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Mathematics
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Multicriteria Decision Making and the Analytic Hierarchy Process
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Multicriteria Decision Making and the Analytic Hierarchy Process

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "Fuzzy Sets, Systems and Decision Making".

Deadline for manuscript submissions: closed (31 December 2021) | Viewed by 26720

Special Issue Editors

Dr. Juan Alfredo Aguarón

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Guest Editor
Grupo Decisión Multicriterio Zaragoza (GDMZ), Facultad de Economía y Empresa, Universidad de Zaragoza, Gran Vía 2, 50005 Zaragoza, Spain
Interests: multicriteria decision making; analytic hierarchy process; group decision making; decision support systems; e-government
Dr. María Teresa Escobar

E-Mail Website
Guest Editor
Grupo Decisión Multicriterio Zaragoza (GDMZ), Facultad de Economía y Empresa, Universidad de Zaragoza, Gran Vía 2, 50005 Zaragoza, Spain
Interests: multicriteria decision making; analytic hierarchy process; group decision making; logistics; e-government; environment

Special Issue Information

Dear Colleagues,

The analytic hierarchy process (AHP), a methodology proposed by Thomas L. Saaty at the end of the 1970s, is a multicriteria decision technique that has experienced great development in both theoretical and practical terms since its origins. It stands out, among other reasons, for making it possible to incorporate tangible and intangible aspects in the resolution of decision-making problems, as well as its adaptation to multiple-actor decision-making contexts.

With regard to methodological developments, it is worth highlighting its extension to networks called analytic network process (ANP), which allows the incorporation of the dependence between the different elements involved in a decision-making problem. In terms of its development in practice, it has been used to support decision making in a wide variety of areas, such as industry, environment, health, education, government, etc.

Both the development of methodological issues in AHP/ANP and the practical applications of this methodology in decision making remain of interest to researchers. This Special Issue is therefore focused on current developments in multicriteria decision making and the analytic hierarchy process. This Special Issue provides a platform for researchers from academia to present their new and unpublished work in the field of the analytic hierarchy process and analytic network process. This will help to foster future research within the field of multicriteria decision making.

Topics of interest include (but are not limited to):

  • Theoretical aspects in AHP/ANP
  • Interactive AHP methods
  • Fuzzy and stochastic AHP
  • Group decision making in AHP
  • Consistency in AHP
  • Applications of AHP with real data
  • Software implementation
  • New trends in AHP

Dr. Juan Alfredo Aguarón
Dr. María Teresa Escobar
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 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

  • multicriteria decision making
  • analytic hierarchy process
  • analytic network process
  • group decision making

Published Papers (10 papers)

