Search Results (231)

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

To systematically address the intricate multiple criteria decision-making (MCDM) challenges to practical situations where uncertain and hesitant information plays a critical role in guiding optimal choices. In this article, we introduce the concept of $\mathfrak{m}$-polar Q-hesitant fuzzy ($\mathcal{MPQHF}$) $\mathfrak{B}\mathrm{C}\mathbb{K}/\mathfrak{B}\mathrm{C}\mathbb{I}$ algebras, combining $\mathfrak{m}$-PFS theory with Q-hesitant fuzzy set theory in the framework of $\mathfrak{B}\mathrm{C}\mathbb{K}$/$\mathfrak{B}\mathrm{C}\mathbb{I}$ algebras. This innovative approach enhances the attitudes of uncertainty, vagueness, and hesitance of data in decision-making processes. We investigate the features and actions of this proposed hybrid approach to fuzzy sets and hesitant fuzzy sets, focusing on $\mathcal{MPQHF}$ subalgebras, and explore the characteristics of several kinds of ideals under $\mathfrak{B}\mathrm{C}\mathbb{K}$/$\mathfrak{B}\mathrm{C}\mathbb{I}$ algebras. It also showed that it can better represent complex levels of uncertainty than regular sets. The proposed method’s theoretical framework offers a better way to show uncertain data in areas like engineering, computer science, and computational mathematics. By linking theoretical advancements of $\mathcal{MPQHF}$ sets with practical applications, we highlight the benefits and challenges of this approach. Demonstrating the practical uses of the $\mathcal{MPQHF}$ sets aims to encourage broader adoption. Symmetry plays a vital role in algebraic structure and is used in various fields like decision-making, encryption, pattern recognition problems, and automata theory. Furthermore, this work enhances the understanding of algebraic structures and offers a robust tool for career exploration and development through improved decision-making methodologies. 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

In recent years, the disruption of the prefabricated building supply chain has led to increased construction period delays and cost overruns, limiting the development and popularization of prefabricated buildings in China. Therefore, this study established a vulnerability evaluation index system for the prefabricated building supply chain using the driving force–pressure–state–impact–response (DPSIR) framework. We employed the intuitionistic fuzzy analytic hierarchy process (IFAHP), the projection pursuit (PP) model, and variable weight theory to determine the indicator weights. The IFAHP was utilized to reduce the subjectivity in weight assignment and to obtain the degree of membership, non-membership, and hesitation of experts in evaluating the importance of indicators. The PP model was used to determine objective weights based on the structure of the evaluation data, and variable weight theory was applied to integrate subjective and objective weights according to management needs. We utilized Set Pair Analysis (SPA) to establish a vulnerability evaluation model for the building supply chain, treating evaluation data and evaluation levels as a set pair. By analyzing the degree of identity, difference, and opposition of the set pair, we assessed and predicted the vulnerability of the building supply chain. Taking the Taohua Shantytown project in Nanchang as a case study, the results showed that the primary index with the greatest influence on the vulnerability of the prefabricated building supply chain was the driving force, with a weight of 0.2692, followed by the secondary indices of market demand and policy support, with weights of 0.0753 and 0.0719, respectively. The project’s average vulnerability rating was moderate (Level III), and it showed an improvement trend. During the project’s implementation, the total cost overrun of the prefabricated building supply chain was controlled within 5% of the budget, the construction period delay did not exceed 7% of the plan, and the rate of production safety accidents was below the industry average. The results demonstrated that the vulnerability assessment method for the prefabricated building supply chain based on SPA comprehensively and objectively reflected the vulnerability of the supply chain. It is suggested to improve the transparency and flexibility of the supply chain, strengthen daily management within the supply chain, and enhance collaboration with supply chain partners to reduce vulnerability. 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

