate that the model can effectively distinguish suspicious devices and support the use of the CPF-CODAS approach in terminal forensics of mobile networks. The robustness, symmetry, and advantages of this model over existing MCDM methods are confirmed through sensitivity and comparison analyses. In conclusion, this paper introduces a novel probabilistic decision-support tool that digital forensic specialists can incorporate into their workflow to proactively identify and prevent actions of mobile botnet C&C servers. Full article

The Internet of Medical Things (IoMT) is the latest advancement in the Internet of Things (IoT). Researchers are increasingly drawn to its vast potential applications in secure healthcare systems. The growing use of internet-connected medical device sensors has significantly transformed healthcare, necessitating the development of robust methodologies to assess their integrity. As access to computer networks continues to expand, these sensors have become vulnerable to a wide range of security threats, thereby compromising their integrity. To prevent such lapses, it is essential to understand the complexities of the operational environment and to systematically identify technical vulnerabilities. This paper proposes a unified hesitant fuzzy-based healthcare system for assessing IoMT sensor integrity. The approach integrates the hesitant fuzzy Analytic Network Process (ANP) and the hesitant fuzzy Technique for Order Preference by Similarity to the Ideal Solution (TOPSIS). In this study, a hesitant fuzzy ANP is employed to construct a comprehensive network that illustrates the interrelationships among various integrity criteria. This network incorporates expert input and accounts for inherent uncertainties. The research also offers sensitivity analysis and comparative evaluations to show that the suggested method can analyse many medical device sensors. The unified hesitant fuzzy-based healthcare system presented here offers a systematic and valuable tool for informed decision-making in healthcare. It strengthens both the integrity and security of healthcare systems amid the rapidly evolving landscape of medical technology. Healthcare stakeholders and beyond can significantly benefit from adopting this integrated fuzzy-based approach as they navigate the challenges of modern healthcare. Full article

As vision and mission statements embody the directions set forth by an organization, their connection to the Sustainable Development Goals (SDGs) must be made explicit to guide overall decision-making in taking strides toward the sustainability agenda. The semantic alignment of these strategic statements with the SDGs is investigated in a previous study, although several limitations need further exploration. Thus, this study aims to advance two contributions: (1) utilizing the capabilities of LLMs (Large Language Models) in text semantic analysis and (2) integrating fuzziness into the problem domain by using a novel intuitionistic fuzzy set extension of the PROBID (Preference Ranking On the Basis of Ideal-average Distance) method. First, a systematic approach evaluates the semantic alignment of organizational strategic statements with the SDGs by leveraging the use of LLMs in semantic similarity and relatedness tasks. Second, viewing it as a multi-criteria decision-making (MCDM) problem and recognizing the limitations of LLMs, the evaluations are represented as intuitionistic fuzzy sets (IFSs), which prompted the development of an IF extension of the PROBID method. The proposed IF-PROBID method was then deployed to evaluate the 47 top Philippine corporations. Utilizing ChatGPT 3.5, 7990 prompts with repetitions generated the membership, non-membership, and hesitance scores for each evaluation. Also, we developed a cohort-dependent SDG–vision–mission matrix that categorizes corporations into four distinct classifications. Findings suggest that “highly-aligned” corporations belong to the private and technology sectors, with some in the industrial and real estate sectors. Meanwhile, “weakly-aligned” corporations come from the manufacturing and private sectors. In addition, case-specific insights are presented in this work. The comparative analysis yields a high agreement between the results and those generated by other IF-MCDM extensions. This paper is the first to demonstrate two methodological advances: (1) the integration of LLMs in MCDM problems and (2) the development of the IF-PROBID method that handles the resulting inherently imprecise evaluations. Full article

Microalgae-based carbon sequestration is promising for implementing carbon neutrality and reducing greenhouse gas emissions. However, as the technology remains in its early developmental stages, it presents a range of risks that may deter potential investors. To address these risks, this study proposes a group-based decision-making framework for the risk evaluation of microalgae carbon sequestration projects. Fifteen risk indicators are identified and categorized into four groups, including economic, technical, market, and environmental. To handle uncertainty and vagueness in the assessment, the framework uses trapezoidal fuzzy numbers and hesitant fuzzy linguistic sets to evaluate benchmark values. An expert credibility model is developed to assign weights to expert opinions by combining the subjective RANCOM method and the objective centroid method, both adapted for a fuzzy linguistic environment. A generalized aggregation operator is then used to combine expert evaluations. This operator integrates weighted and ordered averaging techniques and converts probabilistic linguistic terms into trapezoidal fuzzy numbers. The final risk level is determined using a fuzzy comprehensive evaluation method. The results indicate a medium-high level of risk, with a similarity score of 0.960. This suggests that while microalgae carbon sequestration holds great promise, effective planning and risk management are essential. For project managers and investors, this proposed framework helps quantify risk. It provides practical guidance for improving decision-making and strengthening project management. Full article

