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Mathematics
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Application of Multiple Criteria Decision Analysis
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Application of Multiple Criteria Decision Analysis

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "D2: Operations Research and Fuzzy Decision Making".

Deadline for manuscript submissions: 30 September 2026 | Viewed by 4629

Special Issue Editors

Dr. Pavel Anselmo Álvarez

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Guest Editor
Department of Economic and Management Sciences, Universidad Autómoma de Occidente, Culiacan, Mexico
Interests: multiple criteria decision making; group decision making; metaheuristics
Dr. Ernesto León-Castro

E-Mail Website
Guest Editor
Administration Department, Universidad Católica de la Santísima Concepción, Alonso de Ribera 2850, Concepción, Chile
Interests: aggregation operators; fuzzy logic; decision making under uncertainty; innovation and finance
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue explores the diverse applications of Multiple Criteria Decision Analysis (MCDA) and Multiple Criteria of Decision Making (MCDM) across various fields. Decision making is an integral aspect of human behaviour, involving simple and complex choices depending on the significance of their outcomes. In scenarios where substantial value is at stake, it becomes critical to systematically analyze decision-making processes to identify solutions that fulfil the best compromise.

The study of MCDA and MCDM is a multidisciplinary field due to the diverse variety of methodologies and approaches that enrich it, such as fuzzy sets, exact and approximate optimization methods, algorithms, inferences of parameters or rules, modelling and simulation, soft computing, and others that have been applied in diverse real-world applications.

The contributions in this issue highlight innovative methodologies and case studies that illustrate how MCDA and MCDM can effectively address intricate decision problems. These applications span sectors, including, but not limited to, environmental management, education, healthcare, financial management, risk management, supplier selection, diverse management problems, innovation, sustainable development, and others.

In summary, this Special Issue underscores the importance of MCDA and MCDM as powerful tools for navigating complex decision landscapes. It provides insights and practical examples that can inspire further research and application in various disciplines. We encourage authors to submit original research that tackles decision-making problems from diverse perspectives and approaches.

Dr. Pavel Anselmo Álvarez
Dr. Ernesto León-Castro
Guest Editors

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • decision making
  • decision analysis
  • decision support systems
  • negotiation and group decision
  • real world applications
  • applications of MCDM
  • non-classical MCDM methods
  • decision rules
  • theories and methodologies
  • modelling and simulation
  • modelling of MCDM
  • fuzzy sets and MCDM
  • fuzziness in MCDM
  • uncertainty
  • soft computing
  • algorithms
  • operational research
  • multi-objective optimization
  • metaheuristics
  • sustainable development
  • management, assessment, or selection
  • innovation

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Further information on MDPI's Special Issue policies can be found here.

Published Papers (6 papers)

