Showing papers on "Pairwise comparison published in 1993"
TL;DR: In this paper, the importance of predictors in multiple regression, highlights their weaknesses, and proposes a new method for comparing variables, dominance analysis, which is defined as a qualitative relation defined in a pairwise fashion.
Abstract: Whenever multiple regression is used to test and compare theoretically motivated models, it is of interest to determine the relative importance of the predictors. Specifically, researchers seek to rank order and scale variables in terms of their importance and to express global statistics of the model as a function of these measures. This article reviews the many meanings of importance of predictors in multiple regression, highlights their weaknesses, and proposes a new method for comparing variables: dominance analysis. Dominance is a qualitative relation defined in a pairwise fashion: One variable is said to dominate another if it is more useful than its competitor in all subset regressions. Properties of the newly proposed method are described and illustrated
896 citations
TL;DR: In this article, a generalized model for short-term load forecasting is proposed, which combines features from knowledge-based and statistical techniques, and it is based on a generalization model for the weather-load relationship.
Abstract: A recently developed algorithm for short-term load forecasting is generalized. The algorithm combines features from knowledge-based and statistical techniques. It is based on a generalized model for the weather-load relationship which makes it site-independent. Weather variables are investigated, and their relative effect on the load is reported. The algorithm is also fairly robust and inherently updatable, and it provides a systematic method for operator intervention if necessary. This property makes it especially suitable for application in conjunction with demand side management (DSM) programs. The algorithm uses pairwise comparison to quantify categorical variables, and then utilizes regression to obtain the least-squares estimation of the load. The technique has been tested using data from four different sites in Virginia, Massachusetts, Florida, and Washington. The average absolute weekday forecast errors range from 1.22% to 2.7% over all four seasons in a year. >
284 citations
TL;DR: A new definition of consistency is introduced that allows us to locate the roots of inconsistency and is easy to interpret and forms a better basis than the old eigenvalue consistency for selecting a threshold based on common sense.
259 citations
TL;DR: An attempt to evaluate some of the more known techniques in ratio-scale matrices scaling, which includes random generation of a large number of representative matrices to evaluate the various scaling methods according to the specified criteria.
181 citations
TL;DR: Two new approaches for priority derivation when preferences are expressed as interval judgments are explored, one based on a simulation approach and the other based on mathematical programming.
149 citations
TL;DR: This study develops a methodology for predicting the consistency index and consistency ratio when pairwise comparisons are incomplete and can be incorporated into AHP software so that users will have a predicted consistency ratios when making the decision to stop or proceed with more paired comparisons.
129 citations
TL;DR: In this paper, the use of traffic assignment methods with multiobjective decision making to remedy the shortcomings of conventional traffic assignment method is discussed and the optimal flow patterns are determined using three objectives: total travel time for road users, air pollution for nonusers, and travel distance for government.
Abstract: The use of traffic assignment methods with multiobjective decision making to remedy the shortcomings of conventional traffic assignment methods is discussed. The optimal flow patterns are determined using three objectives: total travel time for road users; air pollution for nonusers; and travel distance for government. By using multiobjective decision making and nonlinear programming techniques, a series of noninferior solutions is generated. By combining an eigenvector weighting method with pairwise comparison, a compromise solution for the flow pattern is obtained. As an application example the Taipei network system is discussed. The results show that if other nontraffic-related factors are taken into account, the multiobjective traffic assignment approach is more reasonable and suitable than conventional approaches. >
81 citations
TL;DR: In this paper, the analytic hierarchy process (AHP) has been modified for the manufacturing environment and incorporated into AutoMan, decision support software for microcomputers, which is used to decide on the best way to automate a machine shop.
Abstract: Decisions on adopting new manufacturing technologies are often biased because they are based only on those impacts that can be expressed in financial terms. Multi-criteria decision tools that include nonfinancial impacts avoid this bias. One such tool, the analytic hierarchy process (AHP), has been modified for the manufacturing environment and incorporated into AutoMan, decision support software for microcomputers. The modified AHP is used here to decide on the best way to automate a machine shop. The four steps are: (1) specify criteria and alternatives; (2) weight criteria using pairwise comparison judgments; (3) rate alternatives with respect to criteria; and (4) compute the overall weighted score for each alternative. This approach preserves existing reliable financial information and integrates it with both nonfinancial quantitative performance data and qualitative informed judgments. Judgments are made explicit and checked for consistency. Over 800 industrial managers have purchased AutoMan to impr...
