Search Results (436)

Multi-criteria group decision making (MCGDM) under linguistic uncertainty remains a fundamental challenge in applied mathematics, where decision makers seldom assign crisp numerical evaluations and frequently exhibit heterogeneous risk attitudes shaped by behavioural factors. An integrated mathematical framework, hereafter PLR-3WBC (Probabilistic Linguistic Regret-driven Three-Way Bayesian Consensus), is developed to systematically integrate four methodological components that have each been individually validated in the MCGDM literature: representation of decision information with explicit probability mass on linguistic terms; quantification of decision-maker regret and rejoice psychology under linguistic uncertainty; classification of alternatives into three actionable decision regions rather than a single-valued ranking; and group consensus reaching with credal weight aggregation. Each component has demonstrated its effectiveness in its respective domain; the present framework capitalises on their complementary strengths by embedding them within a single pipeline equipped with formal guarantees, an integration that has not been previously reported. The framework integrates five methodological components: probabilistic linguistic term sets (PLTS) for information representation; the Bayesian best–worst method (BBWM) for credal criterion weighting; a regret–rejoice value function adapted to the linguistic domain for behavioural evaluation; three-way decision (3WD) thresholds derived from a loss-function model for actionable classification; and a distance-based consensus reaching process with feedback mechanism for group convergence. A case study on age-friendliness evaluation of twelve aging urban residential communities under an indicator system of five dimensions and eighteen criteria, with four expert decision makers, demonstrates that PLR-3WBC delivers an actionable three-way classification, recovers a transparent group consensus, and produces rankings broadly consistent with classical TOPSIS, VIKOR, PROMETHEE-II, and BWM-TOPSIS (Spearman rank correlation exceeding 0.97), thereby confirming that the integrated framework preserves the ordinal reliability of these established methods, while additionally delivering three outputs that arise from the methodological integration: an actionable three-way classification enabling discrete budget-aligned decisions, credal weight intervals quantifying the depth of expert agreement on criterion importance, and a behavioural reordering of borderline non-dominated alternatives that reflects the loss-averse psychology of the decision panel and would remain hidden under single-method deployment. Sensitivity analyses with respect to the regret aversion coefficient, the loss function parameters, and the consensus threshold confirm that the qualitative classification is stable across a wide parameter envelope, supporting the practical deployment of PLR-3WBC in age-friendly community renewal programmes. Full article

Industrial Symbiosis (IS) is a key Circular Economy strategy that promotes resource efficiency through collaboration among companies. While previous research has largely focused on established IS business models, increasing attention has been given to sector-specific implementation and the contextual factors that influence its success. This study develops a Multi-Criteria Decision Analysis (MCDA) framework based on the Deck of Cards Method (DCM) to support the sectoral implementation of IS. A key innovation of this study is the incorporation of IS enablers and barriers into a sector-specific MCDA framework, providing a structured approach to support decision-making and implementation. By incorporating stakeholder preferences and prioritizing implementation opportunities, the framework provides a structured basis for decision-making, being replicated and adaptable to other industrial sectors. The framework was applied to the Portuguese cement sector through consultations with experts representing five stakeholder groups, furtherer allowing its validation. The analysis combines the importance assigned by stakeholders to the criteria and the performance of the sector across those criteria. Results for the sector perspective indicate that policy, economic, and technological criteria are perceived as the most important for advancing IS, whereas geographical, social, and management-related aspects receive lower priority. In Portugal, this sector demonstrates stronger performance in economic (17.49–3.04), technological (13.80–5.99), and environmental (14.58–3.19) criteria, while challenges remain in geographical coordination (1.16–7.95), social engagement social (0.79–6.81), and intermediary support (1.15–8.44). These findings highlight the importance of aligning policy, technological development, and organizational mechanisms to facilitate industrial collaboration and resource exchange. The study demonstrates the potential of MCDA as a practical and effective decision-support tool for IS implementation and provides insights for designing targeted strategies to strengthen sectoral Industrial Symbiosis. Full article

