José Ignacio Peláez

A new measure of consistency for positive reciprocal matrices

Abstract The analytic hierarchy process (AHP) provides a decision maker with a way of examining the consistency of entries in a pairwise comparison matrix and the hierarchy as a whole through the consistency ratio measure. It has always seemed to us that this commonly used measure could be improved upon. The purpose of this paper is to present an alternative consistency measure and demonstrate how it might be applied in different types of matrices.

LAMA: A linguistic aggregation of majority additive operator

A problem that we had encountered in the aggregation process, is how to aggregate the elements that have cardinality >1. The purpose of this article is to present a new aggregation operator of linguistic labels that uses the cardinality of these elements, the linguistic aggregation of majority additive (LAMA) operator. We also present an extension of the LAMA operator under the two‐tuple fuzzy linguistic representation model.

Majority additive–ordered weighting averaging: A new neat ordered weighting averaging operator based on the majority process

A problem that we had encountered in the aggregation process is how to aggregate the elements that have cardinality greater than one. The most common operators used in the aggregation process produce reasonable results, but, at the same time, when the items to aggregate have cardinality greater than one, they may produce distributed problems. The purpose of this article is to present a new neat ordered weighting averaging (OWA) operator that uses the cardinality of these elements to calculate their weights.

Analysis of OWA operators in decision making for modelling the majority concept

The majority concept plays a main role in decision making processes where one of the main problems is to define a decision strategy which takes into account the individual opinions of the decision makers to produce an overall opinion which synthesizes the opinions of the majority of the decision makers. The reduction of the individual values into a representative value of majority is usually performed trough an aggregation process. The most common operator used in these processes is the OWA operator, in which the majority concept can be modelled using fuzzy logic and linguistic quantifiers. In this work the fusion processes and the semantic used for modelling the majority concept in the OWA operators are analyzed and compared in order to present different approach to obtain a feasible majority aggregation value for the decision making problem.

Estimation of missing judgments in AHP pairwise matrices using a neural network-based model

Selecting relevant features to make a decision and expressing the relationships between these features is not a simple task. The decision maker must precisely define the alternatives and criteria which are more important for the decision making process. The Analytic Hierarchy Process (AHP) uses hierarchical structures to facilitate this process. The comparison is realized using pairwise matrices, which are filled in according to the decision maker judgments. Subsequently, matrix consistency is tested and priorities are obtained by calculating the matrix principal eigenvector. Given an incomplete pairwise matrix, two procedures must be performed: first, it must be completed with suitable values for the missing entries and, second, the matrix must be improved until a satisfactory level of consistency is reached. Several methods are used to fill in missing entries for incomplete pairwise matrices with correct comparison values. Additionally, once pairwise matrices are complete and if comparison judgments between pairs are not consistent, some methods must be used to improve the matrix consistency and, therefore, to obtain coherent results. In this paper a model based on the Multi-Layer Perceptron (MLP) neural network is presented. Given an AHP pairwise matrix, this model is capable of completing missing values and improving the matrix consistency at the same time.

A method for improving the consistency of judgements

The Analytic Hierarchy Process provides the decision maker with a method for improving the consistency of pairwise comparison matrices. Although it is one of the most commonly used method it presents some disadvantages related generally with the consistency problem. The purpose of this paper is to provide an alternative method for improving consistency and show how it can be applied to pairwise comparison matrices. The contribution to this method and also its limitations are shown at the end.

A Majority Model in Group Decision Making Using QMA-OWA Operators

Group decision‐making problems are situations where a number of experts work in a decision process to obtain a final value that is representative of the global opinion. One of the main problems in this context is to design aggregation operators that take into account the individual opinions of the decision makers. One of the most important operators used for synthesizing the individual opinions in a representative value of majority in the OWA operator, where the majority concept used aggregation processes, is modeled using fuzzy logic and linguistic quantifiers. In this work the semantic of majority used in OWA operators is analyzed, and it is shown how its application in group decision‐making problems does not produce representative results of the concept expressed by the quantifier. To solve this type of problem, two aggregation operators, QMA–OWA, are proposed that use two quantification strategies and a quantified normalization process to model the semantic of the linguistic quantifiers in the group decision‐making process.

A System of Insolvency Prediction for industrial companies using a financial alternative model with neural networks

Abstract We find in the accounting literature the use of neural networks (NN) for the prediction of insolvency data from the last financial year before the bankruptcy, with a success rate below 85%. The objective of this work is to increase the predictive power of the NN models to discriminate between solvent and insolvent companies incorporating for this purpose a new set of financial ratios. A sample of about 500 European industrial companies that have filed for bankruptcy between 2007 and 2009 was confronted with about 500 solvent companies, matched by year, country and asset size. To do this, we have used five sets of different input data for training the NN. For each input set, 20 NN have been trained for each number of neurons in hidden layer, from 1 to 50 neurons, giving a total of 5 000 trained NN. The proposed model predicts correctly the 92.5 and 92.1 percent of the estimates of the training set and testing set (accuracy), respectively, using financial information for two years prior to bankruptcy.

Reconstruction methods for AHP pairwise matrices

Habitually, decision-makers are exposed to situations that require a lot of knowledge and expertise. Therefore, they need tools to help them choose the best possible alternatives. Analytic hierarchical process (AHP) is one of those tools and it is widely used in many fields. While the use of AHP is very simple, there is a situation that becomes complex: the consistency of the pairwise matrices. In order to obtain the consistent pairwise matrix from the inconsistent one, reconstruction methods can be used, but they cannot guarantee getting the right matrix according to the judgments of the decision maker. This situation does not allow proper evaluation of methods reliability, i.e. it is not possible to obtain a reliable ranking of alternatives based on an inconsistent matrix. In this work, a new way to evaluate the reliability of matrix reconstruction methods is proposed. This technique uses a novel measure for alternatives ranking comparison (based on element positions and distances), which is introduced in order to compare several matrix reconstruction methods. Finally, in order to demonstrate the extensibility of this new reliability measure, two reconstruction methods based on bio-inspired models (a Genetic Algorithm and the Firefly Algorithm) are presented and evaluated by using the aforementioned reliability measure.

Ischemia classification via ECG using MLP neural networks

AbstractThis paper proposes a two stage system based in neural network models to classify ischemia via ECG analysis. Two systems based on artificial neural network (ANN) models have been developed in order to discriminate inferolateral and anteroposterior ischemia from normal electrocardiogram (ECG) and other heart diseases. This method includes pre-processing and classification modules. ECG segmentation and wavelet transform were used as pre-processing stage to improve classical multilayer perceptron (MLP) network. A new set of about 800 ECG were collected from different clinics in order to create a new ECG Database to train ANN models. The best specificity of all models in the test phases was found as 88.49%, and the best sensitivity was obtained as 80.75%.