58 citations
TL;DR: In this article, a Monte Carlo study was conducted to evaluate the effects of modelling assumptions and design parameters on the behaviour of interactive methods for the discrete choice MCDM problem, based on explicit value function models.
Abstract: This paper describes a Monte Carlo study conducted to evaluate the effects of modelling assumptions and design parameters on the behaviour of interactive methods for the discrete choice MCDM problem, based on explicit value function models. The purpose of the study is to identify those assumptions and parameters which lead to the most efficient use of preference judgements made by the decision maker, and to the greatest robustness to judgmental errors. It is concluded that nonlinearities in the value function need to be modelled, achieved here by use of a piecewise linear form. It was also found that search for indifference points, rather than using simple preference judgements alone, is of great advantage, best realized by expressing judgements in terms of pairwise trade-offs. Methods incorporating these features are highly robust to judgmental errors. Interactive methods of this class are compared with a priori fitting of similar value functions, and found to give a very similar quality of solution.
49 citations
TL;DR: In this article, the quality of a consistent decision maker's judgments using the Analytic Hierarchy Process (AHP) is placed in the context of the entropy of the resulting vector of priorities.
Abstract: A decision maker using the Analytic Hierarchy Process (AHP) could be consistent, and still provide no information in the resulting vector of priorities. An extreme example would be a pairwise comparison judgment matrix filled with 1s which is totally consistent under the various definitions of consistency, but has provided no information about the prioritization of alternatives resulting from the decision maker's judgments. In this paper, the quality of a consistent decision maker's judgments using the Analytic Hierarchy Process is placed in the context of the entropy of the resulting vector of priorities. Indeed, it is the purpose of this paper to provide a formal definition of this notion ofentropy of a priority vector, and to provide a framework for a quantitative measurement of the information content of consistent pairwise comparison judgment matrices of a decision maker who is using the Analytic Hierarchy Process. We will prove that the entropy of the vector of priorities for consistent matrices follows a normal distribution and discuss some general considerations of this result.
48 citations
TL;DR: Using neuro-fuzzy approach, two quantification methods of pairwise comparisons are presented in order to derive the associated weights of different objects and are compared with Guttman's method and Saaty's analytic hierarchy process.
TL;DR: In this paper, the authors examine the implications of Jensen's proposal and illustrate the effect of the constant a as a comparison reliability factor on the ordinal ranking of alternatives, and argue that the methodology put forward by Jensen is a useful diagnostic tool for analyzing ordinal structure of pairwise comparisons and for spotting potentially contentious applications.
TL;DR: In this article, a simple and usubtle method is presented for estimating the landscape preferences of a private non-industrial forest landowner, where scenic beauties of forest landscapes were compared pairwise; verbal comparisons were converted into numerical values using the same techniques as applied in the Analytic Hierarchy Process.
Abstract: A simple and usubtle method is presented for estimating the landscape preferences of a private non‐industrial forest landowner. Scenic beauties of forest landscapes were compared pairwise; verbal comparisons were converted into numerical values using the same techniques as applied in the Analytic Hierarchy Process. Using the eigenvalue method and a scaling method, scenic beauty indices for forest stands, expressed on a ratio scale, were computed. Regression models that predict the scenic beauty of forest stands according to the preferences of the person in question were estimated, using mensurational forest stand parameters as predictors. Encouraging results on the applicability of the method were obtained in practical tests: the method proved to be worth developing further.
TL;DR: In this article, the authors investigated the effect of different reference items for the first (n - 1) pairwise comparisons of the Incomplete Analytic Hierarchy Process (AHP).
TL;DR: The Dempster-Shafer theory of evidence is applied to a multiattribute decision-making problem whereby the decision maker must compromise with available alternatives, none of which exactly satisfies his ideal.
