Julio Benítez
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Previous Organizations / Institutes
The organizations / institutes from the scholar's other articles in the past ten years
Research Subjects
Julio Benítez has a total of 61 co-authors. Here are the top co-authors by number of shared publications:
- Sanzhang Xu
Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huaian 223003, China
13 shared publications - Joaquín Izquierdo
Polytechnic University of Valencia
12 shared publications Xiaoji Liu
12 shared publications- Jianlong Chen
School of Mathematics, Southeast University
8 shared publications - Xitlali Delgado-Galván
Department of Geomatics and Hydraulic Engineering, University of Guanajuato, Guanajuato 36000, Mexico
7 shared publications - Néstor Thome
Instituto Universitario de Matemática Multidisciplinar Universitat Politècnica de València 46022 Valencia Spain
6 shared publications
Latest Publications
- Open Access
- 31 July 2026
- Published by Universitat Politecnica de Valencia in Modelling in Science Education and Learning
- Vol. 19, 45-62
Propuestas para un primer curso universitario de probabilidad
La teoría de la probabilidad permite realizar aplicaciones prácticas poco después de su introducción. Este artículo presenta una lista de proyectos académicos que pueden llevar a cabo estudiantes universitarios de primer o segundo curso. Tales proyectos conectan la teoría con situaciones del mundo real que implican que los alumnos se interesen con la materia y además obligan a trabajar de forma numérica. Estos proyectos refuerzan la comprensión y potencian la adquisición de algunas competencias transversales y fundamentales detalladas en el artículo.
- 31 July 2026
- Published by Universitat Politecnica de Valencia in Modelling in Science Education and Learning
- Vol. 19, 45-62
Open AccessPropuestas para un primer curso universitario de probabilidad
La teoría de la probabilidad permite realizar aplicaciones prácticas poco después de su introducción. Este artículo presenta una lista de proyectos académicos que pueden llevar a cabo estudiantes universitarios de primer o segundo curso. Tales proyectos conectan la teoría con situaciones del mundo real que implican que los alumnos se interesen con la materia y además obligan a trabajar de forma numérica. Estos proyectos refuerzan la comprensión y potencian la adquisición de algunas competencias transversales y fundamentales detalladas en el artículo.
- 8 November 2025
- Published by Springer Nature in TOP
- Vol. 34 (2) , 207-224
Additive pairwise comparisons matrices
- 8 November 2025
- Published by Springer Nature in TOP
- Vol. 34 (2) , 207-224
Additive pairwise comparisons matrices
- 22 May 2025
- Published by Politechnika Wroclawska Oficyna Wydawnicza in Operations Research and Decisions
- Vol. 35 (4) , 1-10
A new and simple method to get the priority vector for reciprocal matrices
A new optimization method is proposed to find the priority vector of a non-consistent reciprocal matrix, which leads to the solution of a constrained least-squares problem, specially suited for large matrices. Two different approaches are used to solve this problem: the first approach uses QR decomposition, and the second approach performs the singular value decomposition, leading to simple solutions. In addition, a comparison of the proposed method with other methods used in the consulted bibliography is made to obtain the priority vector, and finally, an illustrative example is shown.
- 22 May 2025
- Published by Politechnika Wroclawska Oficyna Wydawnicza in Operations Research and Decisions
- Vol. 35 (4) , 1-10
A new and simple method to get the priority vector for reciprocal matrices
A new optimization method is proposed to find the priority vector of a non-consistent reciprocal matrix, which leads to the solution of a constrained least-squares problem, specially suited for large matrices. Two different approaches are used to solve this problem: the first approach uses QR decomposition, and the second approach performs the singular value decomposition, leading to simple solutions. In addition, a comparison of the proposed method with other methods used in the consulted bibliography is made to obtain the priority vector, and finally, an illustrative example is shown.
