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Mathematics
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Applied Mathematics and Applications of Multi-Criteria Decision-Making Methods
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Applied Mathematics and Applications of Multi-Criteria Decision-Making Methods

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: 31 December 2025 | Viewed by 6867

Special Issue Editor

Dr. Valério Salomon

E-Mail Website
Guest Editor
School of Engineering and Sciences, Universidade Estadual Paulista, São Paul 01049-010, Brazil
Interests: analytic hierarchy process; fuzzy sets; supply chain management
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Multi-criteria decision-making (MCDM), a discipline where a dozen methods have been developed to solve decision problems involving more than one criterion (sometimes conflicting criteria), is still attracting the attention of researchers worldwide. One of the reasons for this is the flexibility of the methods that can be adapted to solve almost any decision problem, if not all. Decision problems solved via MCDM spread to diverse fields including computing, engineering, health and medicine, logistics and transportation, management, politics, and government, to name a few.

We are pleased to invite you to submit practical and original research for this Special Issue (SI) of Mathematics dedicated to MCDM. Within the scope of the journal, the research must focus on the mathematical modeling of MCDM: How were the criteria weights or alternative scores measured and obtained? How were these data treated? How were the results analyzed?

Studies from case researches are especially welcomed, since our aim is to publish papers on new applications of multi-criteria decision-making (MCDM) methods. Theoretical or methodological studies will also be accepted, as long as they include a practical example in their contribution. Furthermore, literature reviews will be considered, since MCDM theory continues to evolve.

The following provide a very comprehensive, but not exclusive, list of topics for the SI:

  • Artificial intelligence.
  • Behavioral issues.
  • Computing and software.
  • Crisis, disaster, and emergency management.
  • Decision support systems.
  • Energy and fuel consumption.
  • Environmental, social, and corporate governance.
  • Finance and economics.
  • Fuzzy sets approaches.
  • Group decision-making.
  • Human resources management.
  • Information and communication technology.
  • Logistics and transportation.
  • Marketing.
  • Negotiation and conflict resolution.
  • Operations and production management.
  • Project management.
  • Quality management.
  • Supply chain management.
  • Tourism.
  • Urban planning and smart cities.

Dr. Valério Salomon
Guest Editor

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 100 words) can be sent to the Editorial Office for announcement on this website.

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

  • analytic hierarchy process (AHP)
  • analytic network process (ANP)
  • best–worst method (BWM)
  • complex proportional assessment (COPRAS)
  • data envelopment analysis (DEA)
  • elimination and choice translating reality (ELECTRE)
  • full consistency method (FUCOM)
  • multi-attribute utility theory (MAUT)
  • multi-attribute value theory (MAVT)
  • step-wise weights assessment ratio analysis (SWARA)
  • technique for order preference by similarity to ideal solution (TOPSIS)

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Published Papers (5 papers)

