Na otimização de produtos e processos industriais todas as medidas de qualidade devem ser consideradas simultaneamente. No setor alimentício para a avaliação de produtos são considerados, além de medidas usuais de qualidade, dados de painéis sensoriais. Esta dissertação apresenta o estudo de um método desenvolvido especificamente em um contexto de otimização de produtos com variáveis sensoriais: o método de Comparação Indireta aos Pares (CIP). Para coleta de dados, o CIP baseia-se na comparação pareada de amostras e para análise de dados utiliza elementos do AHP (Processo Analítico Hierárquico, na sigla em inglês). Neste método, são propostas extensões com vistas a torná-lo mais confiável e aumentar sua aplicabilidade. Para atingir esse propósito são feitas adaptações em diferentes procedimentos de coleta de dados sensoriais, assim como a validação de valores de referência utilizados na análise de dados e a construção de tabelas com valores de referência para casos onde o método CIP é aplicado. As melhorias propostas no método de CIP são ilustradas através de uma aplicação prática em uma empresa alimentícia, onde, deseja-se otimizar o processo de desenvolvimento de uma barra de chocolate. O método CIP é utilizado para determinar o percentual de ingredientes utilizados na formulação da barra de chocolate. / In the optimization of products and industrial processes several quality measures must be considered simultaneously. When analyzing food products, in addition to the usual measures of quality, the performance of products as measured by a sensory panel should be also taken into account. In this thesis we analyze a method developed specifically for the optimization of products with sensory variables: the Indirect Pairwise Comparison (IPC) method. Regarding the sensory data collection the IPC is based in the pairwise comparison of samples; as for data analysis, the method uses elements of the AHP (Analytical Hierarchical Process). Extensions are proposed in the IPC in order to improve its reliability and applicability. For that matter we propose adaptations in different procedures for sensory data collection. We also validate some reference values used in the IPC’s data analysis framework and develop tables with reference values for special cases where the IPC method is applied. The proposed improvements are illustrated through a practical application in a food industry. In the case study it is desired to optimize the development of a chocolate bar. The IPC is used to determine the percentage of ingredients used in the product recipe.

For many decisions validation of their outcomes is invariably problematic to objectively assess. Therefore to aid analysis and validation of decision outcomes, approaches which provide improved traceability and more semantically meaningful measurements of the decision process are required. Hence, this research investigates traceability, transparency, interactivity and auditability to improve the decision making process. Approaches and evaluation measures are proposed to facilitate a richer decision making experience. Multi-Criteria Decision Analysis (MCDA) seeks to determine the suitability of alternatives of a goal with respect to multiple criteria. A key component of prominent MCDA methods is the concept of pairwise comparison. For a set of elements, pairwise comparison enables an accurate and transparent extraction and codification of a decision maker’s preferences, though facilitating a separation of concerns. From a set of pairwise comparisons, a ranking of the elements under consideration can be calculated. There are scenarios when a set of pairwise comparisons undergo alteration, both for individual and multiple decision makers. A set of measures of compromise are proposed to quantify the alteration that a set of pairwise comparisons undergo in such scenarios. The measures seek to provide a decision maker with meaningful knowledge regarding how their views have altered. A set of pairwise comparisons may be inconsistent. When inconsistency is present it adversely affects a ranking of the elements derived from the comparisons. Moreover inconsistency within pairwise comparisons used for consideration of more than a handful of elements is almost inevitable. Existing approaches that seek to alter a set of comparisons to reduce inconsistency lack traceability, flexibility, and specific consideration of alteration to the judgments in a way that is meaningful to a decision maker. An approach to inconsistency reduction is proposed that seeks to address these issues. For many decisions the opinions of multiple decision makers are utilized, either to avail of their combined expertise or to incorporate conflicting views. Aggregation of multiple decision makers’ pairwise companions seek to combine the views of the group into a single representation of views. An approach to group aggregation of pairwise comparisons is proposed that models compromise between the decision makers, facilitates decision maker constraints, considers inconsistency reduction during aggregation and dynamically incorporates decision maker weights of importance. With internet access becoming widespread being able to garner the views of a large group of decision makers’ views has become feasible. An approach to the aggregation of a large group of decision makers’ preferences is proposed. The approach facilitates understanding regarding both the agreement and conflict within the group during calculation of an overall group consensus. A Multi-Objective Optimisation Decision Software (MOODS) prototype tool has been developed that implements both the new measures of compromise and the proposed approaches to inconsistency reduction and group aggregation.