Algorithmic prediction models are increasingly used to support decision-making in high-stakes environments, including emergency departments (ED). However, aggregate performance metrics may obscure systematic differences in classification errors or calibration across subgroups. This study presents a stage-wise, multi-metric, and interpretable fairness auditing framework for ED prediction. The framework compares mitigation strategies across data-, model-, and decision-level interventions, evaluates subgroup fairness using complementary classification and calibration criteria including equalized odds difference (EOD) and expected calibration error (ECE) disparity, and incorporates interpretability analyses based on SHapley Additive exPlanations (SHAP) and the calibration adjustment difference (CAD) to characterize changes in feature-contribution patterns and subgroup-specific probability adjustments after mitigation. The framework was applied to 126,819 ED encounters from MIMIC-IV-ED using measurements recorded within the first 2 h after arrival, and penalized logistic regression and random forest models were compared under reweighting, reduction, and multicalibration. Baseline AUROC values were 0.748 ± 0.028 for random forest and 0.746 ± 0.028 for penalized logistic regression. Reduction and multicalibration largely preserved discrimination performance, whereas reweighting was associated with reduced AUROC and AUPRC. Reweighting most clearly reduced EOD-based classification disparity, particularly for age, yielding reductions of 80.6% in random forest and 86.4% in penalized logistic regression. By contrast, multicalibration most consistently reduced ECE-based calibration disparity for sex and age but did not consistently improve EOD-based classification disparity. In the interpretability analyses, SHAP indicated that data- and model-level mitigation altered feature-contribution patterns, whereas CAD showed that decision-level mitigation produced subgroup-specific probability adjustments that varied in direction and magnitude across groups. These findings reveal trade-offs among discrimination performance, classification fairness, and calibration fairness, indicating that fairness mitigation should be guided by a clearly defined target fairness objective. Pre-deployment fairness auditing should therefore combine complementary fairness metrics with interpretability analyses to evaluate both subgroup-level outcomes and unintended changes in model behavior. Full article

Smart shipping and achieving net-zero emissions have become pressing priorities in maritime transport, yet limited research has integrated sustainable shipping development with green finance decision-making. To address this gap, this study applies the AHP–RDEMATEL–TOPSIS approach to analyze the interrelationships and relative importance of key sustainability factors and to identify optimal green financing instruments. Incorporating ESG dimensions, the research conducted a survey of large international exporters in Taiwan and senior managers of shipping companies. The results reveal that green infrastructure is the most critical factor for container shipping lines, while energy efficiency and renewable energy technologies are dominant for bulk carriers and shippers. Corporate reputation and image emerge as primary factors impacted across all three groups. In financing decisions, green bonds are most suitable for container lines, whereas green equities are best suited for bulk carriers. This study bridges the theoretical gap between sustainability assessment and finance, providing practical guidance for shipping companies’ financial departments seeking to align decarbonization goals with effective green financing solutions. Ultimately, the primary contribution of this study lies in establishing an empirically validated, multi-criteria decision support framework that empowers maritime stakeholders to systematically optimize their green investment portfolios amid the global transition towards net-zero emissions. Full article

Objects in nature tend to occupy the minimum volume (or minimum area in two-dimensional space). In decision making processes, decisions involve the grouping of decision points within a given environment, and the existence of a closed-form representing this group decision is noteworthy. Current group decision-making models often rely on arithmetic and geometric operators, neglecting the inherent spatial information embedded within the decision space. When the structure formed by decision groups is associated with a convex structure representing it that occupies the least volume or area; the decision-making structure also needs to be re-evaluated geometrically in addition to operations in the literature. In this context, this article is a novel perspective on the introduction of the Shapeless Intuitionistic Fuzzy Set (S-IFS) which is an extension of intuitionistic fuzzy sets. The operations and structure of these sets, which are a new extension with the convex structure formed by the IF decision points, are examined. A numerical micromobility risk assessment case is presented to demonstrate the application of S-IFS in multi criteria decision making procedures. To compare S-IFS with the literature, a new score function has also been proposed to Circular Intuitionistic Fuzzy Set (C-IFS) with the perspective of the proposed fuzzy set. The effect of including the uncertainty in the geometric structure of group decisions into the result is clearly revealed by comparing the point group decisions of IFS, the circle covering group decisions of C-IFS, and the convex group decisions occupying the smallest area in two dimensions of the proposed S-IFS. This article aims to lead the examination of the geometric structure of fuzzy sets in group decisions, the inclusion of uncertainty in decision-making processes in a geometric sense, and the structure of group decisions in n-dimensions according to convex and concave formations for future studies. Full article

Rapid urbanization has intensified congestion, environmental pressures, and transport inequities, thereby increasing interest in Smart Urban Mobility (SUM) as an approach that combines digital technologies, sustainable transport strategies, and data-informed decision-making to respond to these challenges. However, the evaluation of SUM remains fragmented due to the absence of harmonized assessment frameworks and the diversity of methodologies applied across smart city contexts. This study presents a systematic literature review of evaluation approaches and indicator architectures for SUM in smart city contexts. Using a PRISMA-guided screening process, 33 eligible studies were selected from 412 retrieved records. Three main methodological groups were identified: quantitative approaches, multi-criteria decision-making methods, and qualitative or participatory frameworks. A total of 273 indicators were organized into eight factor categories, confirming the multidimensional nature of smart mobility assessment while also revealing limited consistency in indicator selection and application across studies. Across the selected studies, current evaluation practices are increasingly linked to project prioritization, planning, and decision support; however, their effectiveness remains constrained by data inconsistencies, governance fragmentation, and insufficient user inclusion. These findings highlight the need for assessment frameworks that are sufficiently comparable to enable cross-city learning, yet flexible enough to reflect local contexts and institutional realities. Full article