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Research

31 pages, 3795 KB  
Article
A Novel Consistency Index CI-G: Recruiting Compatibility Index G for Consistency Analysis
by Claudio Garuti and Enrique Mu
Mathematics 2025, 13(16), 2666; https://doi.org/10.3390/math13162666 - 19 Aug 2025
Viewed by 448
Abstract
Consistency indices quantify the degree of transitivity and proportionality violations in a pairwise comparison matrix (PCM), forming a cornerstone of the Analytic Hierarchy Process (AHP) and Analytic Network Process (ANP). Several methods have been proposed to compute consistency, including those based on the [...] Read more.
Consistency indices quantify the degree of transitivity and proportionality violations in a pairwise comparison matrix (PCM), forming a cornerstone of the Analytic Hierarchy Process (AHP) and Analytic Network Process (ANP). Several methods have been proposed to compute consistency, including those based on the maximum eigenvalue, dot product, Jaccard index, and the Bose index. However, these methods often overlook two critical aspects: (i) vector projection or directional alignment, and (ii) the weight or importance of individual elements within a pointwise evaluative structure. The first limitation is particularly impactful. Adjustments made during the consistency improvement process affect the final priority vector disproportionately when heavily weighted elements are involved. Although consistency may improve numerically through such adjustments, the resulting priority vector can deviate significantly, especially when the true vector is known. This indicates that approaches neglecting projection and weighting considerations may yield internally consistent yet externally incompatible vectors, thereby compromising the validity of the analysis. This study builds on the idea that consistency and compatibility are intrinsically related; they are two sides of the same coin and should be considered complementary. To address these limitations, it introduces a novel metric, the Consistency Index G (CI-G) based on the compatibility index G. This measure evaluates how well the columns of a PCM align with its principal eigenvector, using CI-G as a diagnostic component. The proposed approach not only refines consistency measurement but also enhances the accuracy and reliability of derived priorities. Full article
(This article belongs to the Special Issue Applied Mathematics and Applications of Multi-Criteria Decision-Making Methods)
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27 pages, 340 KB  
Article
The Robust Malmquist Productivity Index: A Framework for Measuring Productivity Changes over Time Under Uncertainty
by Pejman Peykani, Roya Soltani, Cristina Tanasescu, Seyed Ehsan Shojaie and Alireza Jandaghian
Mathematics 2025, 13(11), 1727; https://doi.org/10.3390/math13111727 - 23 May 2025
Cited by 1 | Viewed by 1099
Abstract
The purpose of this study is to propose a novel approach for measuring productivity changes in decision-making units (DMUs) over time and evaluating the performance of each DMU under uncertainty in terms of progress, regression, and stagnation. To achieve this, the Malmquist productivity [...] Read more.
The purpose of this study is to propose a novel approach for measuring productivity changes in decision-making units (DMUs) over time and evaluating the performance of each DMU under uncertainty in terms of progress, regression, and stagnation. To achieve this, the Malmquist productivity index (MPI) and the data envelopment analysis (DEA) models are extended, and a new productivity index capable of handling uncertain data are introduced through a robust optimization approach. Robust optimization is recognized as one of the most applicable and effective methods in uncertain programming. The implementation and calculation of the proposed index are demonstrated using data from 15 actively traded stocks in the petroleum products industry on the Tehran stock exchange over two consecutive years. The results reveal that a significant number of stocks exhibit an unfavorable trend, marked by a decline in productivity. The findings highlight the efficacy and effectiveness of the proposed robust Malmquist productivity index (RMPI) in measuring and identifying productivity trends for each stock under data uncertainty. Full article
(This article belongs to the Special Issue Applied Mathematics and Applications of Multi-Criteria Decision-Making Methods)
32 pages, 756 KB  
Article
Ranking of Autonomous Technologies for Sustainable Logistics Activities in the Confectionery Industry
by Mladen Božić, Svetlana Dabić-Miletić, Milan Andrejić and Dragan Djurdjević
Mathematics 2025, 13(3), 498; https://doi.org/10.3390/math13030498 - 2 Feb 2025
Cited by 1 | Viewed by 1300
Abstract
The food supply chain (FSC) faces significant challenges, including the short shelf life of products, stringent food safety standards, and the growing demand for online ordering. These challenges underscore the need for a resilient and sustainable FSC, particularly in the confectionery industry, which [...] Read more.
