Mathematics

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41 pages, 3015 KiB

Open AccessArticle

Are Brazilian Higher Education Institutions Efficient in Their Graduate Activities? A Two-Stage Dynamic Data-Envelopment-Analysis Cooperative Approach

by Lívia Mariana Lopes de Souza Torres and Francisco S. Ramos

Mathematics 2024, 12(6), 884; https://doi.org/10.3390/math12060884 - 17 Mar 2024

Viewed by 594

Abstract

Higher education evaluation presents itself as a worldwide trend. It aims to improve performance due to its importance for economic and personal growth. Graduate activities are essential for Brazilian research and innovation systems. However, previous studies have disregarded the importance of this educational [...] Read more.

Higher education evaluation presents itself as a worldwide trend. It aims to improve performance due to its importance for economic and personal growth. Graduate activities are essential for Brazilian research and innovation systems. However, previous studies have disregarded the importance of this educational level and have evaluated efficiency by jointly considering teaching and research or only undergraduate courses. Therefore, this study contributes to Brazilian reality by proving a national graduate activities efficiency evaluation that considers them as a two-stage system (formative and scientific production stages). The study provides three main methodological contributions by presenting a new centralized two-stage dynamic network data envelopment analysis (DNDEA) model with shared resources. Besides measuring efficiency, an efficiency decomposition based on a leader–follower assumption shows managers how much efficiency can alter when one of the stages needs to be prioritized. Finally, a new framework based on modified virtual inputs and outputs provides a bi-dimensional representation of the efficiency frontier. Results indicate the usefulness of the approach for ranking universities, and the need to improve scientific production, highlighting the negative impacts of COVID-19 on the formative process efficiency and showing no significant regional discrepancies regarding performance. Full article

(This article belongs to the Special Issue Advanced Applications of Multi-Criteria Decision-Making Methods in Operational Research)

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20 pages, 3232 KiB

Open AccessArticle

Multi-Criteria Decision under Uncertainty as Applied to Resource Allocation and Its Computing Implementation

by Petr Iakovlevitch Ekel, Matheus Pereira Libório, Laura Cozzi Ribeiro, Mateus Alberto Dorna de Oliveira Ferreira and Joel Gomes Pereira Junior

Mathematics 2024, 12(6), 868; https://doi.org/10.3390/math12060868 - 15 Mar 2024

Viewed by 626

Abstract

This research addresses the problem of multi-objective resource allocation or resource deficits, offering robust answers to planning decisions that involve the elementary question: “How is it done?”. The solution to the problem is realized using the general scheme of multi-criteria decision-making in uncertain [...] Read more.

This research addresses the problem of multi-objective resource allocation or resource deficits, offering robust answers to planning decisions that involve the elementary question: “How is it done?”. The solution to the problem is realized using the general scheme of multi-criteria decision-making in uncertain conditions. The bases of the proposed scheme are associated with the possibilistic approach, which involves the generalization of fuzzy sets from the classical approach to process the uncertainty of information to produce robust (non-dominated) solutions in multi-criteria analysis. Applying this general scheme makes it possible to reduce regions of decision uncertainty through the maximum use of available quantitative information. In the case where quantitative information analysis is insufficient to obtain a unique solution, the proposed approach presupposes the appropriation of qualitative data extracted from experts, who express their opinions considering their knowledge, experience, and intuition. The information on the qualitative character can be represented in diverse preference formats processed by transformation functions to provide homogeneous information for decision procedures used at the final decision stage. The presented results have been implemented within the system of multi-criteria decision-making under uncertain conditions described in the paper. Its functioning is illustrated by solving the typical problem in investment planning activities. Full article

(This article belongs to the Special Issue Advanced Applications of Multi-Criteria Decision-Making Methods in Operational Research)

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13 pages, 398 KiB

Open AccessArticle

Consistency Improvement in the Analytic Hierarchy Process

by Valerio Antonio Pamplona Salomon and Luiz Flavio Autran Monteiro Gomes

Mathematics 2024, 12(6), 828; https://doi.org/10.3390/math12060828 - 12 Mar 2024

Viewed by 835

Abstract

Consistency checking is one of the reasons for the Analytic Hierarchy Process (AHP) leadership in publications on multiple criteria decision-making (MCDM). Consistency is a measure of the quality of data input in the AHP. The theory of AHP provides indicators for the consistency [...] Read more.

