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This book is a collection of selected papers presented at the SIGEF conference, held at the Faculty of Economics and Business of the University of Girona (Spain), 06-08 July, 2015.

This edition of the conference has been presented with the slogan “Scientific methods for the treatment of uncertainty in social sciences”. There are different ways for dealing with uncertainty in management. The book focuses on soft computing theories and their role in assessing uncertainty in a complex world.

It gives a comprehensive overview of quantitative management topics and discusses some of the most recent developments in all the areas of business and management in soft computing including Decision Making, Expert Systems and Forgotten Effects Theory, Forecasting Models, Fuzzy Logic and Fuzzy Sets, Modelling and Simulation Techniques, Neural Networks and Genetic Algorithms and Optimization and Control. The book might be of great interest for anyone working in the area of management and business economics and might be especially useful for scientists and graduate students doing research in these fields.



Decision Making


New Aggregation Methods for Decision-Making in the Selection of Business Opportunities

We analyse decision-making process in the selection of business opportunities. A new mathematical application based on OWA operator and selection index is developed. We consider the use of the OWA distance (OWAD), the OWA adequacy coefficient (OWAAC) and the OWA index of maximum and minimum level OWAIMAM operators. The study proposes a fuzzy significance vector (FS), which can aggregate information according to the importance of its characteristics. The introduction of the selection OWA operator using fuzzy significance vector can reflect decision with different degrees of optimism through normalization process where the maximum value of the aggregated information can be higher than 1. These methods are called FS-OWAAC, FS-OWAD and FS-OWAIMAM operator. By using FS-OWA operator, we can parameterize attitudinal character of decisor and the importance of characteristics of the information. A numerical example is developed in decision-making process for the selection of opportunities to start a new business within different sectors according to preference of decisor and environmental factors.

Fabio R. Blanco-Mesa, Anna M. Gil-Lafuente, José M. Merigó

Credit Analysis Using a Combination of Fuzzy Robust PCA and a Classification Algorithm

Classification is a key part of credit analysis and bankruptcy prediction and new powerful classification methods coming from artificial intelligence are often applied. Most often classification methods require pre-processing of data. This paper presents a two-part classification process that combines a pre-processing step that uses fuzzy robust principal component analysis (FRPCA) and a classification step. Combinations of three FRPCA algorithms and two different classifiers, similarity classifier and fuzzy k-nearest neighbor classifier, are tested to find the combination that gives the most accurate mean classification result. Tests are run with a small Australian credit data set that can be considered “rough” and to require “robust” methods, due to the small number of observations. The created principal components are used as inputs in the classification methods. Results obtained indicate a mean classification accuracies of over 80 % for all combinations. It becomes clear that parameters of the used methods clearly affect the results and emphasis is put on finding suitable parameters.

Onesfole Kurama, Pasi Luukka, Mikael Collan

Fuzzy TOPSIS for an Integrative Sustainability Performance Assessment: A Proposal for Wearing Apparel Industry

It is particularly important assessing sustainability in an integrative way considering different stakeholder perspectives to overcome the weaknesses of reductionist approaches to measure sustainability. This integration could help organizations to understand and engage with their stakeholders; and could contribute to sustainable development. The objective of this paper is developing stakeholder methodological approach, based on an application of fuzzy multi-criteria decision-making method (MCDM), to improve the contributions to organizations to sustainable development considering the particular sustainability interests of stakeholders into corporate sustainability performance measurement. With the aim of illustrating the proposed methodology in a specific industry, this study is focused on the wearing apparel industry

Elena Escrig-Olmedo, María-Ángeles Fernández-Izquierdo, María-Jesús Muñoz-Torres, Juana-María Rivera-Lirio

On the Orness of SUOWA Operators

There is in the literature a great variety of functions utilized in the aggregation processes. For this reason, numerous indicators have been suggested to understand the behavior of such functions. One of the measures proposed for this purpose is the orness, which allows to know the degree of closeness to the maximum. The aim of this paper is to provide the orness of some specific cases of SUOWA operators, a family of aggregation functions that simultaneously generalize weighted means and OWA operators.