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Research

35 pages, 585 KB  
Article
On Devising Carbon Offset Investments by Multiple-Objective Portfolio Selection and Exploring Multiple-Objective Capital Asset Pricing Models
by Yue Qi, Jianing Huang, Zhujun Qi and Yingying Li
Mathematics 2026, 14(6), 1080; https://doi.org/10.3390/math14061080 - 23 Mar 2026
Viewed by 168
Abstract
Humans face environmental deterioration. Scholars have identified carbon dioxide as one of the culprits, and they emphasize carbon offset. Researchers are investigating carbon offset investments. Some researchers have encouragingly deployed multivariate variational mode decomposition methods, but they have not fully optimized them. Some [...] Read more.
Humans face environmental deterioration. Scholars have identified carbon dioxide as one of the culprits, and they emphasize carbon offset. Researchers are investigating carbon offset investments. Some researchers have encouragingly deployed multivariate variational mode decomposition methods, but they have not fully optimized them. Some researchers have opportunely assessed capital asset pricing models, but they have not fully justified them. We devise multiple-objective portfolio selection models, fully optimize them, and dominate carbon offset indexes. We extend the classical methodology of advancing from portfolio selection to capital asset pricing models into the methodology of advancing from multiple-objective portfolio selection to multiple-objective capital asset pricing models. Specifically, we explore multiple-objective capital asset pricing models by numerically verifying many tangent lines (instead of the traditionally singular tangent line) and suggesting a tangent plane (instead of tangent lines). For multiple-objective zero-covariance capital asset pricing models, we numerically compute a set of zero-covariance portfolios (instead of the traditionally singular zero-covariance portfolio) and suggest picking an advantageous zero-covariance portfolio. We consider the second-level indicators of carbon offset and generalize three-objective portfolio selection to k-objective portfolio selection. As for contributions, first, this paper’s methodology is to logically advance from multiple-objective portfolio selection to multiple-objective capital asset pricing models, whereas the literature typically covers multiple-objective portfolio selection alone and barely covers multiple-objective capital asset pricing models. Second, this paper numerically demonstrates some difficulties and proposes hypothetical solutions in the process of obtaining multiple-objective capital asset pricing models. Full article
(This article belongs to the Special Issue Application of Multiple Criteria Decision Analysis)
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25 pages, 598 KB  
Article
Study on an Enterprise Resilience Evaluation Model for Listed Real Estate Companies Based on the Entropy-Weighted TOPSIS Method
by Baojing Zhang, Yan Zheng, Dongqi Xie and Yipeng Zheng
Mathematics 2026, 14(6), 987; https://doi.org/10.3390/math14060987 - 14 Mar 2026
Viewed by 251
Abstract
In the context of a deep structural adjustment of China’s real estate sector and heightened macroeconomic uncertainty, quantitatively assessing the resilience of listed real estate enterprises is crucial for preventing systemic risk and promoting sustainable development. This paper proposes a multidimensional resilience evaluation [...] Read more.
In the context of a deep structural adjustment of China’s real estate sector and heightened macroeconomic uncertainty, quantitatively assessing the resilience of listed real estate enterprises is crucial for preventing systemic risk and promoting sustainable development. This paper proposes a multidimensional resilience evaluation framework for 37 Chinese A-share listed real estate firms using panel data from 2017–2024. An index system covering four dimensions—solvency and liquidity, profitability and cash flow, operational efficiency and asset structure, and growth and value—is constructed on the basis of financial ratios. The entropy-weighted TOPSIS method is employed to derive a composite resilience index, while principal component analysis (PCA) provides a complementary robustness check of the rankings. The empirical results indicate that (1) operational efficiency and asset structure receive the highest objective weight, followed by solvency and liquidity, whereas the weights of profitability, cash flow, and growth–value dimensions are relatively lower; at the indicator level, accounts receivable turnover, inventory turnover and the cash-to-short-term-debt ratio play a leading role, underscoring the central importance of liquidity safety and asset turnover under the “three red lines” regulatory regime. (2) Firms such as Shahe Co., Shenzhen, China, Huafa Co., Zhuhai, China and Wantong Development, Beijing, China exhibit persistently higher resilience scores, characterized by lower leverage, stronger cash buffers and faster operating turnover, whereas firms such as Yunnan Metropolitan Investment, Kunming, China, Greenland Holdings, Shanghai, China, Bright Real Estate, Shanghai, China and Rongsheng Development, Langfang, China remain at the lower tail of the resilience distribution with high leverage, tight liquidity and volatile profitability. (3) The resilience rankings obtained from entropy-weighted TOPSIS and PCA are positively and significantly correlated at the 1% level, suggesting a moderate level of consistency between distance-based and variance-based evaluation schemes. Building on these findings, this paper proposes resilience-oriented policy recommendations for regulators and managers in terms of differentiated prudential regulation, capital-structure and debt-maturity optimization, operational efficiency enhancement, and the integration of digital transformation and ESG governance. Full article