Na otimização de produtos e processos industriais todas as medidas de qualidade devem ser consideradas simultaneamente. No setor alimentício para a avaliação de produtos são considerados, além de medidas usuais de qualidade, dados de painéis sensoriais. Esta dissertação apresenta o estudo de um método desenvolvido especificamente em um contexto de otimização de produtos com variáveis sensoriais: o método de Comparação Indireta aos Pares (CIP). Para coleta de dados, o CIP baseia-se na comparação pareada de amostras e para análise de dados utiliza elementos do AHP (Processo Analítico Hierárquico, na sigla em inglês). Neste método, são propostas extensões com vistas a torná-lo mais confiável e aumentar sua aplicabilidade. Para atingir esse propósito são feitas adaptações em diferentes procedimentos de coleta de dados sensoriais, assim como a validação de valores de referência utilizados na análise de dados e a construção de tabelas com valores de referência para casos onde o método CIP é aplicado. As melhorias propostas no método de CIP são ilustradas através de uma aplicação prática em uma empresa alimentícia, onde, deseja-se otimizar o processo de desenvolvimento de uma barra de chocolate. O método CIP é utilizado para determinar o percentual de ingredientes utilizados na formulação da barra de chocolate. / In the optimization of products and industrial processes several quality measures must be considered simultaneously. When analyzing food products, in addition to the usual measures of quality, the performance of products as measured by a sensory panel should be also taken into account. In this thesis we analyze a method developed specifically for the optimization of products with sensory variables: the Indirect Pairwise Comparison (IPC) method. Regarding the sensory data collection the IPC is based in the pairwise comparison of samples; as for data analysis, the method uses elements of the AHP (Analytical Hierarchical Process). Extensions are proposed in the IPC in order to improve its reliability and applicability. For that matter we propose adaptations in different procedures for sensory data collection. We also validate some reference values used in the IPC’s data analysis framework and develop tables with reference values for special cases where the IPC method is applied. The proposed improvements are illustrated through a practical application in a food industry. In the case study it is desired to optimize the development of a chocolate bar. The IPC is used to determine the percentage of ingredients used in the product recipe.

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/Thesis / Ph.D. Industrial Engineering 2013

Na otimização de produtos e processos industriais todas as medidas de qualidade devem ser consideradas simultaneamente. No setor alimentício para a avaliação de produtos são considerados, além de medidas usuais de qualidade, dados de painéis sensoriais. Esta dissertação apresenta o estudo de um método desenvolvido especificamente em um contexto de otimização de produtos com variáveis sensoriais: o método de Comparação Indireta aos Pares (CIP). Para coleta de dados, o CIP baseia-se na comparação pareada de amostras e para análise de dados utiliza elementos do AHP (Processo Analítico Hierárquico, na sigla em inglês). Neste método, são propostas extensões com vistas a torná-lo mais confiável e aumentar sua aplicabilidade. Para atingir esse propósito são feitas adaptações em diferentes procedimentos de coleta de dados sensoriais, assim como a validação de valores de referência utilizados na análise de dados e a construção de tabelas com valores de referência para casos onde o método CIP é aplicado. As melhorias propostas no método de CIP são ilustradas através de uma aplicação prática em uma empresa alimentícia, onde, deseja-se otimizar o processo de desenvolvimento de uma barra de chocolate. O método CIP é utilizado para determinar o percentual de ingredientes utilizados na formulação da barra de chocolate. / In the optimization of products and industrial processes several quality measures must be considered simultaneously. When analyzing food products, in addition to the usual measures of quality, the performance of products as measured by a sensory panel should be also taken into account. In this thesis we analyze a method developed specifically for the optimization of products with sensory variables: the Indirect Pairwise Comparison (IPC) method. Regarding the sensory data collection the IPC is based in the pairwise comparison of samples; as for data analysis, the method uses elements of the AHP (Analytical Hierarchical Process). Extensions are proposed in the IPC in order to improve its reliability and applicability. For that matter we propose adaptations in different procedures for sensory data collection. We also validate some reference values used in the IPC’s data analysis framework and develop tables with reference values for special cases where the IPC method is applied. The proposed improvements are illustrated through a practical application in a food industry. In the case study it is desired to optimize the development of a chocolate bar. The IPC is used to determine the percentage of ingredients used in the product recipe.