Bonifacio Llamazares

OWA Operators in Portfolio Selection

Portfolio choice is the process of selecting the optimal proportion of various assets. One of the most well-known methods is the mean-variance approach developed by Harry Markowitz. This paper introduces the ordered weighted average (OWA) in the mean-variance model. The key idea is that the mean and the variance can be extended with the OWA operator being able to consider different degrees of optimism or pessimism in the analysis. Thus, this method can adapt to a wide range of scenarios providing a deeper representation of the available information from the most pessimistic situation to the most optimistic one.

Sigifredo Laengle, Gino Loyola, José M. Merigó

Expert Systems and Forgotten Effects Theory


Application of the Forgotten Effects Model to the Agency Theory

During the financial crisis, interest problems between shareholders (principal) and managers (agent) have raised due to the evidence of the dishonest behaviour of the Chief Executive Officer (CEO). Based on the agency theory, we use the model of forgotten effects in order to identify different solutions for each kind of agency problems. The aim of this study is to reduce agency problems and facilitate the companies’ success, providing useful information to improve the decision-making process in management.

Elena Arroyo, Elvira Cassú

Determining the Influence Variables in the Pork Price, Based on Expert Systems

The meat industry is the most important economic activity in the agro-food sector. Globally, the pork meat is the most consumed, beating the poultry. The price of raw materials of natural type is based on reference quotes made from wholesale source products, and those are general prices. The contract wholesales publishes a price every week of the year. In this paper we studied the elements or circumstances, which we have named variables, that influence the price of pork and the quantification of each one’s weight (degree of influence) has on the price quoted. This study is based in fuzzy logic through the use of the theory of


developed by Kaufmann (


) and Kaufmann and Gil Aluja (



Josep M. Jaile-Benitez, Joan Carles Ferrer-Comalat, Salvador Linares-Mustarós

Forgotten Effects Analysis Between the Regional Economic Activity of Michoacan and Welfare of Its Inhabitants

The creation of effective policies for the acceleration of economic, social and environmental development of regions is a demanding issue for government’s agenda. Applying the Forgotten Effects Theory, this research aims to quantify the incidence of economic activity on the welfare level of citizens. In this paper we analyze 10 regions located in the Latin-American State of Michoacán, México, each with different characteristics and specificities. Results show the relevant cumulative indirect effect that the primary sector has on family income and occupation. Manufacturing activities display high indirect cumulative effect on higher education and health. Construction and service sectors play a dominant role in environmental quality. This research presents a first step in order to release the nature of the problem and to show to what extent, in quantitative terms, the economic activity types influence welfare. This analysis could help decision makers for the effective allocation of resources and the creation of sustainable policies.

Anna M. Gil-Lafuente, Jaume Balvey, Víctor G. Alfaro-García, Gerardo G. Alfaro-Calderón

Interval Numbers Versus Correlational Approaches Analyzing Corporate Social Responsibility

Our purpose is to explore the relationship between Corporate Social Responsibility (CSR), work-life balance (WLB) and effectiveness comparing (a) a correlational approach, (b) expertons method, and (c) uncertain averaging operators (UA, UWA, UPA, and UPWA). These methodologies are common in the field of economics and engineering, but very innovative in the human resources research, allowing more accurate analyses of workers’ perceptions. The Survey Work-Home Interaction – NijmeGen (SWING -SSC) and the Balanced Scorecard (BSC) were used. Results showed differences between companies with different levels of CSR development on individual effectiveness, and relations between WLB and individual effectiveness. Expertons methodology and uncertain averaging operators allows more accurate results than correlational statistics.