(This article belongs to the Special Issue Application of Multiple Criteria Decision Analysis)
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31 pages, 1090 KB  
Article
Blockchain Technology for Green Supply Chain Management in the Maritime Industry: Integrating Extended Grey Relational Analysis, SWARA, and ARAS Methods Under Z-Information
by Amir Karbassi Yazdi, Yong Tan, Mohammad Amin Khoobbakht, Gonzalo Valdés González and Lanndon Ocampo
Mathematics 2026, 14(2), 246; https://doi.org/10.3390/math14020246 - 8 Jan 2026
Viewed by 679
Abstract
Blockchain technology has attracted considerable attention in the supply chain literature for its potential to enhance operational traceability, transparency, and trust, as well as to advance greening initiatives. Given current supply chain configurations, exploring barriers to implementation is a consequential agenda, and current [...] Read more.
Blockchain technology has attracted considerable attention in the supply chain literature for its potential to enhance operational traceability, transparency, and trust, as well as to advance greening initiatives. Given current supply chain configurations, exploring barriers to implementation is a consequential agenda, and current studies have devoted substantial effort to identifying and offering guidance to address them. Despite recent findings, insights into how blockchain technology adoption can support green supply chain management are missing, particularly in the maritime sector, which receives limited attention. Thus, this work outlines a methodological approach to examine the suitability of maritime routes for addressing barriers to implementing blockchain technology in green supply chain management. Viewing the evaluation as a multi-criteria decision-making (MCDM) problem, the proposed approach performs the following actions on a case study evaluating four maritime lines. Firstly, from the 13 identified barriers in the literature review and expert interviews, nine relevant barriers were determined after one round of a Delphi process. These barriers eventually comprise the set of evaluation criteria. Secondly, to satisfy the assumption of criterion independence in most MCDM methods, this work proposes a novel extended grey relational analysis (GRA) that allows for the measurement of criterion independence based on the concept of grey relational space. Proposed here for the first time, the extended GRA offers a distribution-free overall independence index for each criterion based on pattern similarity. Finally, an integration of SWARA (Stepwise Weight Assessment Ratio Analysis) and ARAS (Additive Ratio Assessment) methods under Z-information is developed to address the evaluation problem involving expert judgments in a highly uncertain decision-making context. Results show that transaction-level uncertainty is the most critical barrier to blockchain adoption, followed by technology risks and higher sustainability costs. Among the four maritime lines, Line 3 is best prepared for a blockchain-enabled green supply chain. The agreement between these results and those of other MCDM methods is shown in the comparative analysis. Also, ranking remains unchanged even when the criteria weights are adjusted. The proposed approach provides a computationally efficient and tractable framework for maritime managers to make informed decisions about blockchain adoption to promote green supply chains. Full article
(This article belongs to the Special Issue Application of Multiple Criteria Decision Analysis)
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33 pages, 1213 KB  
Article
A Novel Integrated Fuzzy Analytic Hierarchy Process with a 4-Tuple Hedge Algebra Semantics for Assessing the Level of Digital Transformation of Enterprises
by Nhu Van Kien, Hoang Van Thong, Nguyen Cat Ho and Luu Quoc Dat
Mathematics 2025, 13(21), 3539; https://doi.org/10.3390/math13213539 - 4 Nov 2025
Cited by 1 | Viewed by 545
Abstract
Hedge algebra is a powerful and flexible tool for handling linguistic information, enabling precise quantitative computations and enhancing the effectiveness of multi-criteria decision-making (MCDM). This study proposes a novel integrated fuzzy MCDM approach that combines an enhanced fuzzy analytic hierarchy process (EFAHP) with [...] Read more.
