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[EN] A new decomposition for square matrices is constructed by using two known matrix decompositions. A new characterization of the core-EP order is obtained by using this new matrix decomposition. We also use this matrix decomposition to investigate the minus, star, sharp and core partial orders in the setting of complex matrices., The present research is supported by the National Natural Science Foundation of China (No. 11771076). The first author is supported by the National Science Foundation of Jiangsu, Province of China (No. BK20191047) and the National Science Foundation of Jiangsu Education Committee (No. 19KJB110005).

In this paper, we consider Moore-Penrose invertible, group invertible, and core invertible elements in rings with involution to characterize EP, generalized normal, generalized Hermitian elements and generalized partial isometries. As a consequence, we obtain new characterizations for elements in rings with involution to be normal and Hermitian elements.

Highlights • This paper proposes a MCDM framework to support risk evaluation for maintenance activities. • The ANP is proposed to select the best maintenance strategy on the basis of real systems’ features. • The ELECTRE III is used to prioritise the main risks related to the interventions of the selected maintenance policy. • The proposed framework is applied to a core subsystem of a real-world marine salt manufacture firm., This paper intends to contribute with a multi-criteria decision-making (MCDM) framework to support risk evaluation for maintenance activities carried out on critical systems in industry. We propose to first select the best maintenance strategy tailored to companies’ requirements and systems’ features, and second to perform a risk prioritisation aimed at highlighting priorities of intervention. The Analytic Network Process (ANP) is suggested to select the maintenance policy representing the best trade-off considering the complex and varied interdependencies amongst a diversity of clustered elements characterising the system. Then, the main risks related to the interventions associated to the selected maintenance policy are ranked using the ELimination Et Choix Traduisant la REalité III (ELECTRE III) method, using the same criteria weighted by the previous ANP application. This hybrid MCDM framework is applied to a core subsystem of a real-world marine salt manufacture firm.

A young woman was brought to the emergency department after sustaining a gunshot wound to right cervical zone 2. Prehospital personnel describe abundant external bleeding at the accident site. She was admitted to the trauma unit in a 7-minute cardiorespiratory arrest, intubated. A massive transfusion started with 2 units of packed red blood cells and 2 units of fresh frozen plasma through high-flow venous accesses. A hemostatic Foley balloon was inserted through the cervical wound (figure 1A). Her extended focused assessment with sonography in trauma was negative for the abdomen and thorax. After 3 minutes of advanced cardiopulmonary resuscitation, she recovered spontaneous rhythm. During the next few minutes, the patient entered deep shock with blood pressure 70/30 mm Hg, heart rate 110 beats per minute. As she did not achieve hemodynamic improvement despite transfusions, she was transferred to the operating room. An anterior sternocleidomastoid incision was made, maintaining hemostatic control with a Foley balloon. During the cervical surgical exploration, an undamaged common external and internal carotid artery was observed, with bleeding visible behind the neurovascular bundle (figure 1B). Do you suspect a vertebral artery (VA) injury? Figure 1 (A) Gunshot …

[EN] Human factors are intrinsically involved at virtually any level of most industrial/business activities, and may be responsible for several accidents and incidents, if not correctly identified and managed. Focusing on the significance of human behaviour in industry, this article proposes a multi-criteria decision-making (MCDM)-based approach to support organizational risk assessment in industrial environments. The decision-making trial and evaluation laboratory (DEMATEL) method is proposed as a mathematical framework to evaluate mutual relationships within a set of human factors involved in industrial processes, with the aim of highlighting priorities of intervention. A case study related to a manufacturing process of a real-world winery is presented, and the proposed approach is applied to rank human factors resulting from a previous organisational risk evaluation from which suitable inference engines may be developed to better support risk management., This research was funded by Universitat Politècnica de València: 114417.

This contribution proposes a Multi-Criteria Decision-Making (MCDM)-based approach to support organizational risk assessment in industrial environments

[EN] Let R be a unital ring with involution. In Section 2, for given two core invertible elements a, b. R, we investigate mainly the absorption law for the core inverse in virtue of the equality of the projections aa and .In Section 3, we study several relations concerning the projections a a and bb , where a . a{1, 2, 4} and b . b{1, 2, 3}. Some well- known results are extended to the *- reducing ring case. As an application, EP elements in a *- reducing ring are considered., This research was supported by the National Natural Science Foundation of China [grant number 11371089]. The first author is grateful to China Scholarship Councilor giving him a scholarship for his further study in Universitat Politecnica de Valencia Spain.

En este trabajo se presenta una aplicación y comprobación del método de jerarquías analíticas (AHP, por sus siglas en inglés) a la toma de decisiones respecto a la gestión de fugas que llevará a cabo una empresa de suministro de agua potable. En la evaluación de alternativas serán considerados no solo los costos del desarrollo del proyecto, sino también algunas externalidades sociales y ambientales, con la finalidad de que la decisión tomada se ajuste más a la realidad de la empresa y su entorno. Para la correcta aplicación de AHP y para la validación de los resultados obtenidos, se hace hincapié en los requisitos que se deben cumplir en la construcción de matrices de comparación para ser consideradas válidas. Estas características son: positividad de sus componentes, homogeneidad, reciprocidad y consistencia, presentando esta última considerable complejidad, lo que ha motivado la generación de opciones para su mejora.