Consistency checking is one of the reasons for the Analytic Hierarchy Process (AHP) leadership in publications on multiple criteria decision-making (MCDM). Consistency is a measure of the quality of data input in the AHP. The theory of AHP provides indicators for the consistency of data. When an indicator is out of the desired interval, the data must be reviewed. This article presents a method for improving the consistency of reviewing the data input in an AHP application. First, a conventional literature review is presented on the theme. Then, an innovative tool of artificial intelligence is shown to confirm the main result of the conventional review: this topic is still attracting interest from AHP and MCDM researchers. Finally, a simple technique for consistency improvement is presented and illustrated with a practical case of MCDM: supplier selection by a company. Full article

(This article belongs to the Special Issue Advanced Applications of Multi-Criteria Decision-Making Methods in Operational Research)

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22 pages, 3070 KiB

Open AccessArticle

A New Multi-Target Three-Way Threat Assessment Method with Heterogeneous Information and Attribute Relevance

by Yang Gao and Na Lyu

Mathematics 2024, 12(5), 691; https://doi.org/10.3390/math12050691 - 27 Feb 2024

Viewed by 576

Abstract

Target threat assessment provides support for combat decision making. The multi-target threat assessment method based on a three-way decision can obtain threat classification while receiving threat ranking, thus avoiding the limitation of traditional two-way decisions. However, the heterogeneous situation information, attribute relevance, and [...] Read more.

Target threat assessment provides support for combat decision making. The multi-target threat assessment method based on a three-way decision can obtain threat classification while receiving threat ranking, thus avoiding the limitation of traditional two-way decisions. However, the heterogeneous situation information, attribute relevance, and adaptive information processing needs in complex battlefield environment bring challenges to existing methods. Therefore, this paper proposes a new multi-target three-way threat assessment method with heterogeneous information and attribute relevance. Firstly, dynamic assessment information is represented by heterogeneous information, and attribute weights are calculated by heterogeneous Criteria Importance Through Intercriteria Correlation (CRITIC). Then, the conditional probability is calculated by the heterogeneous weighted Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), and the adaptive risk avoidance coefficients are constructed by calculating the uncertainty of the assessment value, and then the relative loss function matrices are constructed. Finally, the comprehensive loss function matrices are obtained by the weighted Heronian mean (HM) operator, and the comprehensive thresholds are calculated to obtain the three-way rules. The case study shows that compared with the existing methods, the proposed method can effectively handle the heterogeneous information and attribute relevance, and obtain the risk avoidance coefficients without presetting or field subjective settings, which is more suitable for the complex mission environment. Full article

(This article belongs to the Special Issue Advanced Applications of Multi-Criteria Decision-Making Methods in Operational Research)

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29 pages, 404 KiB

Open AccessArticle

An Exploration of Prediction Performance Based on Projection Pursuit Regression in Conjunction with Data Envelopment Analysis: A Comparison with Artificial Neural Networks and Support Vector Regression

by Xiaohong Yu and Wengao Lou

Mathematics 2023, 11(23), 4775; https://doi.org/10.3390/math11234775 - 26 Nov 2023

Cited by 4 | Viewed by 1172

Abstract

Data envelopment analysis (DEA) is a leading approach in performance analysis and discovering newer benchmarks, and the traditional DEA models cannot forecast the future efficiency of decision-making units (DMUs). Machine learning, such as the artificial neural networks (ANNs), support vector machine/regression (SVM/SVR), projection [...] Read more.

