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Advances in Multi-Criteria Decision Making Methods with Applications

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A Special Issue of Mathematics (ISSN 2227-7390) belonging to the section "D2: Operations Research and Fuzzy Decision Making".

Deadline for manuscript submissions: 31 October 2026 | Viewed by 15767

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Editors

Dr. Gabriella Marcarelli

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Guest Editor

Department of Law, Economics, Management and Quantitative Methods, University of Sannio, Italy
Interests: multi-criteria decision-making methods; analytic hierarchy process; consistency and transitivity measures for pairwise comparison matrices; group decisions

Dr. Pietro Amenta

E-Mail Website
Guest Editor

Department of Law, Economics, Management and Quantitative Methods, University of Sannio, Italy
Interests: AHP; multi-group decision-making problem; multivariate data analysis; linear algebra; statistical analysis of preferences

Dr. Antonio Lucadamo

E-Mail Website
Guest Editor

Department of Law, Economics, Management and Quantitative Methods, University of Sannio, Italy
Interests: multidimensional data analysis; multicollinearity problem in logistic regression; robustness in classification techniques and regression models; consistency of pairwise comparison matrices and aggregation of judgments in the analytic hierarchy process; structural equation modeling in tourism; circular data

Special Issue Information

Dear Colleagues,

Multi-criteria decision-making (MCDM) approaches help decision-makers face problems characterized by multiple conflicting criteria. They include analytical tools and methods that have been widely used over the past few decades to solve complex decision-making problems in various fields, such as economics, finance, logistics, environmental remediation, business, engineering, medicine, law, etc.

Over the past 40 years, numerous multiple-criteria methods have been developed. The software available has made MCDM methods more accessible, increasing their use amongst researchers and the user community. Recently, there have been suggestions for combining two or more methods.

We invite researchers and practitioners to submit original research and critical survey manuscripts that propose MCDM approaches and their applications in real-life-related problems.

This Special Issue focuses on, but is not limited to, the following topics:

Decision analysis;
Decision support systems;
Group decision-making;
Integrated approaches for modeling decision-making;
Soft-computing techniques for MCDM;
Consistency measures;
Pairwise comparisons.

Dr. Gabriella Marcarelli
Dr. Pietro Amenta
Dr. Antonio Lucadamo
Guest Editors

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Keywords

multi-criteria decision-making (MCDM)
group decision-making
pairwise comparisons
decision analysis
decision support systems
group decision-making
integrated approaches for modeling decision-making
soft-computing techniques for MCDM
consistency measures
pairwise comparisons

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Published Papers (10 papers)

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Research

26 pages, 5916 KB

Open AccessArticle

A Novel Expanding-Window Tensor TOPSIS (EWTT) Approach for Dynamic Sustainability Ranking of Countries

by Ali Özarslan and Orhan Balcı

Mathematics 2026, 14(17), 3054; https://doi.org/10.3390/math14173054 - 25 Aug 2026

Viewed by 287

Abstract

This study proposes the Expanding-Window Tensor TOPSIS method, a novel dynamic multi-criteria decision analysis framework that integrates temporal feature extraction with an expanding-window estimation scheme. The method structures panel data as a third-order tensor and extracts three time-series features—linear trend, mean, and standard deviation—from rolling windows for each alternative-criterion pair. These features are retained as distinct dimensions of the decision matrix. At each target year, normalization bounds, entropy weights, and ideal solutions are calculated based on the information accumulated up to that year, thereby avoiding look-ahead bias. A burn-in threshold prevents unreliable early estimates, while complementary diagnostics assess the convergence of weights and sensitivity to the window width. The method yields a dynamic score matrix representing the evolution of the relative position of each alternative over time. The proposed framework is applied to the ND-GAIN Country Index, which includes data for 152 countries from 2000 to 2024. The dynamic rankings have high face validity, almost perfect robustness to the choice of window width and burn-in threshold, fast convergence of the entropy weights, and robustness to changes in the alternative set. Extensive robustness checks—including Monte Carlo weight-uncertainty analysis, comparisons with alternative weighting (CRITIC, standard-deviation-based, equal weighting) and aggregation (VIKOR) methods, and benchmarks against Dynamic TOPSIS-Entropy and a rolling-window variant—confirm the insensitivity of the findings to the choice of weighting and aggregation strategy. The methodology is not domain-specific and offers a transparent and diagnostically rich tool for dynamic performance evaluation. Full article

(This article belongs to the Special Issue Advances in Multi-Criteria Decision Making Methods with Applications)