Decision making is an essential activity for humans and often becomes complex in the presence of uncertainty or insufficient knowledge. This research aims at estimating preferences using pairwise comparisons. A decision maker uses pairwise comparison when he/she is unable to directly assign criteria weights or scores to the available options. The judgments provided in pairwise comparisons may not always be consistent for several reasons. Experimentation has been used to obtain statistical evidence related to the widely-used consistency measures. The results highlight the need to propose new consistency measures. Two new consistency measures - termed congruence and dissonance - are proposed to aid the decision maker in the process of elicitation. Inconsistencies in pairwise comparisons are of two types i.e. cardinal and ordinal. It is shown that both cardinal and ordinal consistency can be improved with the help of these two measures. A heuristic method is then devised to detect and remove intransitive judgments. The results suggest that the devised method is feasible for improving ordinal consistency and is computationally more efficient than the optimization-based methods. There exist situations when revision of judgments is not allowed and prioritization is required without attempting to remove inconsistency. A new prioritization method has been proposed using the graph-theoretic approach. Although the performance of the proposed prioritization method was found to be comparable to other approaches, it has practical limitation in terms of computation time. As a consequence, the problem of prioritization is explored as an optimization problem. A new method based on multi-objective optimization is formulated that offers multiple non-dominated solutions and outperforms all other relevant methods for inconsistent set of judgments. A priority estimation tool (PriEsT) has been developed that implements the proposed consistency measures and prioritization methods. In order to show the benefits of PriEsT, a case study involving Telecom infrastructure selection is presented.

The Finkelstein and Schoenfeld (FS) test is a popular generalized pairwise comparison approach to analyze prioritized composite endpoints (e.g., components are assessed in order of clinical importance). Power and sample size estimation for the FS test, however, are generally done via simulation studies. This simulation approach can be extremely computationally burdensome, compounded by an increasing number of composite endpoints and with increasing sample size. We propose an analytic solution to calculate power and sample size for commonly encountered two-component hierarchical composite endpoints. The power formulas are derived assuming underlying distributions in each of the component outcomes on the population level, which provide a computationally efficient and practical alternative to the standard simulation approach. The proposed analytic approach is extended to derive conditional power formulas, which are used in combination with the promising zone methodology to perform sample size re-estimation in the setting of adaptive clinical trials. Prioritized composite endpoints with more than two components are also investigated. Extensive Monte Carlo simulation studies were conducted to demonstrate that the performance of the proposed analytic approach is consistent with that of the standard simulation approach. We also demonstrate through simulations that the proposed methodology possesses generally desirable objective properties including robustness to mis-specified underlying distributional assumptions. We illustrate our proposed methods through application of the proposed formulas by calculating power and sample size for the Transthyretin Amyloidosis Cardiomyopathy Clinical Trial (ATTR-ACT) and the EMPULSE trial for empagliozin treatment of acute heart failure.

Pairwise comparison matrices (PCMs) play a key role in multi-criteria decision making, especially in the analytic hierarchy process. It could be necessary for an expert to compare alternatives based on various criteria. However, for a variety of reasons, such as lack of time or insufficient knowledge, it may happen that the expert cannot provide judgments on all pairs of alternatives. In this case, an incomplete pairwise comparison matrix is formed. In the first research part, an optimization algorithm is proposed for the optimal completion of an incomplete PCM. It is intended to numerically minimize a constrained eigenvalue problem, in which the objective function is difficult to write explicitly in terms of variables. Numerical simulations are carried out to examine the performance of the algorithm. The simulation results show that the proposed algorithm is capable of solving the minimization of the constrained eigenvalue problem. In the second part, a comparative analysis of eleven completion methods is studied. The similarity of the eleven completion methods is analyzed on the basis of numerical simulations and hierarchical clustering. Numerical simulations are performed for PCMs of different orders considering various numbers of missing comparisons. The results suggest the existence of a cluster of five extremely similar methods, and a method significantly dissimilar from all the others. In the third part, the filling in patterns (arrangements of known comparisons) of incomplete PCMs based on their graph representation are investigated under given conditions: regularity, diameter and number of vertices, but without prior information. Regular and quasi-regular graphs with minimal diameter are proposed. Finally, the simulation results indicate that the proposed graphs indeed provide better weight vectors than alternative graphs with the same number of comparisons. This research problem’s contributions include a list of (quasi-)regular graphs with diameters of 2 and 3, and vertices from 5 up to 24.

