Comparative Analysis of AI Techniques to Correct the Inconsistency in the Analytic Hierarchy Process Matrix

The Analytic Hierarchy Process (AHP) is one of the most used techniques for decision making. The complex properties of its structure allow considering the subjectivity in the judgment of the experts but also arising a considerable degree of inconsistency when the pairwise judgments of the alternatives are computed. This research paper makes a comparison between two artificial intelligence methods for diminishing the inconsistency in the AHP pairwise comparison matrixes, the Backpropagation Neural Network (BPN) and Support Vector Machines (SVM).Eje: XV Workshop de Agentes y Sistemas InteligentesRed de Universidades con Carreras de Informática (RedUNCI

Comparative Analysis of AI Techniques to Correct the Inconsistency in the Analytic Hierarchy Process Matrix

The Analytic Hierarchy Process (AHP) is one of the most used techniques for decision making. The complex properties of its structure allow considering the subjectivity in the judgment of the experts but also arising a considerable degree of inconsistency when the pairwise judgments of the alternatives are computed. This research paper makes a comparison between two artificial intelligence methods for diminishing the inconsistency in the AHP pairwise comparison matrixes, the Backpropagation Neural Network (BPN) and Support Vector Machines (SVM).Eje: XV Workshop de Agentes y Sistemas InteligentesRed de Universidades con Carreras de Informática (RedUNCI

Genetic Algorithms Applied to Inconsistent Matrices Correction in the Analytic Hierarchy Process (AHP)

Making Decision in non-structured problems is not a simple task. For this reason, decision makers use Decision Support Systems (DSS). These kinds of systems implement techniques and algorithms in order to improve the decision process. Analytic Hierarchy Process (AHP) is one of these techniques which yields a ranking scale of alternatives based on criteria and alternative matrices. These matrices make a pairwise comparison between a set of elements compared and must be complete and consistent in order to be processed with AHP. Incompleteness and inconsistency emerge as a consequence of the large data required to be compared by an expert, which exceeds his or her human abilities. Genetic Algorithms (GA) is a powerful used technique which provides simplicity, broad applicability and flexibility for search problems. In this work a GA model is exposed, being its aims to help the expert to fill the matrix and provide reasonable judgments by suggesting possible values.Sociedad Argentina de Informática e Investigación Operativ

Genetic Algorithms Applied to Inconsistent Matrices Correction in the Analytic Hierarchy Process (AHP)

Making Decision in non-structured problems is not a simple task. For this reason, decision makers use Decision Support Systems (DSS). These kinds of systems implement techniques and algorithms in order to improve the decision process. Analytic Hierarchy Process (AHP) is one of these techniques which yields a ranking scale of alternatives based on criteria and alternative matrices. These matrices make a pairwise comparison between a set of elements compared and must be complete and consistent in order to be processed with AHP. Incompleteness and inconsistency emerge as a consequence of the large data required to be compared by an expert, which exceeds his or her human abilities. Genetic Algorithms (GA) is a powerful used technique which provides simplicity, broad applicability and flexibility for search problems. In this work a GA model is exposed, being its aims to help the expert to fill the matrix and provide reasonable judgments by suggesting possible values.Sociedad Argentina de Informática e Investigación Operativ

Pairwise comparison matrix in multiple criteria decision making

The measurement scales, consistency index, inconsistency issues, missing judgment estimation and priority derivation methods have been extensively studied in the pairwise comparison matrix (PCM). Various approaches have been proposed to handle these problems, and made great contributions to the decision making. This paper reviews the literature of the main developments of the PCM. There are plenty of literature related to these issues, thus we mainly focus on the literature published in 37 peer reviewed international journals from 2010 to 2015 (searched via ISI Web of science). We attempt to analyze and classify these literatures so as to find the current hot research topics and research techniques in the PCM, and point out the future directions on the PCM. It is hoped that this paper will provide a comprehensive literature review on PCM, and act as informative summary of the main developments of the PCM for the researchers for their future research. First published online: 02 Sep 201

Comparative Analysis of AI Techniques to Correct the Inconsistency in the Analytic Hierarchy Process Matrix

The Analytic Hierarchy Process (AHP) is one of the most used techniques for decision making. The complex properties of its structure allow considering the subjectivity in the judgment of the experts but also arising a considerable degree of inconsistency when the pairwise judgments of the alternatives are computed. This research paper makes a comparison between two artificial intelligence methods for diminishing the inconsistency in the AHP pairwise comparison matrixes, the Backpropagation Neural Network (BPN) and Support Vector Machines (SVM).Eje: XV Workshop de Agentes y Sistemas InteligentesRed de Universidades con Carreras de Informática (RedUNCI

A Pairwise Comparison Matrix Framework for Large-Scale Decision Making

abstract: A Pairwise Comparison Matrix (PCM) is used to compute for relative priorities of criteria or alternatives and are integral components of widely applied decision making tools: the Analytic Hierarchy Process (AHP) and its generalized form, the Analytic Network Process (ANP). However, a PCM suffers from several issues limiting its application to large-scale decision problems, specifically: (1) to the curse of dimensionality, that is, a large number of pairwise comparisons need to be elicited from a decision maker (DM), (2) inconsistent and (3) imprecise preferences maybe obtained due to the limited cognitive power of DMs. This dissertation proposes a PCM Framework for Large-Scale Decisions to address these limitations in three phases as follows. The first phase proposes a binary integer program (BIP) to intelligently decompose a PCM into several mutually exclusive subsets using interdependence scores. As a result, the number of pairwise comparisons is reduced and the consistency of the PCM is improved. Since the subsets are disjoint, the most independent pivot element is identified to connect all subsets. This is done to derive the global weights of the elements from the original PCM. The proposed BIP is applied to both AHP and ANP methodologies. However, it is noted that the optimal number of subsets is provided subjectively by the DM and hence is subject to biases and judgement errors. The second phase proposes a trade-off PCM decomposition methodology to decompose a PCM into a number of optimally identified subsets. A BIP is proposed to balance the: (1) time savings by reducing pairwise comparisons, the level of PCM inconsistency, and (2) the accuracy of the weights. The proposed methodology is applied to the AHP to demonstrate its advantages and is compared to established methodologies. In the third phase, a beta distribution is proposed to generalize a wide variety of imprecise pairwise comparison distributions via a method of moments methodology. A Non-Linear Programming model is then developed that calculates PCM element weights which maximizes the preferences of the DM as well as minimizes the inconsistency simultaneously. Comparison experiments are conducted using datasets collected from literature to validate the proposed methodology.Dissertation/ThesisPh.D. Industrial Engineering 201