# Revista de Matemáticas 18(1)

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Ítem Personnel Selection Based on Fuzzy Methods(2011-03-18 00:00:00) Cañós, Lourdes; Casasús, Trinidad; Crespo, Enric; Lara, Tomás; Pérez, Juan C.Más... The decisions of managers regarding the selection of staff strongly determine the success of the company. A correct choice of employees is a source of competitive advantage. We propose a fuzzy method for staff selection, based on competence management and the comparison with the valuation that the company considers the best in each competence (ideal candidate). Our method is based on the Hamming distance and a Matching Level Index. The algorithms, implemented in the software StaffDesigner, allow us to rank the candidates, even when the competences of the ideal candidate have been evaluated only in part. Our approach is applied in a numerical example.Más... Ítem The Decreasing digits and the a, b, c Model: A Proposal for Handling Populations in Shelters(2011-03-18 00:00:00) García G., María J.; Hernández R., José G.; Hernández G., Gilberto J.Más... Happened a catastrophe, some one of the impacted population should their move from its homes, toward refuges or shelters. To guarantee the essential services in the shelter, it is necessary to know the population size that remain in it, knowing that it will be a random number and that it responds mainly to rate the arrival and departure people. Since the arrivals and exits can be visualized as birth and dead process, it has been planned to emulate this situation making use of the sequences that are derived of two very simple concepts: The Decreasing digits (Dd) and the A, B, C model. The contribution of this work is their objective: To show like one can make use of the derived expressions of the A, B, C model and the decreasing digits, to obtain a population estimation that remains in a shelter, as consequence of a catastrophe.Más... Ítem Minimal Reducts with Grasp(2011-03-18 00:00:00) Mendez Gurrola, Iris Iddaly; Laureano Cruces, Ana Lilia; Ramírez Rodríguez, JavierMás... The proper detection of patient level of dementia is important to offer the suitable treatment. The diagnosis is based on certain criteria, reflected in the clinical examinations. From these examinations emerge the limitations and the degree in which each patient is in. In order to reduce the total of limitations to be evaluated, we used the rough set theory, this theory has been applied in areas of the artificial intelligence such as decision analysis, expert systems, knowledge discovery, classification with multiple attributes. In our case this theory is applied to find the minimal limitations set or reduct that generate the same classification that considering all the limitations, to fulfill this purpose we development an algorithm GRASP (Greedy Randomized Adaptive Search Procedure).Más... Ítem Heuristic for Solving the Multiple Alignment Sequence Problem(2011-03-18 00:00:00) Mora Gutiérrez, Roman Anselmo; Ramírez Rodríguez, Javier; Elizondo Cortéz, MayraMás... In this paper we developed a new algorithm for solving the problem of multiple sequence alignment (AM S), which is a hybrid metaheuristic based on harmony search and simulated annealing. The hybrid was validated with the methodology of Julie Thompson. This is a basic algorithm and and results obtained during this stage are encouraging.Más... Ítem A Non-Standard Generating Function for Continuous Dual q-Hahn polynomials(2011-03-18 00:00:00) Atakishiyeva, Mesuma; Atakishiyev, NatigMás... We study a non-standard form of generating function for the three-parameter continuous dual q-Hahn polynomials $p_{n} (x; a, b, | q)$, which has surfaced in a recent work of the present authors on the construction of lifting $q$-difference operators in the Askey scheme of basic hypergeometric polynomials. We show that the resulting generating function identity for the continuous dual q-Hahn polynomials $ p_{n} (x; a, b, c | q)$ can be explicitly stated in terms of Jackson’s $q$-exponential functions $e_{q} (z)$.Más... Ítem Heuristics for the Robust Coloring Problem(2011-03-18 00:00:00) Gutiérrez Andrade, Miguel Ángel; Lara Velázquez, Pedro; Lopez Bracho, Rafael; Ramírez Rodríguez, JavierMás... Let $G$ and $\bar{G}$ be complementary graphs. Given a penalty function defined on the edges of $G$, we will say that the rigidity of a $k$-coloring of $G$ is the sum of the penalties of the edges of G joining vertices of the same color. Based on the previous definition, the Robust Coloring Problem (RCP) is stated as the search of the minimum rigidity $k$-coloring. In this work a comparison of heuristics based on simulated annealing, GRASP and scatter search is presented. These are the best results for the RCP that have been obtained.Más... Ítem Heuristics for Solving the Multiple Problem Identification of the Responses of Brain and Artificial Neural Networks in the Presence of Usual and Unusual Stimuli by Means of Kalman-Type Filters(2011-03-18 00:00:00) Cardo, Romina; Corvalán, AlvaroMás... We consider the problem of obtaining information about the recognition of logical inconsistencies with already imprinted patterns of a subnetwork of a neural network, both cerebral and artificially designed, by means of the measurement of the event related potentials (ERP). One of the subsequent aims, it is the detection of logical inconsistencies of the speech, not purely semantic, but of the recognition of not coherent phrases with