Novelty on the Matrices of Weighing

Novelty on the Matrices of Weighing

María J. García G. (Minimax Consultores, Venezuela), Gilberto J. Hernández G. (Minimax Consultores, Venezuela) and José G. Hernández R. (Minimax Consultores, Venezuela)
DOI: 10.4018/978-1-5225-7214-5.ch022

Abstract

This chapter relates some social aspects, such as playfulness, customer service, and citizen safety with one of the simplest multicriteria techniques to implement, matrixes of weighing (MOW, matrices de ponderación [MDP]). Taking as starting point the work matrixes of weighing and catastrophes, a brief review is made of the MOW, highlighting new applications of the same, as well as new concepts that have emerged from its use. The objective of this work will be to present some applications of the matrixes of weighing, while explaining what they are and how they apply, the multilayer matrix of weighing with multiplicative factors (ML-MOWwMf). To achieve this general objective and secondary objectives, this chapter will make use of the integrated-adaptable methodology for the development of decision support system (IAMDSS [MIASAD])
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Introduction

To beginnings of the second decade of the XXIst century, it was commented, in the work Matrixes Of Weighing and catastrophes (Hernández, García & Hernández, 2011), that the Matrixes Of Weighing (MOW [MDP]), although, undoubtedly, one of the multicriteria models, simpler to implement, does not produce many quotations in the specialized literature. They may even be confused with other decision making methods, which make use of matrices, as is the case of the linguistic decision matrix (Xu, Wu & Zhang, 2014; Wu, Xu & Xu, 2016), or the meta-matrix with which she works Gaspars-Wieloch (2017), or the extreme case of Chow et al. (2015), who mention the transition matrix, the stochastic matrix, and the perturbation matrices, but when they use the abbreviation MDP, are referring to Markov Decision Process and not to Matrixes Of Weighing (MOW, Matrices De Ponderación [MDP].

Different is the situation in relation to the decision matrix presented by Jassbi, Ribeiro & Dargam (2014), which in its structure coincides with the MDP, differing in the management and subsequent use made by their authors. A similar situation occurs in the work of Li, Kou & Peng (2016), where the initial individual decision matrix practically coincides with a MDP, only that it follows another series of steps, including fuzzy logic, which leads to very different results.

In recent years, in the sense of missed appointments and cross quotes, the situation has not varied much, however, if new possible applications of the MDP are found, as well as new ways of expressing them.

This paper discussed the Matrixes Of Weighing with multiplicative factors (MOWwMf [MDPcFm]), which had already been mentioned in the work of Hernández, García & Hernández (2011) and are discussed the Multilayer Matrix Of Weighing with Multiplicative factors (ML-MOWwMf [MDPcFm-MC]), which have been presented in more recent works (García et al., 2017; Hernández, García & Hernández, 2012; Jeney, 2014).

At the same time comments are made on MDP applications in different fields of human endeavor, such as the Sports fantastic leagues (SFL [LFD]) (Hernández et al., 2014), the location of vehicles to protect the population (García, Hernández & Hernández, 2014) and in the effects, that can have on the citizens the control of inventories (García et al., 2017).

From the above the objective of this work is to present some applications of the Matrixes Of Weighing, while explain what they are and how they apply, the Multilayer Matrix Of Weighing with Multiplicative factors (ML-MOWwMf).

In pursuing this overall objective, the following specific objectives arise:

Present an update of the Matrixes Of Weighing (MDP), including a discussion of the Multilayer Matrix Of Weighing with Multiplicative factors (MDPcFm-MC).

Examine some situations where MDP can be useful: participate in Sports fantastic leagues (SFL [LFD]), Location of vehicles to handle emergencies (LVHE [UVAE]) and to face measures that affect the control of inventories (IC [CI]).

Construct three MDPcFm-MC to solve, each one, of the previously mentioned situations: the LFD, the UVAE and the CI.

Key Terms in this Chapter

Sport Fantastic Leagues (SFL [LFD]): They are a new way of living sports, where participants, in groups of approximately twelve people, enjoy the experiences of their favorite sports, compete, following established rules and without necessarily being close to each other, and almost always away from sports arenas. These participants, accumulate points, according to the performance of the athletes, who compete in the real world and that they have selected for their respective squads.

Matrices of Weighing (MOW [MDP]): They are simply a numerical arrangement of rows and columns, which allow hierarchy and even facilitate the selection of alternatives, in accordance with a set of established criteria. The MDP are one of the simplest multicriteria models to construct and implement. However, their simplicity, they can offer very robust solutions when it comes to hierarchizing and, specially, selecting alternatives.

Multilayer Matrix of Weighing With Multiplicative Factors (ML-MOWwMf [MDPcFm-MC]): They are MDPcFm, which in addition to hierarchizing and facilitating the selection of alternatives, in turn allow assessment and knowledge of the real influence of each of the criteria, through which these alternatives are being evaluated. Additionally, they facilitate valuations under multiple scenarios.

Inventories Control (IC [CI]): It is one of the most relevant and delicate tasks of logistics and by extension of the organization. It is related to the final product and all the components that are needed in its production process, whether they are a direct part of it or are necessary for the proper operability of the organization. Through the control of inventories, it must be ensured that each of these components must be available at the time, conditions and quantities required, so that production does not stop.

Location of Vehicles to Handle Emergencies (LVHE [UVAE]): It is a necessity that arises in very large cities, which generally tend to have strong traffic problems, as an appropriate vehicle location to handle emergencies, in specific locations, it can guarantee that these come more quickly where they are needed. Of these vehicles for emergencies, mainly include ambulances, fire trucks and police vehicles.

Matrices of Weighing With Multiplicative Factors (MOWwMf [MDPcFm]): They are MDP, which manage a concept taken from the Multiattribute Models (MM), the multiplicative factors, which give them a greater diversity and field of application.

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