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Research

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20 pages, 2342 KiB  
Article
A Hybrid Analytic Hierarchy Process and Likert Scale Approach for the Quality Assessment of Medical Education Programs
by Alfonso Maria Ponsiglione, Francesco Amato, Santolo Cozzolino, Giuseppe Russo, Maria Romano and Giovanni Improta
Mathematics 2022, 10(9), 1426; https://doi.org/10.3390/math10091426 - 24 Apr 2022
Cited by 33 | Viewed by 3435
Abstract
The quality assessment of training courses is of utmost importance in the medical education field to improve the quality of the training. This work proposes a hybrid multicriteria decision-making approach based on two methodologies, a Likert scale (LS) and the analytic hierarchy process [...] Read more.
The quality assessment of training courses is of utmost importance in the medical education field to improve the quality of the training. This work proposes a hybrid multicriteria decision-making approach based on two methodologies, a Likert scale (LS) and the analytic hierarchy process (AHP), for the quality assessment of medical education programs. On one hand, the qualitative LS method was adopted to estimate the degree of consensus on specific topics; on the other hand, the quantitative AHP technique was employed to prioritize parameters involved in complex decision-making problems. The approach was validated in a real scenario for evaluating healthcare training activities carried out at the Centre of Biotechnology of the National Hospital A.O.R.N. “A. Cardarelli” of Naples (Italy). The rational combination of the two methodologies proved to be a promising decision-making tool for decision makers to identify those aspects of a medical education program characterized by a lower user satisfaction degree (revealed by the LS) and a higher priority degree (revealed by the AHP), potentially suggesting strategies to increase the quality of the service provided and to reduce the waste of resources. The results show how this hybrid approach can provide decision makers with helpful information to select the most important characteristics of the delivered education program and to possibly improve the weakest ones, thus enhancing the whole quality of the training courses. Full article
(This article belongs to the Special Issue Multicriteria Decision Making and the Analytic Hierarchy Process)
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20 pages, 6632 KiB  
Article
Identification of Homogeneous Groups of Actors in a Local AHP-Multiactor Context with a High Number of Decision-Makers: A Bayesian Stochastic Search
by Alfredo Altuzarra, Pilar Gargallo, José María Moreno-Jiménez and Manuel Salvador
Mathematics 2022, 10(3), 519; https://doi.org/10.3390/math10030519 - 06 Feb 2022
Cited by 2 | Viewed by 1184
Abstract
The identification of homogeneous groups of actors in a local AHP-multiactor context based on their preferences is an open problem, particularly when the number of decision-makers is high. To solve this problem in the case of using stochastic AHP, this paper proposes a [...] Read more.
The identification of homogeneous groups of actors in a local AHP-multiactor context based on their preferences is an open problem, particularly when the number of decision-makers is high. To solve this problem in the case of using stochastic AHP, this paper proposes a new Bayesian stochastic search methodology for large-scale problems (number of decision-makers greater than 20). The new methodology, based on Bayesian tools for model comparison and selection, takes advantage of the individual preference structures distributions obtained from stochastic AHP to allow the identification of homogeneous groups of actors with a maximum common incompatibility threshold. The methodology offers a heuristic approach with several near-optimal partitions, calculated by the Occam’s window, that capture the uncertainty that is inherent when considering intangible aspects (AHP). This uncertainty is also reflected in the graphs that show the similarities of the decision-maker’s opinions and that can be used to achieve representative collective positions by constructing agreement paths in negotiation processes. If a small number of actors is considered, the proposed algorithm (AHP Bayesian clustering) significantly reduces the computational time of group identification with respect to an exhaustive search method. The methodology is illustrated by a real case of citizen participation based on e-Cognocracy. Full article
(This article belongs to the Special Issue Multicriteria Decision Making and the Analytic Hierarchy Process)
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20 pages, 607 KiB  
Article
Geometric Compatibility Indexes in a Local AHP-Group Decision Making Context: A Framework for Reducing Incompatibility
by Juan Aguarón, María Teresa Escobar, José María Moreno-Jiménez and Alberto Turón
Mathematics 2022, 10(2), 278; https://doi.org/10.3390/math10020278 - 17 Jan 2022
Cited by 3 | Viewed by 1240
Abstract
This paper deals with the measurement of the compatibility in a local AHP-Group Decision Making context. Compatibility between two individuals or decision makers is understood as the property that reflects the proximity between their positions or preferences, usually measured by a distance function. [...] Read more.
This paper deals with the measurement of the compatibility in a local AHP-Group Decision Making context. Compatibility between two individuals or decision makers is understood as the property that reflects the proximity between their positions or preferences, usually measured by a distance function. An acceptable level of incompatibility between the individual and the group positions will favour the acceptance of the collective position by the individuals. To facilitate the compatibility measurement, the paper utilises four indicators based on log quadratic distances between matrices or vectors which can be employed in accordance with the information that is available from the individual decision makers and from the group. The indicators make it possible to measure compatibility in decision problems, regardless of how the collective position and the priorities are obtained. The paper also presents a theoretical framework and a general, semi-automatic procedure for reducing the incompatibility measured by the four indicators. Using relative variations, the procedure identifies and slightly modifies the judgement of the collective matrix that further improves the indicator. This process is undertaken without modifying the initial information provided by the individuals. A numerical example illustrates the application of the theoretical framework and the procedure. Full article