Sefa Boria-Reverter, Montserrat Yepes-Baldó, Marina Romeo, Luis Torres

Second-Order Changes on Personnel Assignment Under Uncertainty

In this work we present some basics about the commitment in organizations and how it influences this heavily on the change to a new strategy in the organization. This task involves using the Hamming Distance (fuzzy logic) to measure the level of commitment to employees with the new strategy to establish. The process consists of four states to the changes in strategy called second-order, in such a process it includes the assessment of parameters through fuzzy numbers. In this regard, we propose estimating parameters a and b, using Expertons as a first approximation and to provide justification to the calculations of the second order change SOC (Sigismund and Oran



Ruben Chavez, Federico González-Santoyo, Beatriz Flores, Juan J. Flores

Forecasting Models


Advanced Spectral Methods and Their Potential in Forecasting Fuzzy-Valued and Multivariate Financial Time Series

In this paper we explore the effectiveness of two nonparametric methods, based upon a matrix spectral decomposition approach, namely the

Independent Component Analysis

(ICA) and the

Singular Spectrum Analysis

(SSA). The intended area of applications is that of forecasting fuzzy-valued and multivariate time series. Given a multivariate time series, ICA assumes that each of its components is a mixture of several independent underlying factors. Separating such distinct time-varying causal factors becomes crucial in multivariate financial time series analysis, when attempting to explain past co-movements and to predict future evolutions. The multivariate extension of SSA (MSSA) can be employed as a powerful prediction tool, either separately, or in conjunction with ICA. As a first application, we use MSSA to recurrently forecasting triangular-shaped fuzzy monthly exchange rates, thus aiming at capturing both the randomness and the fuzziness of the financial process. A hybrid ICA-SSA approach is also proposed. The primarily role of ICA is to reveal certain fundamental factors behind several parallel series of foreign exchange rates. More accurate predictions can be performed via these independent components, after their separation. MSSA is employed to compute forecasts of independent factors. Afterwards, these forecasts of underlying factors are remixed into the forecasts of observable foreign exchange rates.

Vasile Georgescu, Sorin-Manuel Delureanu

Goodness of Aggregation Operators in a Diagnostic Fuzzy Model of Business Failure

The aim of the following paper is proposed a mechanism of analysis useful to verify the capacity of the Vigier and Terceño (


) diagnostic fuzzy model to predict diseases. The model is enriched by the inclusion of aggregation operators because this allows reducing the detected map of causes or diseases in strategic areas of continuous monitoring. And at the same time this causes can be disaggregated once some alert indicator is identified. The capacity of explanation and prediction of estimated diseases are measured through this mechanism; and also are detected the monitoring key areas that warning insolvency situations. In this approach are introduced aggregation operators of causes of business failure, and a goodness measure using approximate solutions. This index of goodness allows testing the degree of fit of the predictions of the model. Also, as an example, the empirical estimation and the verification of the improvement proposal to a set of small and medium- sized enterprises (SMEs) of the construction sector are presented.

Valeria Scherger, Hernán P. Vigier, Antonio Terceño-Gómez, M. Glòria Barberà-Mariné

Forecasting Global Growth in an Uncertain Environment

Forecasting is an integral part of economic decision making. However, the current forecasting algorithms offer poor precision in solution of uncertainty problems. In this paper, a novel forecasting model for world GDP growth rate using fuzzy regression was proposed.

Nigar A. Abdullayeva

Fuzzy NN Time Series Forecasting

The kNN time series forecasting method is based on a very simple idea. kNN forecasting is base on the idea that similar training samples most likely will have similar output values. One has to look for a certain number of nearest neighbors, according to some distance. The first idea that comes to mind when we see the nearest neighbor time series forecasting technique is to weigh the contribution of the different neighbors according to distance to the present observation. The fuzzy version of the nearest neighbor time series forecasting technique implicitly weighs the contribution of the different neighbors to the prediction, using the fuzzy membership of the linguistic terms as a kind of distance to the current observation. The training phase compiles all different scenarios of what has been observed in the time series’ past as a set of fuzzy rules. When we encounter a new situation and need to predict the future outcome, just like in normal fuzzy inference systems, the current observation is fuzzyfied, the set of rules is traversed to see which ones of them are activated (i.e., their antecedents are satisfied) and the outcome of the forecast is defuzzyfied by the common center of gravity rule.