Data envelopment analysis (DEA) is a leading approach in performance analysis and discovering newer benchmarks, and the traditional DEA models cannot forecast the future efficiency of decision-making units (DMUs). Machine learning, such as the artificial neural networks (ANNs), support vector machine/regression (SVM/SVR), projection pursuit regression (PPR), etc., have been viewed as beneficial for managers in predicting system behaviors. PPR is especially suitable for small and non-normal distribution samples, the usual cases in DEA analysis. This paper integrates DEA and PPR to cover the shortcomings we faced while using DEA and DEA-BPNN, DEA-SVR, etc. This study explores the advantages of combining these complementary methods into an integrated performance measurement and prediction model. Firstly, the DEA approach is used to evaluate and rank the efficiency of DMUs. Secondly, we establish two DEA-PPR combined models to describe the DEA efficiency scores (also called the production function) and the DEA-efficient frontier function. The first combined model’s input variables are input–output indicators in the DEA model, and the output variable is the DEA efficiency. In the second model, its input variables are input or output indicators in the DEA model, and the output variable is the optimal input indicator for input-oriented DEA or the output indicator for output-oriented DEA. We conducted positive research on two examples with actual data and virtual small, medium-sized, and large samples. Compared with the DEA-BPNN and DEA-SVR models, the results show that the DEA-PPR combined model has more vital global optimization ability, better convergence, higher accuracy, and a simple topology. The DEA-PPR model can obtain robust results for both small and large cases. The DEA-BPNN and DEA-SVR models cannot obtain robust results for small and medium-sized samples due to overfitting. For large samples, the DEA-PPR model outperforms DEA-BPNN, DEA-SVR, etc. The DEA-PPR combined model possesses better suitability, applicability, and reliability than the DEA-BPNN model, the DEA-SVR model, etc. Full article

(This article belongs to the Special Issue Advanced Applications of Multi-Criteria Decision-Making Methods in Operational Research)

34 pages, 3905 KiB

Open AccessArticle

New Hybrid EC-Promethee Method with Multiple Iterations of Random Weight Ranges: Applied to the Choice of Policing Strategies

by Marcio Pereira Basilio, Valdecy Pereira and Fatih Yigit

Mathematics 2023, 11(21), 4432; https://doi.org/10.3390/math11214432 - 26 Oct 2023

Cited by 4 | Viewed by 3264

Abstract

The decision-making process is part of everyday life for people and organizations. When modeling the solutions to problems, just as important as the choice of criteria and alternatives is the definition of the weights of the criteria. This study will present a new [...] Read more.

The decision-making process is part of everyday life for people and organizations. When modeling the solutions to problems, just as important as the choice of criteria and alternatives is the definition of the weights of the criteria. This study will present a new hybrid method for weighting criteria. The technique combines the ENTROPY and CRITIC methods with the PROMETHE method to create EC-PROMETHEE. The innovation consists of using a weight range per criterion. The construction of a weight range per criterion preserves the characteristics of each technique. Each weight range includes lower and upper limits, which combine to generate random numbers, producing “t” sets of weights per criterion, allowing “t” final rankings to be obtained. The alternatives receive a value corresponding to their position with each ranking generated. At the end of the process, they are ranked in descending order, thus obtaining the final ranking. The method was applied to the decision support problem of choosing policing strategies to reduce crime. The model used a decision matrix with twenty criteria and fourteen alternatives evaluated in seven different scenarios. The results obtained after 10,000 iterations proved consistent, allowing the decision maker to see how each alternative behaved according to the weights used. The practical implication observed concerning traditional models, where a single final ranking is generated for a single set of weights, is the reversal of positions after “t” iterations compared to a single iteration. The method allows managers to make decisions with reduced uncertainty, improving the quality of their decisions. In future research, we propose creating a web tool to make this method easier to use, and propose other tools are produced in Python and R. Full article