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23 pages, 402 KB

Open AccessArticle

Incorporating a New Weighting Scheme into Decomposition Ensemble Models for Forecasting Air Passenger Flow by Combining Fuzzy Cognitive Maps with Grey Relational Analysis

by Yi-Chung Hu, Geng Wu and Yu-Chao Cheng

Mathematics 2026, 14(15), 2804; https://doi.org/10.3390/math14152804 - 4 Aug 2026

Viewed by 292

Abstract

Previous studies in passenger flow forecasting commonly employ decomposition ensemble models with linear addition, treating individual single-component forecasts with equal weights, to produce ensemble forecasts. It is known that fuzzy cognitive maps (FCMs) in multiple criteria decision-making are capable of modeling system dynamics by catching the causal relationships between the concepts describing a system. To enhance the forecasting ability of decomposition ensemble models with linear addition, this study aims to develop weighting schemes based on FCMs and grey relational analysis (GRA). Time series are decomposed into several components, and neural networks are applied to forecast individual components. Then, GRA is applied to assess the weights for individual single-component forecasts. To obtain ensemble forecasts, an optimal FCM determined by a genetic algorithm is used to determine the final combination weights for individual single-component forecasts. In comparison with benchmark models, the results show that the proposed FCM-based decomposition ensemble models significantly effectively improve the forecasting accuracy of air passenger flow in Taiwan across different forecasting horizons. Full article

(This article belongs to the Special Issue Advances in Multi-Criteria Decision Making Methods with Applications)

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41 pages, 1132 KB

Open AccessArticle

A Criterion-Driven Consistency Indicator for Evaluating Multicriteria Sorting and Clustering Results

by Maiquiel Schmidt de Oliveira, Flavio Trojan, Vilmar Steffen and Maressa Fontana Mezoni

Mathematics 2026, 14(11), 1881; https://doi.org/10.3390/math14111881 - 28 May 2026

Viewed by 520

Abstract

This study investigates the role of data structure in multicriteria sorting by integrating supervised and unsupervised approaches. Specifically, a hybrid framework combining TOPSIS-Sort-B and cluster analysis is proposed to define class boundaries and evaluate sorting quality. Unlike traditional studies that focus primarily on methodological performance, this work emphasizes the impact of criteria conflict and trade-offs on class formation and stability. A unified performance-based labeling scheme is introduced, and a Criterion-Driven Consistency Indicator (CDCI) is used to quantify intra-class similarity. This indicator assesses the extent to which alternatives within the same class exhibit similar performance across criteria, offering a complementary perspective to conventional distance-based metrics. The proposed framework is validated through multiple case studies with distinct structural characteristics, including a highly structured dataset, a trade-off-intensive electric vehicle dataset, and an intermediate supplier selection problem. The results show that sorting outcomes are largely driven by the intrinsic structure of the data rather than by the choice of method. Datasets with low criteria conflict yield high class consistency and clear separation, whereas strong trade-offs lead to reduced cohesion and overlapping class boundaries, especially for intermediate alternatives. Overall, the study demonstrates that incorporating criteria-level information is essential for the robust evaluation of multicriteria sorting. The proposed approach enhances interpretability, reduces subjectivity in class definition, and provides new insights into the relationship between data structure and sorting consistency. Full article

(This article belongs to the Special Issue Advances in Multi-Criteria Decision Making Methods with Applications)

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29 pages, 491 KB

Open AccessFeature PaperArticle

A MCDM-Based Framework for Quantifying Reproducibility Readiness in Machine Learning Research

by Paulina Leščinskaitė, Remigijus Paulavičius and Ernestas Filatovas

Mathematics 2026, 14(9), 1536; https://doi.org/10.3390/math14091536 - 1 May 2026

Viewed by 688

Abstract

Machine Learning (ML) is increasingly used across scientific domains, raising concerns about the reproducibility of published results. Reproducibility is a fundamental principle of scientific research, yet many ML research works remain difficult to reproduce due to missing artifacts and insufficient reporting. This study addresses the lack of practical quantitative methods for assessing reproducibility in ML research by proposing a paper-level evaluation framework based on Multi-Criteria Decision Making (MCDM). Through a synthesis of theoretical and data-driven analyses, we identified seven key reproducibility criteria: data and code availability, the inclusion of a README and trained models, hyperparameter and training descriptions, and paper readability. These criteria are then aggregated into a unified quantitative score for ‘R1’ level reproducibility readiness using the Weighted Sum Model (WSM) and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). In the baseline evaluation, equal criterion weights were employed, while the Analytic Hierarchy Process (AHP) was demonstrated as a practical approach for deriving context-dependent weights tailored to diverse stakeholder priorities. The framework was applied to an annotated set of 139 randomly sampled ML research papers and benchmarked against an existing reproducibility label, achieving an accuracy of