Juan J. Flores, Federico González-Santoyo, Beatriz Flores, Rubén Molina

Fuzzy Logic and Fuzzy Sets


A Methodology for the Valuation of Quality Management System in a Fuzzy Environment

The needs and demands of the present markets have favoured the development of Quality Management. Among the different strategies related to quality management that an organisation can develop, the establishment of quality systems in accordance with the requirements established in ISO 9000 standards has acquired a special importance. The worldwide implementation and certification of ISO 9001 quality management systems have increased significantly during the lasts years. However, the contribution of ISO 9000 certification is a controversial issue. While firms continue to seek certification and some researchers support its value, other studies suggest that it has little value to companies. This work provides a tool that facilitates the valuation of the ISO 9001 quality system in large and small companies. To make it, given the uncertainty this process involves, the use of fuzzy math is very useful.

José M. Brotons-Martínez, Manuel E. Sansalvador-Selles

A Qualitative Study to Strong Allee Effect with Fuzzy Parameters

The Allee effect is related to those aspects of dynamical of populations Connected with a decreasing in individual fitness when the population size diminishes to very low levels. In this work we propose a fuzzy approach to Allee effect that permits to deal with uncertainty. This fuzzy proposal is considering the Allee effect with fuzzy parameters from two points of view.

Xavier Bertran, Dolors Corominas, Narcis Clara

Distribution of Financial Resources Using a Fuzzy Transportation Model

The classical transportation model refers to the shipment of a product of


sources of supply or origins to


points of demand or destinations. The aim is to assign the offer available at each source, so that demand of destinations be satisfied, both to minimize the total costs of transport or some measure of distance, or else to maximize the profit total. The use of fuzzy numbers makes it possible to consider the aspects of an imprecise environment. The application areas of the transportation problem can be extended when some parameters are fuzzy. In this paper we present an application of a fuzzy transportation model to obtain the best distribution of the means of financing available by a company, to meet its needs, with the goal of minimizing the costs when they are expressed by triangular fuzzy numbers.

Luisa L. Lazzari, Patricia I. Moulia

Clustering Variables Based on Fuzzy Equivalence Relations

We develop a method of grouping (clustering) variables based on fuzzy equivalence relations. We first compute the pairwise relationship (correlation) matrix between the variables and transform the matrix into a fuzzy compatibility relation. Then a fuzzy equivalence relation is constructed by computing the transitive closure of the compatibility relation. Finally, by taking all appropriate α-cuts, we obtain a hierarchical type of variable clustering. As examples, we use the proposed method first as a variable clustering tool in a regression model and secondly as a new way of performing factor analysis.

Kingsley S. Adjenughwure, George N. Botzoris, Basil K. Papadopoulos

Fuzzy EOQ Inventory Model With and Without Production as an Enterprise Improvement Strategy

This work presents a theoretical extension to the inventory model EOQ with and without production, representing all variables as fuzzy quantities. The model is compared against the classical EOQ model with and without production. In this comparison, crisp and fuzzy data were used, and the results and conclusions were contrasted. We present the advantages of the fuzzy theory vs. classical theory in decision-making in the enterprise.

Federico González-Santoyo, Beatriz Flores, Anna M. Gil-Lafuente, Juan J. Flores

Modelling and Simulation Techniques


A Bibliometric Overview of Financial Studies

Academic research in modern finance has been developing over the last decades. Many important contributions have been published in the main journals of the field. This paper analyzes scholarly research in finance by using bibliometric indicators. The main results are summarized in three fundamental issues. First, the citation structure in finance is presented. Next, the paper studies the influence of financial journals by using a wide range of indicators including publications, citations and the


-index. The paper ends with an overview of the most influential papers. In general, the results are in accordance with the expectations where the Journal of Finance, the Journal of Financial Economics and the Review of Financial Studies are the most popular journals and the USA is clearly the dominant country in finance.