Hedge algebra is a powerful and flexible tool for handling linguistic information, enabling precise quantitative computations and enhancing the effectiveness of multi-criteria decision-making (MCDM). This study proposes a novel integrated fuzzy MCDM approach that combines an enhanced fuzzy analytic hierarchy process (EFAHP) with a 4-tuple hedge algebra semantics model to assess digital transformation in retail enterprises. In this approach, the EFAHP method is integrated with hedge algebra to determine the priorities of pillars and criteria while providing a rigorous mathematical mechanism to transform ambiguous linguistic evaluations into numerical values. This transformation leverages the semantic structure of linguistic variable domains and incorporates fuzziness measures for both atomic words and intensity-modifying words (hedges). Furthermore, a new consistency index formula is introduced to evaluate the reliability of the EFAHP results, with validation being limited to the case study dataset. The 4-tuple hedge algebra semantic model is then employed to assess and rank the digital transformation levels of retail enterprises in Vietnam. Finally, a sensitivity analysis verifies the robustness of the proposed approach by illustrating how variations in pillar and criterion weights influence enterprise rankings. Full article
(This article belongs to the Special Issue Application of Multiple Criteria Decision Analysis)
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14 pages, 838 KB  
Article
Fuzzy TOPSIS Reinvented: Retaining Linguistic Information Through Interval-Valued Analysis
by Abdolhanan Aminoroaya, Abdollah Hadi-Vencheh, Ali Jamshidi and Amir Karbassi Yazdi
Mathematics 2025, 13(17), 2819; https://doi.org/10.3390/math13172819 - 2 Sep 2025
Viewed by 1221
Abstract
In real-world decision-making situations, experts often rely on subjective and imprecise judgments, frequently expressed using linguistic terms. While fuzzy logic offers a valuable tool to capture and process such uncertainty, traditional methods often convert fuzzy inputs into crisp values too early in the [...] Read more.
In real-world decision-making situations, experts often rely on subjective and imprecise judgments, frequently expressed using linguistic terms. While fuzzy logic offers a valuable tool to capture and process such uncertainty, traditional methods often convert fuzzy inputs into crisp values too early in the process. This premature defuzzification can result in significant loss of information and reduced interpretability. To address this issue, the present study introduces an enhanced fuzzy TOPSIS model that utilizes expected interval representations instead of early crisp transformation. This approach allows the original fuzzy data to be preserved throughout the analysis, leading to more transparent, realistic, and informative decision outcomes. The practical application of the proposed method is demonstrated through a supplier selection case study, which illustrates the model’s capability to handle real-world, complex, and qualitative decision environments. By explicitly linking the method to this domain, the study provides a concrete anchor for practitioners and decision-makers seeking transparent and robust evaluation tools. Full article
(This article belongs to the Special Issue Application of Multiple Criteria Decision Analysis)
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12 pages, 882 KB  
Article
Classifying Decision Strategies in Multi-Attribute Decision-Making: A Multi-Dimensional Scaling and Hierarchical Cluster Analysis of Simulation Data
by Kazuhisa Takemura, Yuki Tamari and Takashi Ideno
Mathematics 2025, 13(17), 2778; https://doi.org/10.3390/math13172778 - 29 Aug 2025
Cited by 1 | Viewed by 1101
Abstract
Previous studies on decision strategies in multi-attribute decision-making (MADM) have primarily relied on computational simulations to assess strategy performance under varying conditions, with particular emphasis on comparisons to the weighted additive rule (WAD) and on evaluations of the cognitive effort required. In contrast, [...] Read more.
Previous studies on decision strategies in multi-attribute decision-making (MADM) have primarily relied on computational simulations to assess strategy performance under varying conditions, with particular emphasis on comparisons to the weighted additive rule (WAD) and on evaluations of the cognitive effort required. In contrast, considerably less attention has been devoted to examining the consistency of decision outcomes across different strategies or to developing a systematic classification of strategies based on outcome similarity. To address this gap, the present study investigates the characteristics of decision strategies by analyzing the concordance rates of choices made under identical conditions, along with measures of decision accuracy and information-processing effort. We conducted a hierarchical cluster analysis and applied multi-dimensional scaling (MDS) to a choice concordance matrix derived from simulations using the Mersenne Twister method. In addition, linear multiple regression analyses were performed using the MDS coordinates as predictors of both decision accuracy and cognitive effort. The cluster analysis revealed a primary bifurcation between two major groups: one centered around the Disjunctive (DIS) rule, and another encompassing compensatory strategies such as WAD. Notably, although the Lexicographic (LEX) rule is traditionally considered non-compensatory, it exhibited high similarity in choice patterns to compensatory strategies when assessed via concordance rates. In contrast, DIS-based strategies produced markedly distinct choice patterns. Full article
(This article belongs to the Special Issue Application of Multiple Criteria Decision Analysis)
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