0.64

, a precision of

0.40

, and a recall of

0.70

. These results demonstrate that MCDM provides a feasible, interpretable, and flexible foundation for quantifying reproducibility readiness, allowing the assessment to be adapted to different decision-making contexts through customized criterion weighting. Full article

(This article belongs to the Special Issue Advances in Multi-Criteria Decision Making Methods with Applications)

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22 pages, 944 KB

Open AccessArticle

Hybrid Application of Multi-Criteria Decision-Making Methods for Municipal Investments: A Case Study Focusing on Equity in Istanbul

by Melike Cari, Betul Kara, Nezir Aydin, Bahar Yalcin Kavus, Tolga Kudret Karaca and Ertugrul Ayyildiz

Mathematics 2026, 14(8), 1356; https://doi.org/10.3390/math14081356 - 18 Apr 2026

Cited by 2 | Viewed by 741

Abstract

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 article belongs to the Special Issue Advances in Multi-Criteria Decision Making Methods with Applications)

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26 pages, 1507 KB

Open AccessArticle

A Novel ANP-DEMATEL Framework for Multi-Criteria Decision-Making in Adaptive E-Learning Systems

by Maja Gligora Marković, Nikola Kadoić and Božidar Kovačić

Mathematics 2025, 13(22), 3714; https://doi.org/10.3390/math13223714 - 19 Nov 2025

Cited by 3 | Viewed by 1158

Abstract

E-learning systems that support personalized learning require sophisticated decision-making methods to adapt content to students optimally. This paper deals with applying multi-criteria decision-making methods in assigning learning objects in an e-learning system to students based on relevant customization criteria. The novelty of this study lies in the application of ANP and DEMATEL to improve content adaptation for students. Structuring the decision-making problem according to the DEMATEL and using ANP for prioritization has made the entire selection of learning objects better with respect to cognitive and learning styles and Bloom’s taxonomy levels. The method consists of various forms. In the first, DEMATEL has identified dependencies between criteria and clusters, mentioning their influence values on a 0–4 scale. A linear transformation model quantified the compatibility level of a student profile to a learning material. The transformed DEMATEL results were incorporated in all the interdependencies among criteria. The unweighted supermatrix was normalized by cluster weights assigned by experts before the iterative computation led to the converging weighted supermatrix. The outcome was that the individual students made these final priority rankings for learning materials. A pilot experiment was carried out to validate the system, and the results revealed that in the experimental group, the personalized learning environment showed the maximum statistical improvement over the control group. The research was conducted in Croatia, and the participants were students (N = 77) from two public universities and one polytechnic. Ultimately, the newly developed combined ANP-DEMATEL approach was effective in an instantaneous result-optimized dynamic learning path generation, ensuring knowledge acquisition. This research further contributes to developing intelligent educational systems by demonstrating how ANP and DEMATEL can be used synergistically to improve e-learning personalization. Future work could include optimizing weight assignment strategies or using new learning contexts to further adaptivity. Full article

(This article belongs to the Special Issue Advances in Multi-Criteria Decision Making Methods with Applications)

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22 pages, 1472 KB

Open AccessArticle

Industrial Palletizing Robots: A Distance-Based Objective Weighting Benchmarking

by Nhat-Luong Nhieu, Hoang-Kha Nguyen and Nguyen Truong Thinh

Mathematics 2025, 13(20), 3313; https://doi.org/10.3390/math13203313 - 17 Oct 2025

Cited by 2 | Viewed by 1572

Abstract

In the context of increasingly strong digital transformation and production automation, choosing the right palletizing robot plays a key role in optimizing operational efficiency in industrial chains. However, the wide variety of robot types and specifications complicates decision-making and increases the risk of biased judgments. To overcome this challenge, this study develops an objective multi-criteria decision-making (MCDM) framework that integrates two complementary methods for selecting the optimal industrial pal-letizing robot in the context of modern manufacturing that is increasingly dependent on intelligent automation solutions. Specifically, an improved CRITIC approach is employed to determine objective criteria weights by refining the measurement of contrast intensity and inter-criteria conflict, while normalization ensures comparability of heterogeneous robot parameters. CRADIS is then applied to rank the alternatives based on their relative closeness to the ideal solution. The contributions of this study are twofold: methodological, enhancing the objectivity and robustness of weighting through refined CRITIC and normalization, and practical, offering a reproducible evaluation framework for managers when choosing industrial robots. Application to eight palletizing robots demonstrates that “repeatability” and “power consumption” significantly influence rankings. Sensitivity analysis further confirms the model’s stability and reliability. These findings not only support evidence-based investment decisions but also provide a foundation for extending the method to other industrial technology selection problems. Full article