- Open Access
A study on the 1-$Γ$ inverse of tensors via the M-Product
In this paper, we will study the issue about the 1-$Γ$ inverse, where $Γ\in\{†, D, *\}$, via the M-product. The aim of the current study is threefold. Firstly, the definition and characteristic of the 1-$Γ$ inverse is introduced. Equivalent conditions for a tensor to be a 1-$Γ$ inverse are established. Secondly, using the singular value decomposition, the corresponding numerical algorithms for computing the 1-$Γ$ inverse are given. Finally, the solutions of the multilinear equations related 1-$Γ$ inverse are studied, and numerical calculations are given to verify our conclusions.Open AccessA study on the 1-$Γ$ inverse of tensors via the M-Product
In this paper, we will study the issue about the 1-$Γ$ inverse, where $Γ\in\{†, D, *\}$, via the M-product. The aim of the current study is threefold. Firstly, the definition and characteristic of the 1-$Γ$ inverse is introduced. Equivalent conditions for a tensor to be a 1-$Γ$ inverse are established. Secondly, using the singular value decomposition, the corresponding numerical algorithms for computing the 1-$Γ$ inverse are given. Finally, the solutions of the multilinear equations related 1-$Γ$ inverse are studied, and numerical calculations are given to verify our conclusions. - Open Access
- 1 January 2025
- Published by Walter de Gruyter GmbH in Open Mathematics
- Vol. 23 (1)
The hyperbolic CS decomposition of tensors based on the C-product
This paper studies the issues about the hyperbolic CS decomposition of tensors under the C-product. The aim of this paper is fourfold. Firstly, we establish the CS decomposition of a complex unitary tensor, including the thin version and the standard version. The corresponding numerical algorithm is also given. Next, we define three kinds of tensors, i.e., the strong unitary tensor, the mode-1 strong unitary tensor, the mode-2 strong unitary tensor, and we give the CS decomposition of the last two kind of tensors aforementioned. Numerical algorithms are also obtained to compute the two types of the CS decompositions. Moreover, we give the definition of another three classes of tensors, called the -orthogonal tensor, the mode-1 strong -orthogonal tensor and the mode-2 strong -orthogonal tensor. The corresponding hyperbolic CS decompositions and numerical algorithms are also established. Finally, we give an application to the computation of the C-eigenvalues of the orthogonal tensor. Numerical examples are given to test our results.- 1 January 2025
- Published by Walter de Gruyter GmbH in Open Mathematics
- Vol. 23 (1)
Open AccessThe hyperbolic CS decomposition of tensors based on the C-product
This paper studies the issues about the hyperbolic CS decomposition of tensors under the C-product. The aim of this paper is fourfold. Firstly, we establish the CS decomposition of a complex unitary tensor, including the thin version and the standard version. The corresponding numerical algorithm is also given. Next, we define three kinds of tensors, i.e., the strong unitary tensor, the mode-1 strong unitary tensor, the mode-2 strong unitary tensor, and we give the CS decomposition of the last two kind of tensors aforementioned. Numerical algorithms are also obtained to compute the two types of the CS decompositions. Moreover, we give the definition of another three classes of tensors, called the -orthogonal tensor, the mode-1 strong -orthogonal tensor and the mode-2 strong -orthogonal tensor. The corresponding hyperbolic CS decompositions and numerical algorithms are also established. Finally, we give an application to the computation of the C-eigenvalues of the orthogonal tensor. Numerical examples are given to test our results. - Open Access
Computationally efficient orthogonalization for pairwise comparisons method
Orthogonalization is one of few mathematical methods conforming to mathematical standards for approximation. Finding a consistent PC matrix of a given an inconsistent PC matrix is the main goal of a pairwise comparisons method. We introduce an orthogonalization for pairwise comparisons matrix based on a generalized Frobenius inner matrix product. The proposed theory is supported by numerous examples and visualizations.
