Search Results (259)

As cleaner production gains prominence in wooden product manufacturing, green evaluation of process schemes during early design is crucial. However, dust concentration, a key environmental indicator in wood product manufacturing, is often evaluated in a subjective and fragmented manner, which greatly hinders the selection of green process schemes in early design. To address this gap, an adaptability evaluation model for green process schemes was proposed based on process knowledge graphs (PKG) and fuzzy Bayesian network (FBN), with the objective of minimizing dust concentration. First, a PKG for wooden products was constructed based on the requirement-function-structure-characteristic-process-equipment (RFSCPE) ontology using patents and process manuals. Second, candidate process schemes were generated via the PKG, and dust-related causal relationships encoded in the PKG were mapped onto a Bayesian network structure. Third, conditional probabilities were obtained by combining probabilistic hesitant fuzzy sets and experimental dust data. The FBN was then updated to perform probabilistic reasoning on dust concentration. Finally, a case study on a wooden toy car validated the proposed approach, and sensitivity analysis identified the key dust-influencing factors, thereby providing quantitative support for greener process decisions. Full article

Decision-making problems in complex environments are often characterised by uncertainty, vagueness, and dynamically evolving information. In such contexts, decision makers may express hesitant and fluctuating evaluations over time, which cannot be adequately captured by classical hesitant fuzzy frameworks. To address this limitation, time-sequential hesitant fuzzy sets (TSHFSs) have been introduced as an effective tool for modelling temporal hesitancy. However, the development of information measures for TSHFSs, particularly entropy measures for quantifying uncertainty and deriving criteria weights, remains limited. In this paper, we propose a novel class of entropy measures for TSHFSs by constructing transformation mechanisms based on proximity-driven formulations derived from similarity structures. The proposed measures are developed using arithmetic and algebraic operators to capture the dispersion of information across time sequences, enabling a more refined representation of temporal uncertainty. These entropy measures are further integrated into a multi-criteria decision-making (MCDM) framework, where they are employed to determine criteria weights under incomplete information and combined with the TOPSIS method for ranking alternatives. The effectiveness of the proposed framework is validated through comparative analysis with existing TSHFS entropy measures and sensitivity analysis under varying decision conditions. The results demonstrate that the proposed measures maintain ranking consistency while providing improved discrimination and interpretability of alternatives. In particular, the framework effectively captures fluctuating hesitancy and enhances the robustness of decision outcomes in dynamic environments. The proposed approach contributes to the advancement of TSHFS-based decision analysis by offering a mathematically grounded and practically applicable entropy-driven framework for handling time-dependent uncertainty in complex decision-making problems. Full article

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. Full article

Green supply chain management (GSCM) has become essential for organizations seeking to balance environmental sustainability, regulatory compliance, and economic resilience. However, selecting appropriate green supply chain strategies constitutes a complex multicriteria decision-making (MCDM) problem due to diverse sustainability practices, conflicting objectives, dynamic market conditions, and significant uncertainty in expert evaluations. To address these challenges, this study proposes an intelligent multicriteria group decision-making (MCGDM) framework to assess 15 GSCM strategies across 15 environmental, operational, economic, and regulatory criteria. The framework employs complex fractional orthopair fuzzy sets $\left(C_{FOFS}\right)$ to model uncertainty, expert hesitation, and complex-valued judgments. Expert weights are determined using the analytic hierarchy process (AHP), while criteria weights are derived objectively through the entropy method. A modified technique for order preference by similarity to the ideal solution (TOPSIS) is applied to obtain a robust ranking of alternatives. Evaluations from five multidisciplinary experts ensure practical relevance and validity. The results indicate enhanced uncertainty modeling, improved ranking stability, and greater interpretability compared with conventional fuzzy and deterministic approaches. The proposed framework provides a transparent and effective decision support tool for strategic GSCM planning. Full article