In recent years, multi-criteria group decision-making (MCGDM) methods have attracted widespread attention in the academic community. However, most existing MCGDM approaches suffer from limitations in decision-makers’ expressive capacity and the loss of uncertain information. To address these issues, this study proposes a novel multi-criteria group decision-making (MCGDM) framework. First, we developed an evaluation information representation method called the hybrid probabilistic information set (HPIS), which allows DMs to fully express their opinions based on individual cognition using the most suitable form of representation. Second, the criteria importance through inter-criteria correlation (CRITIC) and the combined compromise solution (CoCoSo) methods are extended into the cloud model environment, ensuring that the rich uncertainty information is fully preserved and transmitted throughout the entire evaluation process. Finally, we apply the proposed MCGDM framework to a practical case study evaluating urban flood resilience within an urban agglomeration, to identify its vulnerable components. The results indicate that Baoding, Zhangjiakou, and Chengde are identified as the most vulnerable cities, necessitating immediate and targeted measures to bolster their flood defense capabilities. At the same time, decision-makers can select both qualitative and quantitative comments simultaneously and carry uncertainty information throughout the entire calculation process. Furthermore, the sensitivity and comparative analyses demonstrate the robustness and practical utility of the proposed method under the tested scenarios. Full article

Improving pedestrian safety at urban intersections is a key challenge for achieving safer and more sustainable urban transport systems. This study develops a multi-criteria decision-making model (MCDM) for selecting the most appropriate traffic signal type at pedestrian crossings in different urban zones. Traffic conditions, illegal pedestrian crossings and the number of traffic accidents were taken into account during the modelling, as well as the characteristics of the urban environment. The research involved 66,616 pedestrians at 22 pedestrian crossings located in three urban zones: school zones, central zones, and non-central zones. The data were aggregated using Bayesian (beta-binomial) and classical statistical methods. The OPA-Group method was then used to develop the model. In the decision-making phase, the Ordinal Priority Approach (OPA) was applied as the core MCDM method. It was then extended to the OPA-Group framework to incorporate group-based evaluation in accordance with the model requirements. Additionally, a comprehensive sensitivity analysis was conducted, confirming the robustness and stability of the proposed model. The results show that traditional traffic signals are most suitable for school and non-central zones, whereas countdown traffic signals are recommended for central zones. Push-button traffic signals were identified as the least efficient solution for regulating pedestrian movement at pedestrian crossings. Full article

As Industry 4.0 transforms manufacturing operations, maintenance organizations face a group decision-making problem: how to consolidate diverse expert judgments into a defensible, transparent ranking of the competencies that maintenance personnel most need. This paper applies an integrated Delphi–AHP framework—with explicit notation, operators, and diagnostics—to prioritize maintenance competencies in advanced-manufacturing settings. The Delphi stage consolidates expert-generated items under median–interquartile-range consensus and round-to-round stability rules, while the Analytic Hierarchy Process (AHP) transforms validated pairwise comparisons into ratio-scale priority weights through geometric-mean Aggregation of Individual Judgments (AIJ) and eigenvector derivation. Consistency screening (CI/CR), inter-rater agreement (Kendall’s W), and perturbation-based sensitivity analysis accompany the resulting weight vector. A bounded AI-assisted consistency-check step supports terminology harmonization during Delphi statement consolidation, subject to explicit human-validation constraints. A panel of fifteen industry experts participated in the study; five competency dimensions and twenty-nine indicators were retained through three Delphi rounds. AHP weighting identified Basic Knowledge and Skills as the highest-priority dimension, followed by Safety and Regulation Awareness and Problem-Solving Ability. Aggregated pairwise comparison matrices, local and global weights, and sensitivity results are reported to support reproducibility. The study contributes a rigorously specified application of combined Delphi–AHP to a domain—Industry 4.0 maintenance asset management—where multi-criteria decision analysis has seen limited formal application, and closes common specification gaps in published Delphi–AHP implementations. Full article