Open AccessComputationally efficient orthogonalization for pairwise comparisons method
Orthogonalization is one of few mathematical methods conforming to mathematical standards for approximation. Finding a consistent PC matrix of a given an inconsistent PC matrix is the main goal of a pairwise comparisons method. We introduce an orthogonalization for pairwise comparisons matrix based on a generalized Frobenius inner matrix product. The proposed theory is supported by numerous examples and visualizations.
- 21 June 2023
- Published by Springer Nature in Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
- Vol. 117 (3) , 1-9
New characterizations for the weighted (b, c)-inverse in rings and their applications
- 21 June 2023
- Published by Springer Nature in Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas
- Vol. 117 (3) , 1-9
New characterizations for the weighted (b, c)-inverse in rings and their applications
- Open Access
- 12 April 2023
- Published by MDPI AG in Mathematics
- Vol. 11 (8) , 1822
Two Generalizations of the Core Inverse in Rings with Some Applications
In this paper, we introduce two new generalized core inverses, namely, the -core inverse and the -core inverse; both extend the inverses of the -core inverse, the -core inverse, the core inverse, the core-EP inverse and the -inverse.- 12 April 2023
- Published by MDPI AG in Mathematics
- Vol. 11 (8) , 1822
Open AccessTwo Generalizations of the Core Inverse in Rings with Some Applications
In this paper, we introduce two new generalized core inverses, namely, the -core inverse and the -core inverse; both extend the inverses of the -core inverse, the -core inverse, the core inverse, the core-EP inverse and the -inverse. - 7 September 2022
- Published by Taylor & Francis in Journal of the Operational Research Society
- Vol. 74 (8) , 1860-1877
Efficient sampling of pairwise comparisons in decision-making
Performing pairwise comparisons (PCs) that reflect preferences between pairs of decision-making elements is an approach widely used in decision modelling. For complex problems, the number of elements to be pairwise compared may be very large, something that may lead to a final calculation of not well-supported priorities and, as a consequence, to the drawing of wrong practical conclusions. Decision-making must usually be performed from the available incomplete body of information, and this article explores the possibility of producing reliable results by using just a sample of comparisons. We analyse and solve two specific cases of considerable interest: the sample consists of: (i) a balanced and unbiased set of PCs; and (ii) the PCs obtained by comparing all the elements against a reduced number of pivotal elements. This latter sample includes two practical cases: one in which the eliciting actor is more familiar with the pivotal specific elements; and another in which the Best-Worst method has been previously used to identify the two extreme elements under comparison. The approach employed, developed within linearisation theory, is supported with suitable proofs and examples.
- 7 September 2022
- Published by Taylor & Francis in Journal of the Operational Research Society
- Vol. 74 (8) , 1860-1877
Efficient sampling of pairwise comparisons in decision-making
Performing pairwise comparisons (PCs) that reflect preferences between pairs of decision-making elements is an approach widely used in decision modelling. For complex problems, the number of elements to be pairwise compared may be very large, something that may lead to a final calculation of not well-supported priorities and, as a consequence, to the drawing of wrong practical conclusions. Decision-making must usually be performed from the available incomplete body of information, and this article explores the possibility of producing reliable results by using just a sample of comparisons. We analyse and solve two specific cases of considerable interest: the sample consists of: (i) a balanced and unbiased set of PCs; and (ii) the PCs obtained by comparing all the elements against a reduced number of pivotal elements. This latter sample includes two practical cases: one in which the eliciting actor is more familiar with the pivotal specific elements; and another in which the Best-Worst method has been previously used to identify the two extreme elements under comparison. The approach employed, developed within linearisation theory, is supported with suitable proofs and examples.
- 4 January 2021
- Published by Springer Nature in Ukrainian Mathematical Journal
- Vol. 72 (8) , 1294-1313
Partial Orders Based on the CS Decomposition
- 4 January 2021
- Published by Springer Nature in Ukrainian Mathematical Journal
- Vol. 72 (8) , 1294-1313
Partial Orders Based on the CS Decomposition