<p>Most existing classification algorithms either consider all features as equally important (equal weights), or do not analyze consistency of weights assigned to features. When features are not equally important, assigning consistent weights is a not obvious task. In general we have two cases. The first case assumes that a given sample of data does not contain any clue about the importance of features, so the weights are provided by a pool of experts and they are usually inconsistent. The second case assumes that the given sample contains some information about features importance, hence we can derive the weights directly from the sample. In this thesis we deal with both cases. Pairwise Comparisons and Weighted Support Vector Machines are used for the first case. For the second case a new approach based on the observation that the feature importance could be determined by the discrimination power of features has been proposed. For the first case, we start with pairwise comparisons to rank the importance of features, then we use distance-based inconsistency reduction to refine the weights assessment and make comparisons more precise. As the next step we calculate the weights through the fully-consistent or almost consistent pairwise comparison tables. For the second case, a novel concept of feature domain overlappings has been introduced. It can measure the feature discrimination power. This model is based on the assumption that less overlapping means more discrimination ability, and produces weights characterizing the importance of particular features. For both cases Weighted Support Vector Machines are used to classify the data. Both methods have been tested using two benchmark data sets, Iris and Vertebal.</p> <p>The results were especially superior to those obtained without weights.</p> / Master of Computer Science (MCS)

[pt] Muitos problemas de transportes, assim como de outras áreas do conhecimento, envolvem tomada de decisão. Em decisões complexas, a escolha da melhor alternativa ou plano de ação pode envolver mais de um critério e é necessário estudar como cada ação afeta cada critério. O método AHP, Analytic Hierarchy Process, proposto por Thomas L. Saaty, é um método de decisão multicriterial que funciona para os mais diversos tipos de decisões, solucionando problemas com fatores quantitativos e qualitativos. Ele reúne a opinião dos tomadores de decisão em matrizes de comparação. Este trabalho faz uma revisão geral de conceitos básicos do método, mostrando diferentes maneiras de cálculo da solução. A primeira explorada é o cálculo exato através dos autovalores e autovetores das matrizes. Para esse cálculo, foi utilizado o software francês Scilab, semelhante ao mais conhecido Matlab, mas distibuído gratuitamente na internet. É discutida a questão da consistência dos julgamentos, com maneiras de medi-la e melhorá-la. Finalmente, é feita uma proposta de solução aproximada, que questiona a idéia original de que um certo nível de inconsistência é desejável. É uma solução simplificada que, supondo consistência absoluta, facilita não só os cálculos como o trabalho inicial dos tomadores de decisão. Em vez de comparar todas as alternativas com as outras, duas a duas, passa a ser necessário comparar apenas uma alternativa com as outras. A nova solução aproximada é comparada com a solução exata em três casos retirados da literatura. / [en] Several transportation problems, as well as problems in other knowledge areas, request decision making. In complex decisions, the choice of best alternative or course of action can contain more than one criterion and it is necessary to study how each alternative affects each criterion. The AHP, Analytic Hierarchy Process, proposed by Thomas L. Saaty, is a multicriteria decision method that works well for very diverse decision types, solving problems with tangible and intangible factors. It gathers the opinion of decision makers in comparison matrices. This study makes a general review of basic concepts of the method, showing different manners of calculating the solution. The first one to be displayed is the exact solution using the eigenvalues and eigenvectors of the matrices. For this solution the French software Scilab was used, which is similar to the well-known Matlab, but free and distributed on the web. The issue of judgment consistency is discussed, including ways of measuring and improving it. Finally, a proposal of approximated solution is made, questioning the original idea which says that a certain level of inconsistency is desirable. It is a simplification that, considering absolute consistency, facilitates not only the calculations but also the early work of decision makers when judging the alternatives. Instead of making pair wise comparisons of all alternatives with each other, it becomes necessary to compare only one alternative with the others. The new approximated solution is compared to the real solution in three cases taken from the literature.