a story line. The possibility of the use, with this goal, of ERP obtained of superficially located electrodes on the scalp would be interesting: relevant conclusions would be obtained from a non-invasive method and by means of equipment that is relatively economic, easily transportable and installable. The alternative that we propose is the utilization of Kalman type filters (with necessary modifications). The idea is to deal with the evoked response as a not accessible variable, with a relation (non linear, but locally linealizable) respect to the measurable variable. We study, as guide example, the evolution of a variable that measures, in a neural network of type Hopfield attractors, the adjustment between the conditions of a subnetwork associated with the recognition of some patterns, after a quantity prearranged of iterations.Más... Ítem Creation of a Model of Pollutans Diffusion in Soil-Water System Using a Cellular Automata(2011-03-18 00:00:00) Merino Castro, GlicinaMás... In this paper is presented a developed model for a pollutant diffusion in a soil-water system, for specific conditions in a real study area. A model that allows the observations of the pollutant flow in the soil-water system and its behavior and interaction with the different system elements, is searched with the purpose of orientate and support the processes and techniques application for the pollutant soil and water remediation. The basic model conditions are: 1) The pollutant is introduced to the soil. 2) The pollutant flows from the soil to the water. 3) The introduced pollutant concentration is variable during the process. 4) The pollutant may saturate the soil. 5)The pollutant is adsorbed by the soil. 6) The model is developed in 2D, with the possibility to be expanded to 3D. The model uses a cellular automata that contains different zones with their own function rules. There are four considerate zones: i) Introduction of the pollutant zone. ii) Soil zone (a porous media). iii) Soil-water interaction zone. iv) Water zone.Más... Ítem Optimal Control of Pollution Stock through Ecological Interaction of the Manufacturer and the State(2011-03-18 00:00:00) Grigorieva, Ellina V.; Khailov, Evgenii N.; Kharitonova, E. I.Más... A model of an interaction between a manufacturer and the state where the manufacturer produces a single product and the state controls the level of pollution is created and investigated. A local economy with a stock pollution problem that must choose between productive and environmental investments (control functions) is considered. The model is described by a nonlinear system of two differential equations with two bounded controls. The best optimal strategy is found analytically with the use of the Pontryagin Maximum Principle and Green’s Theorem.Más... Ítem Curvas ROC y Vecinos Cercanos, Propuesta de un Nuevo Algoritmo de Condensación(2011-03-18 00:00:00) Jiménez Padilla, Raquel; Cuevas Covarrubias, CarlosMás... k-NN criteria are non parametric methods of statistical classificaction. They are accurate, versatile and distribution free. However, their computational cost may be too expensive; especially for large sample sizes. We present a new condensation algorithm based on the Binormal model for ROC curves. It transforms the training sample into a small set of low dimensional vetors. Contrasting with other condensation techniques described in the literature, our proposal helps to control the exchange of accuracy for condensation onthe training sample. The results of a Monte Carlo study show that its performance can be very competitive in different realistic scenarios, resulting in better training samples than other frequently used methods.Más... Ítem Regresion PLS y PCA como Solucion al Problema de Multicolinealidad en Regresion Multiple(2011-03-18 00:00:00) Vega Vilca, José Carlos; Guzman, JosuéMás... We present and compare principal components regression and partial least squares regression, and their solution to the problem of multicollinearity. We illustrate the use of both techniques, and demonstrate the superiority of partial least squares.Más... Ítem Fuzzy Regression VS. Ordinary Least Squares Regression: Case Study(2011-03-18 00:00:00) de los Cobos Silva, Sergio Gerardo; Goddard Close, John; Gutiérrez Andrade, Miguel ÁngelMás... The objective of this paper is to disseminate the technique of fuzzy regression and to give a practical example of its use. To this end, classical regression is compared to several fuzzy regression models on a problem concerning the consumer confidence index with respect to the dollar rate, the latter taken as the independent variable. A brief introduction is given to each of the different methodologies employed. The results obtained using the regression algorithms, onewith ordinary least squares and another two with fuzzy regression, are presented. The instances generated using the official historical data for the problem are given and the numerical results obtained with the regression methods are reported.Más... Ítem Integral Equations for the Aggregate Claim Amount(2011-03-18 00:00:00) Pacheco González, Carlos GabrielMás... In the context of insurance mathematics, we study the renewal properties of the so-called aggregate claim amount for the non-discounted and the discounted case. For these models, we set integral equations for the distribution function. Additionally we mention how the integral equation may be used to find an approximation of the distribution.Más...