José M. Merigó, Jian-Bo Yang, Dong-Ling Xu

A Theoretical Approach to Endogenous Development Traps in an Evolutionary Economic System

The representation of evolving economies can be formally represented through evolutionary self-organized systems (ESO), a cellular automata model with endogenous rules of change. Another possibility is to consider economic evolution as the result of the nested application of rules of changes on certain structures we call economic systems. Both approaches show disadvantages: ESO systems are too general and arbitrary, while the application of rules to rules lacks in most cases an effective characterization. In order to get the best out of both worlds we define here a notion of economic ESO systems. We show that the class of these systems is equivalent to a subclass of economic systems. The systems in this subclass can be effectively represented, with the extra bonus that the crucial role we assume knowledge plays in the mechanism of economic evolution becomes explicit. We claim that these systems are particularly fit for representing the notion of “poverty trap”. In fact, they arise in an economic system that is unable to surpass a critical boundary.

Silvia London, Fernando Tohmé

ABC, A Viable Algorithm for the Political Districting Problem

Since 2004, the Federal districting processes have been carried out using a Simulated Annealing based algorithm. However, in 2014, for the local districting of the state of México, a traditional Simulated Annealing technique and an Artificial Bee Colony based algorithm were proposed. Both algorithms used a weight aggregation function to manage the multi-objective nature of the problem, but the population based technique produced better solutions. In this paper, the same techniques are applied to six Mexican states, in order to compare the performance of both algorithms. Results show that the Artificial Bee Colony based algorithm is a viable option for this kind of problems.

Eric-Alfredo Rincón-García, Miguel-Ángel Gutiérrez-Andrade, Sergio-Gerardo de-los-Cobos-Silva, Pedro Lara-Velázquez, Roman-Anselmo Mora-Gutiérrez, Antonin Ponsich

Asymmetric Uncertainty of Mortality and Longevity in the Spanish Population

Using data of specific mortality rates, discriminating between males and females, we estimate mortality and longevity risks for Spain in a period spanning from 1950 to 2012. We employ Dynamic Factor Models, fitted over the differences of the log-mortality rates to forecast mortality rates and we model the short-run dependence relationship in the data set by means of pair-copula constructions. We also compare the forecasting performance of our model with other alternatives in the literature, such as the well-known Lee-Carter Model. Finally, we provide estimations of risk measures such as VaR and Conditional-VaR for different hypothetical populations, which could be of great importance to assess the uncertainty faced by firms such as pension funds or insurance companies, operating in Spain. Our results indicate that mortality and longevity risks are asymmetric, especially in aged populations of males.

Jorge M. Uribe, Helena Chuliá, Montserrat Guillén

Joint Modeling of Health Care Usage and Longevity Uncertainty for an Insurance Portfolio

We study longevity and usage of medical resources of a sample of individuals aged 65 years or more who are covered by a private insurance policy. A longitudinal analysis is presented, where the annual cumulative number of medical coverage requests by each subject characterizes insurance intensity of care until death. We confirm that there is a significant correlation between the longitudinal data on usage level and the survival time processes. We obtain dynamic estimations of event probabilities and we exploit the potential of joint models for personalized survival curve adjustment.

Xavier Piulachs, Ramon Alemany, Montserrat Guillén, Carles Serrat

The Commodities Financialization As a New Source of Uncertainty: The Case of the Incidence of the Interest Rate Over the Maize Price During 1990–2014

The past decade has witnessed the entry of speculative investors as major participants in commodity markets. This phennomenon arises the question of whether these agents influence price dynamics or not. Therefore, the aim of this paper is to explore evidence in order to determine if commodities have behaved in a similar manner to financial assets. This study will focus specifically in the maize market, analyzing the extent to which financial market variables influence price movements. By means of an autoregressive vector system (VAR) the effect of interest rate changes on maize futures prices will be tested. Implications for countries heavily reliant on commodity exports will be drawn from the results of this study.