Food Loss and Waste (FLW) remain major challenges for global food security, environmental sustainability, and economic stability, with nearly one-third of food produced each year being lost or wasted. Although many technologies exist to mitigate FLW, they are often assessed separately, making it difficult for decision-makers to compare options and select solutions suited to specific contexts. This research introduces an explainable decision support system (XDSS) that helps prioritise FLW mitigation strategies while accounting for uncertainty in stakeholder preferences. The proposed framework combines the Best–Worst Method (BWM) with Stochastic Multi-criteria Acceptability Analysis for Group Decision-Making (SMAA-2) to produce transparent and uncertainty-aware rankings. It evaluates one hundred FLW mitigation strategies across five contextual criteria: geographic fit, product category, food supply-chain stage, stakeholder role, and technology type. Rather than producing a single fixed ranking, the system generates probabilistic rank-acceptability profiles that indicate the likelihood of each strategy performing well under different preference conditions. Illustrative scenarios demonstrate that the framework can translate qualitative user preferences into robust prioritisation outcomes, with leading alternatives achieving first-rank-acceptability levels between 62% and 74%. These results indicate that the system can support clearer and more flexible decision-making when preferences are incomplete, inconsistent, or uncertain. Although the current results are based on simulated structured cases, the proposed XDSS provides a transparent methodological foundation for future real-world validation and operational deployment. The framework offers practical value for selecting FLW technologies and for policy planning, contributing to more sustainable food systems and supporting progress toward SDG 12.3. Full article

Aero-engine quality assessment under the RAMS framework faces two persistent challenges: the inherent epistemic and linguistic uncertainty in expert evaluation, and the systematic neglect of inter-dimensional coupling. This paper proposes an integrated assessment method that combines Interval Type-2 Fuzzy Sets (IT2FS)-based group decision-making with Partial Least Squares Structural Equation Modeling (PLS-SEM). At the measurement level, IT2FS encodes dual-layered uncertainty through the Footprint of Uncertainty (FOU); multi-expert judgments are aggregated via the fuzzy weighted geometric average operator and defuzzified using the Karnik–Mendel algorithm. At the structural level, a reflective second-order PLS-SEM model built on the RAMS framework enables parametric estimation and significance testing of inter-dimensional coupling. Validation on a 63-engine turbofan dataset confirms that all measurement model criteria are satisfied, the second-order model explains 82.4% of the variance in overall quality (R² = 0.824), and predictive relevance is strong (Q² = 0.567). Comparative experiments against three benchmark methods demonstrate consistent advantages in quality grade discrimination, information richness, sensitivity to technical improvements, and ranking robustness. These properties position the framework as a statistically rigorous, model-based complement to existing condition-monitoring and digital health management systems for complex propulsion systems, supporting quantitative decision-making within digital engineering programmes. 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

This paper develops novel similarity and dissimilarity measures for $(p,q,r)$-fractional fuzzy sets to enhance information discrimination and decision-making under complex uncertainty. We first introduce axiomatic dissimilarity measures and establish their fundamental mathematical properties, including boundedness, symmetry, monotonicity, and identity conditions. Based on these, we derive corresponding similarity measures that improve discrimination capability. We further propose a multi-criteria group decision-making framework to facilitate robust, accurate ranking of alternatives by integrating the developed measures into a $(p,q,r)$-fractional fuzzy inferior ratio method. The approach evaluates alternatives using relative inferiority relationships and provides stable, reliable rankings in uncertain environments. Illustrative examples demonstrate the proposed method’s effectiveness and applicability, and sensitivity analysis examines decision robustness. Comparative analysis with existing methods confirms the superiority of the proposed framework, showing that it offers stronger discrimination ability and serves as a flexible, reliable tool for complex multi-criteria group decision problems under $(p,q,r)$-fractional fuzzy environments. 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

The main purpose of the research is to rank EU member states by the intensity of their efforts to implement the CE model. Understanding EU member states’ differences is crucial to formulating effective policy measures that foster sustainable development and enhance economic resilience across the EU. The degree of CE development was examined through three sub-indicators: (i) private investment related to CE sectors; (ii) persons employed in CE sectors; and (iii) gross value added as a percentage of GDP. Data from the Eurostat database for the last five available years were used. Hierarchical agglomerative cluster analysis is used to identify groups of structurally similar countries. Countries are ranked using the PROMETHEE II multi-criteria decision-making method with objectively derived CRITIC weights, complemented by GAIA visualisation. The analysis identifies five distinct clusters with a highly heterogeneous CE landscape across the EU. The PROMETHEE-GAIA research results reveal two different paths on which European countries are moving towards CE. The first, characterized by high structural maturity but limited dynamic flexibility, is evident in Sweden and Belgium. And the second path, illustrated by Estonia and Croatia, is distinguished by a rapid pace of transformation and lower historical structural capacities. Full article