(This article belongs to the Special Issue Multicriteria Decision Making and the Analytic Hierarchy Process)
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14 pages, 590 KiB  
Article
An Application of Neutrosophic Set to Relative Importance Assignment in AHP
by Napat Harnpornchai and Wiriyaporn Wonggattaleekam
Mathematics 2021, 9(20), 2636; https://doi.org/10.3390/math9202636 - 19 Oct 2021
Cited by 8 | Viewed by 1729
Abstract
The paper addresses a new facet of problem regarding the application of AHP in the real world. There are occasions that decision makers are not certain about relative importance assignment in pairwise comparison. The decision makers think the relative importance is among a [...] Read more.
The paper addresses a new facet of problem regarding the application of AHP in the real world. There are occasions that decision makers are not certain about relative importance assignment in pairwise comparison. The decision makers think the relative importance is among a set of scales, each of which is associated with a different possibility degree. A Discrete Single Valued Neutrosophic Number (DSVNN) with specified degrees of truth, indeterminacy, and falsity is employed to represent each assignment by taking into account all possible scales according to the decision maker’s thought. Each DSVNN assignment is transformed into a crisp value via a deneutrosophication using a similarity-to-absolute-truth measure. The obtained crisp scales are input to a pairwise comparison matrix for further analysis. The proposed neutrosophic set-based relative importance assignment is another additional novelty of the paper, which is different from all prior studies focusing only on the definition of measurement scales. The presented assignment emulates the real-world approach of decision making in human beings which may consider more than one possibility. It is also shown herein that the single and crisp relative importance assignment in the original AHP by Saaty is just a special case of the proposed methodology. The sensitivity analysis informs that when decision makers have neither absolute truth nor falsity about a scale, the proposed methodology is recommended for obtaining reliable relative importance scale. The applicability of the proposed methodology to the real-world problem is shown through the investment in equity market. Full article
(This article belongs to the Special Issue Multicriteria Decision Making and the Analytic Hierarchy Process)
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39 pages, 1285 KiB  
Article
A Hybrid Multiple Criteria Decision-Making Technique to Evaluate Regional Intellectual Capital: Evidence from China
by Chao Liu, Kexin Li, Peng Jiang, Ding Li, Liping Su, Shuting Lu and Anni Li
Mathematics 2021, 9(14), 1676; https://doi.org/10.3390/math9141676 - 16 Jul 2021
Cited by 8 | Viewed by 2122
Abstract
With the dawn of economic globalization and the knowledge economy, intellectual capital has become the most important factor to determine economic growth. However, due to resource endowment, location conditions, policy differences, and other factors, provinces in China show sizeable differences in regional intellectual [...] Read more.
With the dawn of economic globalization and the knowledge economy, intellectual capital has become the most important factor to determine economic growth. However, due to resource endowment, location conditions, policy differences, and other factors, provinces in China show sizeable differences in regional intellectual capital (RIC), which affects the coordinated development of the regional economy. Evaluating RIC is a typical multiple-criteria decision-making (MCDM) problem. Therefore, this study employs a set of MCDM techniques to solve this problem. First, the Delphi method is used to determine the formal decision structure based on a systematic literature review. A novel hybrid method, namely, the Grey-based Decision-Making Trial and Evaluation Laboratory (DEMATEL) and Analytic Network Process (ANP), i.e., GDANP, is employed to obtain the relative weight of each criterion. Finally, based on the data of 31 provinces in China, the Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) is used to evaluate the RIC. According to the questionnaires filled out by an expert panel, we establish an evaluation index of RIC with 21 criteria. Based on the results of empirical study, the level of RIC in different regions in China is quite different. Furthermore, the RIC ranking is largely consistent with the provincial gross domestic product (GDP) ranking, in line with the current status of development in the regions. Indeed, this paper shows that the proposed hybrid method can effectively measure the level of RIC. Full article
(This article belongs to the Special Issue Multicriteria Decision Making and the Analytic Hierarchy Process)
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23 pages, 658 KiB  
Article
Testing a Recent DEMATEL-Based Proposal to Simplify the Use of ANP
by Erik Schulze-González, Juan-Pascual Pastor-Ferrando and Pablo Aragonés-Beltrán
Mathematics 2021, 9(14), 1605; https://doi.org/10.3390/math9141605 - 07 Jul 2021
Cited by 18 | Viewed by 2383
Abstract
The Analytic Network Process (ANP) is a well-known multi-criteria decision method that allows the relationships between its elements to be incorporated into the model. The large number of questions to be answered is one of the main drawbacks of the method, since it [...] Read more.
The Analytic Network Process (ANP) is a well-known multi-criteria decision method that allows the relationships between its elements to be incorporated into the model. The large number of questions to be answered is one of the main drawbacks of the method, since it is time consuming for decision makers and experts who participate in the decision process. A recent DEMATEL-based ANP proposal can significantly reduce the number and the complexity of questions. This proposal was simply exposed and lacked an experimental test with real cases. The fundamental objective of this work is to answer the question: Does it work? In this work, this new proposal is applied to 45 ANP cases published in the literature. Variants to the verified proposal have also been identified. The results obtained show that the values of the priorities and the ranks obtained with this new proposal are very similar to the results obtained with the ANP, reducing the number of questions required by 42% on average. Additionally, in this work you can find the compilation of the 45 ANP weighted supermatrices to use in your investigations. Full article
(This article belongs to the Special Issue Multicriteria Decision Making and the Analytic Hierarchy Process)