(This article belongs to the Special Issue Advances in Multi-Criteria Decision Making Methods with Applications)

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19 pages, 1825 KB

Open AccessArticle

Exploration of the Critical Factors Influencing the Development of the Metaverse Industry Based on Linguistic Variables

by Chen-Tung Chen and Chen-Hao Wu

Mathematics 2025, 13(11), 1860; https://doi.org/10.3390/math13111860 - 2 Jun 2025

Viewed by 1115

Abstract

Recently, the development of the Metaverse has emerged as a pivotal concern within both industrial and academic realms. The future development of the Metaverse industry is shrouded in uncertainty, complexity, and a dearth of technical and economic information. To address these challenges, this paper integrates the fuzzy Delphi method and fuzzy DEMATEL based on linguistic variables to explore the critical factors of the Metaverse industry. In accordance with the proposed methodology, a case study is presented to explore the critical factors of the Metaverse industry in Taiwan. The results of the empirical analysis demonstrated that the order of importance for the three principal dimensions is as follows: “infrastructure”, “consumer behavior”, and “user experience”. From the perspective of causality, “infrastructure” can be considered a driving dimension, whereas “user experience” can be regarded as a passive dimension. Regarding the critical factors, it can be observed that “virtual and real integration”, “equipment lightweight”, and “network communication” act as driving factors, exhibiting a high degree of correlation with the advancement of the Metaverse industry. Therefore, the proposed method not only possesses a robust theoretical foundation but also offers tangible practical value in the real world. Full article

(This article belongs to the Special Issue Advances in Multi-Criteria Decision Making Methods with Applications)

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20 pages, 3731 KB

Open AccessEditor’s ChoiceArticle

Fuzzy Clustering with Uninorm-Based Distance Measure

by Evgeny Kagan, Alexander Novoselsky and Alexander Rybalov

Mathematics 2025, 13(10), 1661; https://doi.org/10.3390/math13101661 - 19 May 2025

Viewed by 1641

Abstract

In this paper, we suggest an algorithm of fuzzy clustering with a uninorm-based distance measure. The algorithm follows a general scheme of fuzzy c-means (FCM) clustering, but in contrast to the existing algorithm, it implements logical distance between data instances. The centers of the clusters calculated by the algorithm are less dispersed and are concentrated in the areas of the actual centers of the clusters that result in the more accurate recognition of the number of clusters and of data structure. Full article

(This article belongs to the Special Issue Advances in Multi-Criteria Decision Making Methods with Applications)

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29 pages, 1042 KB

Open AccessFeature PaperArticle

Macro-Scale Temporal Attenuation for Electoral Forecasting: A Retrospective Study on Recent Elections

by Alexandru Topîrceanu

Mathematics 2025, 13(4), 604; https://doi.org/10.3390/math13040604 - 12 Feb 2025

Cited by 2 | Viewed by 6021

Abstract

Forecasting election outcomes is a complex scientific challenge with notable societal implications. Existing approaches often combine statistical analysis, machine learning, and economic indicators. However, research in network science has emphasized the importance of temporal factors in the dissemination of opinions. This study presents a macro-scale temporal attenuation (TA) model, which integrates micro-scale opinion dynamics and temporal epidemic theories to enhance forecasting accuracy using pre-election poll data. The findings suggest that the timing of opinion polls significantly influences opinion fluctuations, particularly as election dates approach. Opinion “pulse” is modeled as a temporal function that increases with new poll inputs and declines during stable periods. Two practical variants of the TA model, ETA and PTA, were tested on datasets from ten elections held between 2020 and 2024 around the world. The results indicate that the TA model outperformed several statistical methods, ARIMA models, and best pollster predictions (BPPs) in six out of ten elections. The two TA implementations achieved an average forecasting error of 6.92–6.95 percentage points across all datasets, compared to 7.65 points for BPP and 14.42 points for other statistical methods, demonstrating a performance improvement of 10–83%. Additionally, the TA methods maintained robust performance even with limited poll availability. As global pre-election survey data become more accessible, the TA model is expected to serve as a valuable complement to advanced election-forecasting techniques. Full article

(This article belongs to the Special Issue Advances in Multi-Criteria Decision Making Methods with Applications)

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