The food supply chain (FSC) faces significant challenges, including the short shelf life of products, stringent food safety standards, and the growing demand for online ordering. These challenges underscore the need for a resilient and sustainable FSC, particularly in the confectionery industry, which is further burdened by the demand for innovative and healthier products. The aim of this paper is to optimize material handling activities in warehouse operations within the confectionery industry by ranking and selecting adequate material handling equipment (MHE). This paper proposes a novel hybrid multi-criteria decision-making model that integrates the Simple Aggregation of Preferences Expressed by Ordinal Vectors Group Decision Making (SAPEVO-M), Fuzzy Analytic Hierarchy Process (FAHP), and Fuzzy COmprehensive distance-Based Ranking (FCOBRA) methods. The model was applied to a real-world case study involving four alternative solutions and twelve defined evaluation criteria. The application of the model identified the implementation of an Automated Guided Vehicle system (AGVs) as the optimal alternative, offering substantial automation of logistics activities and addressing identified company challenges. The engagement of AGVs is estimated to reduce operational costs by 20%, improve warehouse operation efficiency by 30%, and decrease CO2 emissions by 25%. The contribution of this paper lies in the development of a methodological framework for evaluating and selecting MHE, as well as in highlighting the importance of optimizing material handling processes in the confectionery industry. Full article
(This article belongs to the Special Issue Applied Mathematics and Applications of Multi-Criteria Decision-Making Methods)
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21 pages, 9497 KB  
Article
Spatial Interpretation of Multi-Criteria Analysis: A Case Study with a Decreasing Number of Criteria and Subjective Approach to Determining Their Importance
by Roman Vavrek
Mathematics 2024, 12(22), 3497; https://doi.org/10.3390/math12223497 - 8 Nov 2024
Cited by 1 | Viewed by 873
Abstract
Municipal activities should not be profitable. Their intention is to provide the highest possible quality of service to citizens and, in this way, contribute to improving their quality of life. For this reason, the evaluation of their performance is very complex and should [...] Read more.
Municipal activities should not be profitable. Their intention is to provide the highest possible quality of service to citizens and, in this way, contribute to improving their quality of life. For this reason, the evaluation of their performance is very complex and should include several aspects, or criteria. The aim of this study is to quantify the agreement of the financial health assessment of the territorial self-government entities in 2020 with the financial health assessment based on a gradually decreasing number of entry criteria. For this purpose, we use a TOPSIS technique, and a total of 26 combinations of criteria are created with a gradually decreasing number of criteria, i.e., five, four, three, and two criteria used. For a description of the results obtained, we use a wide range of mathematical and statistical methods. The tests used include the Jaccard index, Kolmogorov–Smirnov test, Levene test, Moran index, and others. Our results confirm the fact that the outcome of MCDM analysis is directly and significantly affected by the structure and number of entry criteria. The reduction in the number of criteria resulted in a change in the parameters of the overall results. Full article
(This article belongs to the Special Issue Applied Mathematics and Applications of Multi-Criteria Decision-Making Methods)
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15 pages, 343 KB  
Article
Intuitionistic Fuzzy Ordinal Priority Approach with Grey Relational Analysis
by Priyanka Majumder and Valerio Antonio Pamplona Salomon
Mathematics 2024, 12(19), 3156; https://doi.org/10.3390/math12193156 - 9 Oct 2024
Cited by 4 | Viewed by 1801
Abstract
Multi-attribute decision-making (MADM) is a methodology for solving decision problems with a finite set of alternatives. The several methods of MADM require weights for the criteria and the alternatives to provide a solution. The Ordinal Priority Approach (OPA) is a recently proposed method [...] Read more.
Multi-attribute decision-making (MADM) is a methodology for solving decision problems with a finite set of alternatives. The several methods of MADM require weights for the criteria and the alternatives to provide a solution. The Ordinal Priority Approach (OPA) is a recently proposed method for MADM that innovates; it does not require these inputs, just the rankings of criteria and alternatives. This article introduces a new hybrid method for MADM: the Intuitionistic Fuzzy Ordinal Priority Approach with Grey Relational Analysis (OPA-IF-GRA). OPA-IF-GRA combines GRA with OPA-IF, a newer extension of OPA that includes intuitionistic fuzzy sets to incorporate uncertainty into the decision-making process. The article presents an OPA-IF-GRA application for solving an electronics engineering problem, considering four criteria and six alternatives. The solution of OPA-IF-GRA is compared with the solutions obtained with three other MADM methods. Full article
(This article belongs to the Special Issue Applied Mathematics and Applications of Multi-Criteria Decision-Making Methods)
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