María-Teresa Casparri, Esteban Otto-Thomasz, Gonzalo Rondinone

The Fairness/Efficiency Issue Explored Through El Farol Bar Model

The relationship between fairness and efficiency is a central issue for policy makers. To date there is no agreement among economists whether a public policy that pursues fairness entails a loss of efficiency of an economic system, or an oriented towards efficiency policy is able to facilitate the achievement of a higher fairness. In this paper we present the fairness/efficiency issue through the analysis of four agent-based simulations that implement the El Farol Bar Model proposed by Brian Arthur in (


). As El Farol Bar models are not interested in exploring the equity issue, we modified them by introducing a set of measures of efficiency and fairness. Particularly, we assume that fairness is a short run issue and we develop time-based measurements of fairness. The computational analysis shows that selfish agents are able to achieve an efficient use of available resources, but they are incapable of generating a fair use of them. The analysis shows that random choices of agents generate an apparent fairness, which occurs only in the long run. Thus, a suitable relationship between efficiency and fairness could be reached by a public policy which defines an appropriate pay-off matrix able to drive agents’ choices.

Cristina Ponsiglione, Valentina Roma, Fabiola Zampella, Giuseppe Zollo

Neural Networks and Genetic Algorithms


Comparative Analysis Between Sustainable Index and Non-sustainable Index with Genetic Algorithms: Application to OECD Countries

This study analyses the differences in financial portfolio metrics between sustainable index and non-sustainable firms in the market index through the use of the portfolio theory and genetic algorithms from 2007 to 2013. The sample consists in 926 firms of four regions (1) Europe: Germany, Austria, Denmark, Spain, Finland, Italy, Norway, Sweden and United Kingdom, (2) Asia: Japan, (3) America: Canada, United States of America and Mexico and (4) Oceania: Australia. To measure the performance of the portfolio two classical metrics: Jensen’s alpha and Sharpe ratio were considered. We also calculate a conditional metric that measures the number of times the return of a given portfolio exceeds the average market return. The goal is to find a portfolio that maximizes these three metrics using a weighted ratio and compare the results between the sustainable and non-sustainable portfolios. Due to a nonlinear programming problem, we use genetic algorithms to obtain the optimal portfolio. The results show a better performance in sustainable portfolios in eight countries, although the amount of countries increases if only the conditional metric is considered.

Martha-del-Pilar Rodríguez-García, Klender Cortez-Alejandro, Alma-Berenice Méndez-Sáenz

Sovereign Bond Spreads and Economic Variables of European Countries Under the Analysis of Self-organizing Maps

This paper presents an empirical analysis related to sovereign bond spreads and a set of economic variables since 1999 until 2013 for a sample of European countries. The analysis is carried out using an original tool in the financial literature: Self-Organizing Maps. This representation is able to cluster countries-years according to the similarities between their main macroeconomic fundamentals. We find interesting groups of countries and we relate them with their level of sovereign bond spreads. The results reflect the incidence of the last financial crisis over the economies and the effect over the eurozone.

Antonio Terceño-Gómez, Lisana B. Martinez, M. Teresa Sorrosal-Forradellas, M. Belén Guercio

Using Genetic Algorithms to Evolve a Type-2 Fuzzy Logic System for Predicting Bankruptcy

In this paper, we use GAs to design an interval type-2 fuzzy logic system (IT2FLS) for the purpose of predicting bankruptcy. The shape of type-2 membership functions, the parameters giving their spread and location in the fuzzy partitions and the set of fuzzy rules are evolved at the same time, by encoding all together into the chromosome representation. Type-2 FLSs have the potential of outperforming their type-1 FLSs counterparts, because a type-2 fuzzy set has a footprint of uncertainty that gives it more degrees of freedom. The enhanced Karnik-Mendel algorithms are employed for the centroid type-reduction and defuzzification stage. The performance in predicting bankruptcy is evaluated by multiple simulations, in terms of both in-sample learning and out-of sample generalization capability, using a type-1 FLS as a benchmark.