[EN] Several generalizations of Samuelson s inequality are given, including complex data and inequalities concerning random variables in a probability space. The proofs of these generalizations need only a well known result from inner product spaces, namely, Bessel s inequality. Finally we apply these generalizations to locate the eigenvalues of certain matrices and tensors, as well as the complex roots of polynomials, This work was supported by Hunan Provincial Innovation Foundation For Postgraduate under Grant [number CX2016B073]. The first author is thankful to China Scholarship Council for giving him a grant to have a further study in Universidad Politecnica de Valencia, Spain.

[EN] We give several conditions in order that the absorption law for one sided (b,c)-inverses in rings holds. Also, by using centralizers, we obtain the absorption law for the (b,c)-inverse and the reverse order law of the (b,c)-inverse in rings. As applications, we obtain the related results for the inverse along an element, Moore-Penrose inverse, Drazin inverse, group inverse and core inverse., This research is supported by the National Natural Science Foundation of China (no. 11771076 and no. 11871301). The first author is grateful to China Scholarship Council for giving him a scholarship for his further study in Universitat Politecnica de Valencia, Spain.

Fast and judicious decision-making is paramount for the success of many activities and processes. However, various degrees of difficulty may affect the achievement of effective and optimal solutions. Decisions should ideally meet the best trade-off among as many of the involved factors as possible, especially in the case of complex problems. Substantial cognitive and technical skills are indispensable, while not always sufficient, to carry out optimal evaluations. One of the most common causes of wrong decisions derives from uncertainty and vagueness in making forecasts or attributing judgments. The literature shows numerous efforts towards the optimization and modeling of uncertain contexts by means of probabilistic approaches. This paper proposes the use of probability theory to estimate uncertain expert judgments within the framework of the analytic hierarchy process and, more specifically, within a linearization scheme developed by the authors. After describing the necessary probabilistic concepts of interest, the main results are developed. These results can be summarized as using various kinds of random variables with uncertainty embodied in undecided pairwise comparisons. A case study focused on the maintenance management of an industrial water distribution system exemplifies the approach.

[EN] In 2012, Drazin introduced a class of outer generalized inverse in a ring R, the (b, c)-inverse of a for a,b,c is an element of R and denoted by a(parallel to(b,c)). In this paper, rank equalities of A(k)A(parallel to(B,C)) - A parallel to((B,C))A(k) and (A*)(k)A(parallel to(B,C) )-( )A(parallel to(B,C))(A*)(k )are obtained. As applications, we investigate equivalent conditions for the equalities (A*)(k)A(parallel to(B,C)) = A(parallel to(B,C))(A*)(k) and A(k)A(parallel to(B,C)) = A(parallel to(B,C))A(k). As corollaries we obtain rank equalities related to the Moore-Penrose inverse, the core inverse, and the Drazin inverse. The paper finishes with some rank equalities involving different expressions containing A(parallel to(B,C))., The authors wish to thank the editor and reviewers sincerely for their constructive comments and suggestions that have improved the quality of the paper. The second author is grateful to China Scholarship Council for giving him a scholarship for his further study in Universitat Politècnica de València, Spain. This research is supported by the National Natural Science Foundation of China (No. 11771076), the Fundamental Research Funds for the Central Universities (no. KYCX 0055), the Postgraduate Research & Practice Innovation Program of Jiangsu Province (no. KYCX 0055). The second author is supported by the Natural Science Foundation of Jiangsu Education Committee (No. 19KJB110005) and the Natural Science Foundation of Jiangsu Province of China (No. BK20191047).

[EN] Let A be an complex matrix. The (B,C)-inverse A vertical bar(B,C) of A was introduced by Drazin in 2012. For given matrices A and B, several rank equalities related to A vertical bar(B1,C1) and B vertical bar(B2,C2) of A and B are presented. As applications, several rank equalities related to the inverse along an element, the Moore-Penrose inverse, the Drazin inverse, the group inverse and the core inverse are obtained., The second author is grateful to China Scholarship Council for giving him a scholarship for his further study in Universitat Politecnica de Valencia, Spain.

We present a project-based learning experience in the context of linear algebra developed for the recently launched double major in business administration and management/engineering of technology and telecommunication services at the universitat politecnica de valencia 2014–15. Decision-making is used to motivate students towards applying, understanding, and appreciating linear algebra in a diversity of projects. this experience introduces students to the analytic hierarchy process (AHP), a multi-attribute, decision-making technique that is rooted in linear algebra. Through a simulation scenario, each team of students develops a project about any real-world problem consisting of a decision-making process in the presence of multiple intangibles. At the same time, the algebraic fundamentals that make the process valid and consistent are clarified. The students showed great interest in the experience; and the results obtained confirmed that the activities helped them understand several complex concepts related to linear algebra, and fostered a significant interest in a subject traditionally considered frighteningly abstract. Finally, the students appreciated the stimulating insights provided by linear algebra that are crucial in decision-making. This multi-disciplinary experience enables the evaluation of several cross skills and competencies such as critical thinking and ethical leadership. © 2016 Wiley Periodicals, Inc. Comput Appl Eng Educ; View this article online at wileyonlinelibrary.com/journal/cae; DOI 10.1002/cae.21725