Most of the existing evaluation systems for hydrocarbon-bearing play are using various evaluation indicators and fixed weights, which are not sensitive to the subjective/objective cognition or the exploration stages. We construct a multi-level and multi-type play evaluation criteria system with unified standards, the subjective uncertainty of which is formulated by the fuzziness of the indicators. Then, a full-stage dynamic fuzzy multi-criteria decision-making (MCDM) method is presented for play evaluation, in which a dynamic fuzzy-game model is built to combine the objective Criteria Importance Through Intercriteria Correlation (CRITIC) weights improved by the Theil index and the subjective Analytic Hierarchy Process (AHP) weights. This approach can simulate hesitation and strategic trade-offs in the human mind to balance the subjective and objective information. Thereafter, a stage-aware model is developed for play assessment by using dynamic fuzzy comprehensive evaluation, covering the regional exploration, pre-exploration, and evaluation stages. Using the data from plays at different exploration stages in the Tarim Basin, empirical application shows that the evaluation results are consistent with actual exploration judgment. Sensitivity analysis and comparative experiments verify the rationality of parameter setting and the effectiveness and reliability of the presented method. This study offers a practical MCDM for optimizing plays and guiding exploration decisions, which overcomes the limitations of traditional methods, including the lack of a unified evaluation framework, insufficient utilization and integration of multi-source information, inadequate characterization of phased priorities, and limited representation of fuzziness in evaluation indicators. Full article

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. Full article

In order to tackle resilient supplier selection (RSS) of high uncertainty in resilient supply chain management, an effective correlation coefficients-based multicriteria group decision-making (MCGDM) methodology has been constructed. The major contribution of the present study is twofold. Firstly, in view of that extant criteria systems are all in lack of theoretical rationality, this paper establishes a capabilities-based analytical framework for intensive evaluation of supplier resilience by taking processual viewpoints of dynamic capabilities theory and risk management theory. Secondly, to empower the proposed correlation coefficients-based MCGDM methodology, probabilistic dual hesitant fuzzy uncertain unbalanced linguistic set (PDHF_UUBLS) is employed to capture hybrid uncertainties in decision processes of RSS. Then, theoretically compliant correlation coefficients (CCs) for PDHF_UUBLS are developed, including statistics-based CC, information energy-based CC and their weighted versions. Especially, information energy-based CCs overcome limitations of statistics-based CCs in special cases, thus exhibiting general applicability. In addition, a compatibility-based programming model has also been developed to objectively derive an unknown weighting vector for DMUs. Furthermore, illustrative case studies and comparative experiments have been carried out to verify effectiveness and stability of the proposed methodology. Taken together, this paper satisfies the new normal demand of resilience building in supply chain management and presents an effective MCGDM methodology for handling the key problems of RSS. Full article

With the rapid development of intensive marine aquaculture, water quality has become a key factor affecting both economic benefits and ecological safety in marine aquaculture. In the process of actual water quality evaluation, due to the great uncertainty and ambiguity of evaluation indicators, experts find it difficult to evaluate in real number form and are more inclined to use linguistic variables to evaluate indicators, which poses challenges for the construction of water quality evaluation models. An intuitionistic fuzzy set (IFS) is an effective tool for dealing with uncertainty and fuzziness in complex problems. Based on a detailed analysis of existing distance measures for IFS, this study proposes a new distance measure that not only considers membership and non-membership information, but also constructs an allocation function for membership and non-membership, introducing hesitation information into distance metrics. We proposed the definitions and proved the properties. The comparative experiments show that the new distance measure can overcome the shortcomings of existing distance measures. Furthermore, based on the newly proposed distance measure, the IFS TOPSIS method is improved in multi-attribute decision-making applications. Finally, a practical application of marine aquaculture water quality evaluation is used. The results illustrate that when $\alpha$ = 1 the closeness declines from 0.741 to 0.432, when =2 the closeness declines from 0.662 to 0.46, and when =6 the closeness declines from 0.566 to 0.82. The convenience and effectiveness of the new method is demonstrated. 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

The Bonferroni mean operator, as a powerful aggregation operator, is widely applied as a solution to various problems, owing to its strong ability to capture relevance between different variables. Compared with other extensions, the weighted hesitant fuzzy set (WHFS) can depict the fuzziness of relationships between things better. Considering the advantage of weighted hesitant fuzzy sets (describing fuzziness more objectively in real problems), the Bonferroni mean is introduced into weighted hesitant fuzzy set theory. In this paper, by merging and transforming weighted hesitant fuzzy weighted average/geometric (WHFWA/WHFWG) operators, a novel weighted hesitant fuzzy geometric Bonferroni mean (WHFGBM) operator is developed using weighted hesitant fuzzy theory, so as to fuse information and provide idea support for practical tasks under various experts’ common judgment. To show the effectiveness of the novel operator intuitively, the comparison results of symmetric numeric examples are displayed. Full article