Human-centric and sustainable cities have become one of the most popular research areas today. They are based on a holistic approach that aims to both improve people’s quality of life and ensure environmental sustainability. The weighting of numerous tangible and intangible criteria used in the performance evaluation of these cities has emerged as an important problem. The symmetrical representation of vague and imprecise data using fuzzy set theory is an absolute necessity for a successful weighting process. In this study, symmetrical representation of especially intangible criteria is carried out with proportional spherical fuzzy sets. Proportional spherical fuzzy sets provide significant convenience to the expert in determining the membership, non-membership and hesitancy degrees and ensure that the assigned values are more accurate and consistent. In the study, five main human centric and sustainable city (HCSC) criteria and 26 HCSC sub-criteria determined from the literature were weighted. In addition, criteria weights were obtained by classical spherical fuzzy analytic hierarchy process (AHP) for comparison purpose. The first four most important HCSC criteria were determined as water management and conservation, employment/unemployment rate, carbon emission reduction strategies and economic sustainability, respectively. Full article

With the advent of digitization, digital twin technology is gradually becoming one of the core technologies of the Industry 4.0 era, highlighting the increasing importance of digital twin project management. Despite its potential, DT projects face significant risks during implementation, stemming from technical, managerial, and operational complexities. To address these challenges, this study proposes an improved failure mode and effect analysis (FMEA) framework by integrating double hierarchy hesitant fuzzy linguistic term sets (DHHFLTSs) and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). This framework converts qualitative assessments into quantitative metrics and calculates weights using a hybrid approach, enabling more precise risk prioritisation. Application of the model to an automotive manufacturing company’s DT project identified key risks, particularly in the iteration and upgrade phase, emphasising the importance of cross-departmental collaboration and robust digital infrastructure. The proposed model provides a systematic framework for enterprises to assess and mitigate risks, ensuring the successful deployment of DT projects. Full article

Representing and interpreting human opinions within an unstructured framework is inherently complex. Hesitant fuzzy linguistic term sets offer a comprehensive context that facilitates a nuanced understanding of diverse perspectives. This study introduces a methodology that integrates sentiment analysis with hesitant fuzzy linguistic term sets to effectively aggregate and compare news from diverse sources. By employing linguistic scales, our approach enhances the interpretation of various perceptions and attitudes, facilitating comprehensive knowledge extraction and representation. The main objective of this research is to conduct a comparative analysis of news coverage across European countries in relation to the Israel–Gaza war. This analysis aims to capture the multifaceted sensitivities surrounding the ongoing situation, highlighting how different nations perceive the conflict. Full article

The fundamental notions of the intuitionistic hesitant fuzzy set (IHFS) and rough set (RS) are general mathematical tools that may easily manage imprecise and uncertain information. The EDAS (Evaluation based on Distance from Average Solution) approach has an important role in decision-making (DM) problems, particularly in multi-attribute group decision-making (MAGDM) scenarios, where there are many conflicting criteria. This paper aims to introduce the IHFR-EDAS approach, which utilizes the IHF rough averaging aggregation operator. The aggregation operator is crucial for aggregating intuitionistic hesitant fuzzy numbers into a cohesive component. Additionally, we introduce the concepts of the IHF rough weighted averaging (IHFRWA) operator. For the proposed operator, a new accuracy function (AF) and score function (SF) are established. Subsequently, the suggested approach is used to show the IHFR-EDAS model for MAGDM and its stepwise procedure. In conclusion, a numerical example of the constructed model is demonstrated, and a general comparison between the investigated models and the current methods demonstrates that the investigated models are more feasible and efficient than the present methods. Full article

Online product reviews provide valuable insights on user experiences and product qualities. However, issues such as information overload and the limited utilization of review features persist, particularly in personalized rankings for popular items like movies. To address these challenges—information overload in online reviews, limited review feature utilization, and personalized decision-making for high-demand products like movies—we introduce a personalized online decision-making framework that integrates a sentiment model for product attributes with an enhanced hesitant fuzzy scoring function. This framework incorporates the concept of symmetry in sentiment analysis. It employs feature words, sentiment terms, and modifiers to assess user sentiments within a hesitant fuzzy setting, utilizing symmetrical relationships between positive and negative sentiments. The improved fuzzy score function efficiently quantifies sentiment values for product features by considering the symmetrical balance of user opinions. Additionally, review quality assessment incorporates both content and reviewer characteristics, resulting in final attribute evaluations. An attribute weighting system, tailored to diverse product types, further captures product specifics and user inclinations, leveraging symmetry to balance varying user preferences. Validation through multi-genre movie sorting demonstrates the method’s capacity to handle review data across varied products and user tastes, offering a robust tool for enhancing online decision quality, especially for high-demand items. Full article