Vasile Georgescu

Optimization and Control


Hedge for Automotive SMEs Using An Exotic Option

The automotive firms (usually SMEs) work as suppliers for a big automaker, so the former have financial dependence on the latter’s structure. Each of these SMEs, working as supplier for a brand, is likely to find its sales falling or its gross margin shrinking when a depreciation occurs in the automaker’s stock price. Therefore, fluctuation in automaker’s stock price can impact negatively in its suppliers. This paper uses a stochastic model to calculate the premium that the SME must pay for hedge against these losses. Mathematically, it calculates the probability at time cero of automaker’s stock price hitting a specific barrier before the option expires. For these purposes, 2014 intraday quotes have been used.

Javier-Ignacio García-Fronti, Julieta Romina-Sánchez

Obtaining Classification Rules Using LVQ+PSO: An Application to Credit Risk

Credit risk management is a key element of financial corporations. One of the main problems that face credit risk officials is to approve or deny a credit petition. The usual decision making process consists in gathering personal and financial information about the borrower. This paper present a new method that is able to generate classifying rules that work no only on numerical attributes, but also on nominal attributes. This method, called LVQ+PSO, combines a competitive neural network with an optimization technique in order to find a reduced set of classifying rules. These rules constitute a predictive model for credit risk approval. Given the reduced quantity of rules, our method is very useful for credit officers aiming to make decisions about granting a credit. Our method was applied to two credit databases that were extensively analyzed by other competing classification methods. We obtain very satisfactory results. Future research lines are exposed.

Laura Lanzarini, Augusto Villa-Monte, Aurelio Fernández-Bariviera, Patricia Jimbo-Santana

Optimization of Securitized Cash Flows for Toll Roads

In this paper we propose a methodology that can assist in the design of the quantitative aspects of a process of securitization to finance toll roads. Our goal is to provide the process with a series of mechanisms to streamline it, and to optimize the overall result of securitization for both the originator and for the bondholders. While we choose to apply it to toll roads, we believe that with simple adjustments, the proposed methodology can be extended to many securitization processes, and especially those related to infrastructure funding. We define the objective functions to be optimized to obtain the optimum volume of cash flows to securitize for each investment period. After defining the goals consistent with the demands of the highway investor (maximizing results and minimizing the investment recovery time), we can conceptualize the problem of determining the optimal level of funding through securitization. It is a bi-objective programme, in which the company aims to maximize the surplus generated by the project and simultaneously to maximize liquidity. We define, develop and justify the constraints related to the problem and once the bi-objective optimization problem has been set, we approach the resolution of the optimization problem. We opt for multiobjective fuzzy programming to resolve this programme.

Susana Sardá, M. Carmen Molina

SC: A Fuzzy Approximation for Nonlinear Regression Optimization

Nonlinear regression is a statistical technique widely used in research which creates models that conceptualize the relation among many variables that are related in complex forms. These models are widely used in different areas such as economics, biology, finance, engineering, etc. These models are subsequently used for different processes, such as prediction, control or optimization. Many standard regression methods have proved to produce misleading results in certain data sets; this is especially true in ordinary least squares. In this paper a novel system of convergence (SC) is presented as well as its fundamentals and computing experience for some benchmark nonlinear regression optimization problems. An implementation using a novel PSO algorithm with three phases (PSO-3P): stabilization, generation with broad-ranging exploration, and generation with in-depth exploration, is presented and tested on 27 databases of the NIST collection with different degrees of difficulty. Numerical results show that the PSO algorithm provides better results when the SC criterion is used, compared to evaluate the usual objective function.

Sergio-Gerardo de-los-Cobos-Silva, Miguel-Ángel Gutiérrez-Andrade, Eric-Alfredo Rincón-García, Pedro Lara-Velázquez, Roman-Anselmo Mora-Gutiérrez, Antonin Ponsich

Winding Indexes at Specific Traveling Salesman Problems

The resolutions of the different Shortest and Longest Euclidean Hamiltonian Path Problems on the vertices of N-Gons, by means of a geometric and arithmetic algorithm allow us to define winding indexes for Hamiltonian and Quasi-Hamiltonian cycles. New statements characterize orientation of non necessarily regular cycles on N-Gons and deal with the existence or absence of reflective bistarred Hamiltonian tours on vertices of coupled N-Gons.

Raúl O. Dichiara, Blanca I. Niel


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