Traditional multi-criteria decision-making methods often operate on the assumption of symmetry, presupposing that the positive impact of a criterion’s presence is perfectly complementary to the negative impact of its absence. However, in real-world decision problems, this relationship is frequently asymmetric; some criteria act merely as “delighters,” while others represent “must-have” constraints. This study proposes a novel methodology, the Presence–Absence Synthesis (PAS) Method, which addresses this asymmetry by treating the “Presence Effect” and “Absence Effect” of criteria as two independent dimensions. The method is built upon intuitionistic fuzzy sets (IFSs) to effectively model the uncertainty and hesitation inherent in expert evaluations. The applicability of the proposed approach is demonstrated through a real-world workforce management problem aimed at assigning employees to the most suitable tasks based on their competencies in a retail store. In the study, the suitability scores derived from the PAS method are integrated into a mathematical optimization model for weekly employee scheduling, presenting a two-stage decision support framework. The results and comparisons with the Technique for Order Preference by Similarity to Ideal Solution method reveal that the PAS method more effectively distinguishes critical competency gaps (i.e., criteria with high absence effects), leading to more realistic task assignments and a measurable reduction in operational risks, such as skill mismatches and infeasible schedules. Furthermore, sensitivity analysis confirms that the proposed model yields consistent and robust results under varying conditions. Beyond the retail context, the proposed PAS framework is applicable to a wide range of decision-making problems, including healthcare staff allocation, project team formation, supplier selection, and other resource allocation settings where their presence cannot compensate for the absence of critical criteria. Full article

This paper proposes a theoretical framework for studying rough intuitionistic fuzzy filters within the structure of BE-algebras. Building on rough set theory and intuitionistic fuzzy set theory, we introduce rough intuitionistic fuzzy filters via lower and upper approximation operators induced by congruence relations. To further generalize the framework, we define set-valued homomorphisms on BE-algebras and use them to formulate $\Gamma$-rough intuitionistic fuzzy filters. Several structural properties and characterization results are established, including stability under approximation operators, relationships with classical intuitionistic fuzzy filters, and preservation under homomorphic mappings. The proposed approach provides an algebraic mechanism for modeling uncertainty, hesitation, and imprecision in implication-based systems, with potential relevance to uncertainty-aware reasoning in artificial intelligence, decision-support systems, and medical diagnosis. Full article

This paper proposes a novel method, the Convergent Radiation Algorithm (CRA), aimed at multi-attribute group decision-making (MAGDM) in circular intuitionistic fuzzy settings. The approach is aimed at reaching geometric consensus among experts, with uncertainties and hesitancies expressed via circular intuitionistic fuzzy numbers (CIFNs). First, the qualitative judgment in professionals is converted into a geometric space where experts’ assessments are represented as spatial points that reflect the differences between the opinions. All these points are gradually combined with the help of a radiation–reflection–convergence mechanism, which iteratively finds the Optimal Consensus Point (OCP) to minimize the overall weighted divergence over the evaluations. After that, a projection-based scoring method is used to locate good and bad optimal solutions, and the alternatives are ranked based on a comparison of their projection distance. It presents a numerical example with data supplied by the Hubei agro-ecological zone to demonstrate that the offered method helps to capture collective agreement and convergence behavior that is consistent, and makes the decision results readable and reliable. Full article

Fuzzy implication operators are vital in the modeling of uncertain reasoning, particularly in approximate reasoning and fuzzy inference systems. The objective of this survey is to provide a structured and comprehensive overview of fuzzy implication, intuitionistic fuzzy implication, and hesitant fuzzy implication. We examine their properties, representations, and characterizations. We discuss a number of findings about fuzzy negations, fuzzy implications, intuitionistic fuzzy implication, and hesitant fuzzy implications, including their characterizations with respect to the identity principle and ordering property, which lead to fundamental results. Full article