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15 pages, 619 KiB  
Article
Selecting Bloggers for Hotels via an Innovative Mixed MCDM Model
by Jung-Fa Tsai, Chin-Po Wang, Kuei-Lun Chang and Yi-Chung Hu
Mathematics 2021, 9(13), 1555; https://doi.org/10.3390/math9131555 - 02 Jul 2021
Cited by 14 | Viewed by 2653
Abstract
The global coronavirus disease 2019 (COVID-19) outbreak had a great impact on the tourism industry. Numerous hotels have ceased operations. Because of the increasing influence of blogs, various industries have adopted blogs as a publicity and marketing strategy. Companies utilize consumers’ trust and [...] Read more.
The global coronavirus disease 2019 (COVID-19) outbreak had a great impact on the tourism industry. Numerous hotels have ceased operations. Because of the increasing influence of blogs, various industries have adopted blogs as a publicity and marketing strategy. Companies utilize consumers’ trust and loyalty toward bloggers to effectively contact them. Hence, bloggers play a crucial role in the hotel industry. No past study has researched blogger selection by hotel managers. In this study, an innovative mixed multiple-criteria decision-making (MCDM) model including importance-performance analysis (IPA), analytic hierarchy process (AHP), and technique for order preference by similarity to ideal solution (TOPSIS) is established to assist hotel managers in selecting bloggers. We firstly collect the selection criteria via interviews with hotel managers and a review of literature on blogger selection. Messages with stick are understood, remembered, and have an enduring influence on opinions and behavior. Hence, we also introduce the concept of stick to the selection criteria. Based on IPA and the literature review, a hierarchical structure for blogger selection is constructed. Then, AHP and TOPSIS are integrated to assist the case company managers to select suitable bloggers. Full article
(This article belongs to the Special Issue Multicriteria Decision Making and the Analytic Hierarchy Process)
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23 pages, 4210 KiB  
Article
A Multi-Objective Bayesian Approach with Dynamic Optimization (MOBADO). A Hybrid of Decision Theory and Machine Learning Applied to Customs Fraud Control in Spain
by Ignacio González García and Alfonso Mateos Caballero
Mathematics 2021, 9(13), 1529; https://doi.org/10.3390/math9131529 - 29 Jun 2021
Cited by 5 | Viewed by 1951
Abstract
This paper studies the economically significant problem of the optimization of customs fraud control, which is a critical issue for many countries. The European Union (EU) alone handles 4693 tons of goods every minute (2018 figures). Even though 70% of goods are imported [...] Read more.
This paper studies the economically significant problem of the optimization of customs fraud control, which is a critical issue for many countries. The European Union (EU) alone handles 4693 tons of goods every minute (2018 figures). Even though 70% of goods are imported at zero tariff, the EU raised EUR 25.4 billions in 2018, and customs-related income transferred by member states to the EU accounts for nearly 13% of its overall budget. In this field, (a) the conflicting objectives are qualitative and cannot be reduced to a common measure (security and terrorism, health, drug market access control, taxes, etc.); (b) each submitted item has dozens of characteristics; (c) there are constraints; and (d) risk analysis systems have to make decisions in real time. Although the World Customs Organization has promoted the use of artificial intelligence to increase the precision of controls, the problem is very complex due to the data characteristics and interpretability, which is a requirement established by customs officers. In this paper, we propose a new Bayesian-based hybrid approach combining machine learning and multi-objective linear programming (MOLP), called multi-objective Bayesian with dynamic optimization (MOBADO). We demonstrate that it is possible to more than double (with a 237% increase) the precision of current inspection systems, freeing up almost 50% of human resources, and outperform past results with respect to each of the above objectives. MOBADO is an optimization technique that could be combined with any artificial intelligence approach capable of optimizing the quality of multi-objective risk analysis in real time. Full article
(This article belongs to the Special Issue Multicriteria Decision Making and the Analytic Hierarchy Process)
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17 pages, 1816 KiB  
Article
A Multicriteria Decision-Making Model for the Selection of Suitable Renewable Energy Sources
by Chia-Nan Wang, Jui-Chung Kao, Yen-Hui Wang, Van Thanh Nguyen, Viet Tinh Nguyen and Syed Tam Husain
Mathematics 2021, 9(12), 1318; https://doi.org/10.3390/math9121318 - 08 Jun 2021
Cited by 30 | Viewed by 3824
Abstract
With the expansion of its industrial and manufacturing sectors, with the goal of positioning Vietnam as the world’s new production hub, Vietnam is forecast to face a surge in energy demand. Today, the main source of energy of Vietnam is fossil fuels, which [...] Read more.
With the expansion of its industrial and manufacturing sectors, with the goal of positioning Vietnam as the world’s new production hub, Vietnam is forecast to face a surge in energy demand. Today, the main source of energy of Vietnam is fossil fuels, which are not environmentally friendly and are rapidly depleting. The speed of extraction and consumption of fossil fuels is too fast, causing them to become increasingly scarce and gradually depleted. Renewable energy options, such as solar, wind, hydro electrical, and biomass, can be considered as sustainable alternatives to fossil fuels. However, to ensure the effectiveness of renewable energy development initiatives, technological, economic, and environmental must be taken in consideration when choosing a suitable renewable energy resource. In this research, the authors present a multi-criteria decision-making model (MCDM) implementing the grey analytic hierarchy process (G-AHP) method and the weighted aggregates sum product assessment (WASPAS) method for the selection of optimal renewable energy sources for the energy sector of Vietnam. The results of the proposed model have determined that solar energy is the optimal source of renewable energy with a performance score of 0.8822, followed by wind (0.8766), biomass (0.8488), and solid waste energy (0.8135) based on the calculations of the aforementioned methods. Full article
(This article belongs to the Special Issue Multicriteria Decision Making and the Analytic Hierarchy Process)
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Review