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

In this article, to address the uncertainty of preference information in interrelated conflicts in the real world, a hierarchical conflict modeling and analysis approach based on hesitant fuzzy linguistic term sets (HFLTSs) is proposed. First, considering the hesitancy and fuzziness of decision makers (DMs) when expressing preferences in hierarchical conflicts, a preference representation approach based on HFLTSs is introduced. Building upon hesitant fuzzy linguistic preference, four distinct types of hesitant fuzzy stability definitions of the two-level hierarchical graph model for conflict resolution (HGMCR) are extended, and a corresponding algorithm is developed to solve the global conflict hesitant fuzzy equilibrium states. Finally, this study is applied to investigate the outbreak and development of a specific international conflict, verifying the feasibility and effectiveness of the proposed approach. The hesitant fuzzy equilibrium states of an international conflict indicate that the attitudes of domestic forces reflect a nation’s performance in the warand that the conflict may endure for an extended duration. The hierarchical conflict modeling and analysis approach based on HFLTSs allows DMs to express the hesitation and fuzziness of preferences under uncertainty, facilitates the comprehension of the intrinsic logic behind interactions among DMs at various levels, and enhances the analysis to achieve more foresighted equilibria. 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

Complex Intuitionistic Fuzzy Sets (CIFSs) are an advanced form of intuitionistic fuzzy sets that utilize complex numbers to effectively manage uncertainty and hesitation in multi-criteria decision making (MCDM). This paper introduces the Shapley Choquet integral (SCI), which is a powerful tool for integrating information from various sources while considering the importance and interactions among criteria. To address ambiguity and inconsistency, we apply the Aczel–Alsina (AA) t-norm and t-conorm, which offer greater flexibility than traditional norms. We propose two novel aggregation operators within the CIFS framework using the Aczel–Alsina Generalized Shapley Choquet Integral (AAGSCI): the Complex Intuitionistic Fuzzy Aczel–Alsina Weighted Average Generalized Shapley Choquet Integral (CIFAAWAGSCI) and the Complex Intuitionistic Fuzzy Aczel–Alsina Weighted Geometric Generalized Shapley Choquet Integral (CIFAAWGGSCI), along with their special cases. The properties of these operators, including idempotency, boundedness, and monotonicity, are thoroughly investigated. These operators are designed to evaluate complex and asymmetric information in real-life problems. A case study on selecting the optimal bridge design based on structural and aesthetic criteria demonstrates the applicability of the proposed method. Our results indicate that the proposed method yields more consistent and reliable outcomes compared to existing approaches. Full article

This study addresses the challenge of effectively modeling uncertainty and hesitation in complex decision-making environments, where traditional fuzzy and vague set models often fall short. To overcome these limitations, we propose the Fermatean neutrosophic vague soft set (FNVSS), an advanced extension that integrates the concepts of neutrosophic sets with Fermatean membership functions into the framework of vague sets. The FNVSS model enhances the representation of truth, indeterminacy, and falsity degrees, providing greater flexibility and resilience in capturing ambiguous and imprecise information. We systematically develop new operations for the FNVSS, including union, intersection, complementation, the Fermatean neutrosophic vague normalized weighted average (FNVNWA) operator, the generalized Fermatean neutrosophic vague normalized weighted average (GFNVNWA) operator, and an adapted Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method. To demonstrate the practicality of the proposed methodology, we apply it to a solar panel selection problem, where managing uncertainty is crucial. Comparative results indicate that the FNVSS significantly outperforms traditional fuzzy and vague set approaches, leading to more reliable and accurate decision outcomes. This work contributes to the advancement of predictive decision-making systems, particularly in fields requiring high precision, adaptability, and robust uncertainty modeling. Full article

The emergence and popularity of social media have made large-scale group decision-making (LSGDM) problems increasingly common, resulting in significant research interest in this field. LSGDM involves numerous evaluators, which can lead to disagreements and hesitancy among them. Hesitant fuzzy sets (HFSs) become crucial in this context as they capture the uncertainty and hesitancy among evaluators. On the other hand, research on the Consensus Reaching Process (CRP) becomes particularly important in dealing with the inevitable differences among the great number of evaluators. Ways to mitigate these differences to reach an agreement are a crucial area of study. For this reason, this paper presents a new CRP model to deal with LSGDM problems in hesitant fuzzy environments. First, HFSs and Normal-type Hesitant Fuzzy Sets (N-HFSs) are introduced to integrate evaluators’ subgroup and collective opinions, aiming to preserve as much decision information as possible while reducing computational complexity. Subsequently, a CRP with a detailed feedback suggestion generation mechanism is developed, which considers the willingness of evaluators to modify their opinions, thereby improving the effectiveness of reaching an agreement. Finally, a LSGDM framework that does not require any normalization process is proposed, and its feasibility and robustness are demonstrated through a numerical example. Full article