(This article belongs to the Special Issue Advanced Applications of Multi-Criteria Decision-Making Methods in Operational Research)

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18 pages, 355 KiB

Open AccessArticle

Fuzzy Weighted Pareto–Nash Equilibria of Multi-Objective Bi-Matrix Games with Fuzzy Payoffs and Their Applications

by Wen Li, Deyi Li, Yuqiang Feng and Du Zou

Mathematics 2023, 11(20), 4266; https://doi.org/10.3390/math11204266 - 12 Oct 2023

Cited by 1 | Viewed by 1004

Abstract

Based on our previous research, this paper further discusses the multi-objective bi-matrix game with fuzzy payoffs (MBGFP), which is a special case of the fuzzy constrained multi-objective game with fuzzy payoffs. We first prove that any bi-matrix game with interval payoffs (BGIP) has [...] Read more.

Based on our previous research, this paper further discusses the multi-objective bi-matrix game with fuzzy payoffs (MBGFP), which is a special case of the fuzzy constrained multi-objective game with fuzzy payoffs. We first prove that any bi-matrix game with interval payoffs (BGIP) has at least one Pareto–Nash equilibrium. Then, with the help of BGIP, we obtain the necessary and sufficient conditions for the existence of fuzzy Pareto–Nash equilibrium of MBGFP. Secondly, based on the bilinear programming method for calculating Nash equilibrium in crisp bi-matrix games, we established a bilinear programming method with parameters for calculating fuzzy Pareto–Nash equilibrium. By considering the importance of each objective to the players, MBGFP is transformed into a bi-matrix game with fuzzy payoffs (BGFP). Furthermore, we obtained the necessary and sufficient conditions for the existence of fuzzy weighted Pareto–Nash equilibrium and its calculation method. Finally, a practical example is used to illustrate the effectiveness of our proposed calculation method. Full article

(This article belongs to the Special Issue Advanced Applications of Multi-Criteria Decision-Making Methods in Operational Research)

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27 pages, 11212 KiB

Open AccessArticle

Interactive Internet Framework Proposal of WASPAS Method: A Computational Contribution for Decision-Making Analysis

by Flavio Barbara, Marcos dos Santos, Antônio Sergio Silva, Miguel Ângelo Lellis Moreira, Luiz Paulo Fávero, Enderson Luiz Pereira Júnior, Wagner dos Anjos Carvalho, Fernando Martins Muradas, Daniel Augusto de Moura Pereira and Anderson Gonçalves Portella

Mathematics 2023, 11(15), 3375; https://doi.org/10.3390/math11153375 - 2 Aug 2023

Viewed by 1825

Abstract

Concerning the development of computational tools and solutions as a decision-making aid, this paper presents the results of the waspasWEB project, which strives to provide decision-makers with a readily accessible mechanism to employ the weighted aggregated sum product assessment (WASPAS) method. The social [...] Read more.

Concerning the development of computational tools and solutions as a decision-making aid, this paper presents the results of the waspasWEB project, which strives to provide decision-makers with a readily accessible mechanism to employ the weighted aggregated sum product assessment (WASPAS) method. The social contribution of the project encompasses the development of a user-friendly and publicly accessible internet tool, as well as a package launched on the Comprehensive R Archive Network (CRAN) to serve the community of users of the R language. The use of operational research methodologies is crucial to justify decisions, and this effort seeks to advance the adoption of such methodologies, offering managers, researchers, and the general public an intuitive and easily accessible multi-criteria decision-making tool. In this way, we present the technical specifications, usability, and interactivity of the user with the computational platform, being validated its viability through a hypothetical case study. At the end of the research, it exposes the limitations and feasibility of the proposed computational model along with future research. Full article

(This article belongs to the Special Issue Advanced Applications of Multi-Criteria Decision-Making Methods in Operational Research)

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