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13 pages, 418 KiB  
Review
State of the Art Review on the Analytic Hierarchy Process and Urban Mobility
by David Ruiz Bargueño, Valerio Antonio Pamplona Salomon, Fernando Augusto Silva Marins, Pedro Palominos and Luis Armando Marrone
Mathematics 2021, 9(24), 3179; https://doi.org/10.3390/math9243179 - 09 Dec 2021
Cited by 13 | Viewed by 2981
Abstract
Cultural, economical, political, and social developments, added to population increases, favored the consolidation of cities. However, rapid city growth in the last decades has contrasted with the slowness in which states and municipalities responded to the new reality. In this sense, the analytic [...] Read more.
Cultural, economical, political, and social developments, added to population increases, favored the consolidation of cities. However, rapid city growth in the last decades has contrasted with the slowness in which states and municipalities responded to the new reality. In this sense, the analytic hierarchy process (AHP), a leading multiple criteria decision-making (MCDM) method, can be applied in the solution of common demands among municipalities, evaluating alternative plans for urban mobility. Since AHP has been applied to these specific decision problems, our research question is: How has AHP been applied to solve decision problems regarding urban mobility? The objective of this work is to identify the state of the art of AHP applications to urban mobility. To answer the research question, this paper presents a literature review (LR). State of the art review (SAR) is an LR approach expected to deliver results with medium comprehensiveness and results closer to exhaustive. With the support of graphical software, three clusters were identified, in the keywords network: AHP, Innovation & Public Management, and Urban Mobility. In the AHP cluster, research is driven by methodological subjects; on Innovation & Public Management, there is an open discussion on local versus national coordination; and the urban mobility cluster has hybrid or non-AHP applications of MCDM. Full article
(This article belongs to the Special Issue Multicriteria Decision Making and the Analytic Hierarchy Process)
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