Abstract: The Dempster-Shafer theory of evidence is applied to a multiattribute decision-making problem whereby the decision maker (DM) must compromise with available alternatives, none of which exactly satisfies his ideal. The decision mechanism is constrained by the uncertainty inherent in the determination of the relative importance of each attribute element and the classification of existing alternatives. The classification of alternatives is addressed through expert evaluation of the degree to which each element is contained in each available alternative. The relative importance of each attribute element is determined through pairwise comparisons of the elements by the DM and implementation of a ratio-scale quantification method. The belief and plausibility that an alternative will satisfy the DM's ideal are then calculated and combined to rank order the available alternatives. Application to the problem of selecting computer software is given. >
TL;DR: In this paper, the authors test prospect theory in a deterministic multiple criteria decision-making context and conclude that prospect theory is a reasonable model of choice for many individuals in such a context.
Abstract: Prospect theory by Kahneman and Tversky [7] is tested in a deterministic multiple criteria decision-making context. In two experiments conducted in classroom settings subjects made pairwise preference comparisons of condominiums for sale. The results of the experiments indicate that the traditional value model did not explain the subjects' revealed preferences as well as the prospect model. We conclude that prospect theory is a reasonable model of choice for many individuals in such a context.
TL;DR: In this article, it was shown that any such limit, based on a fixed percentage, is inequitable to matrices of different orders to an extent that might call into question the final result.
TL;DR: It is shown that if at least three projections of a volumetric object are known, then a three-dimensional rigid depth interpretation can be inferred from pairwise comparisons between any one of these images and other images in the set.
Abstract: A new technique dramatically simplifies the analysis of matching and depth reconstruction by extracting three-dimensional rigid depth interpretation from pairwise comparisons of weak perspective projections. This method provides a simple linear criterion for testing the correctness of correspondence for a pair of images; the method also provides a description of a one-parameter family of interpretations for each pair of images that satisfies this criterion. We show that if at least three projections of a volumetric object are known, then a three-dimensional (3D) rigid interpretation can be inferred from pairwise comparisons between any one of these images and other images in the set. The 3D interpretation is derived from the intersection of corresponding one-parameter families. The method provides a common computational basis for different processes of depth perception, for example, depth-from-stereo and depth-from-motion. Thus, a single mechanism for these processes in the human visual system would be sufficient. The proposed method does not require information about relative positions of eye(s) or camera(s) for different projections, but this information can be easily incorporated. The method can be applied for pairwise comparison within a single image. If any nontrivial correspondence is found, then several views of the same object are present in the same image. This happens, for example, in views of volumetrically symmetric objects. Symmetry facilitates depth reconstruction; if an object possesses two or more symmetries, its depth can be reconstructed from a single image.
TL;DR: The problem of estimating how similar N objects are when they are compared with each other is investigated, using comparative judgments of all possible pairs of the N objects as data.
Abstract: The problem of estimating how similar N objects are when they are compared with each other is investigated, using comparative judgments of all possible pairs of the N objects as data. The pairwise comparisons focus on the similarity relations instead of the relative importance of each object. A quadratic programming model is also proposed. It processes the similarity-based pairwise comparisons and determines the similarity relations among the N objects. The model has linear constraints; therefore it can be solved easily by transferring it into a system of linear equations. >
TL;DR: In this article, a probabilistic choice model is developed for paired comparisons data about psychophysical stimuli, which is based on Thurstone's Law of Comparative Judgment Case V and assumes that each stimulus is measured on a small number of physical variables.
Abstract: A probabilistic choice model is developed for paired comparisons data about psychophysical stimuli. The model is based on Thurstone's Law of Comparative Judgment Case V and assumes that each stimulus is measured on a small number of physical variables. The utility of a stimulus is related to its values on the physical variables either by means of an additive univariate spline model or by means of multivariate spline model. In the additive univariate spline model, a separate univariate spline transformation is estimated for each physical dimension and the utility of a stimulus is assumed to be an additive combination of these transformed values. In the multivariate spline model, the utility of a stimulus is assumed to be a general multivariate spline function in the physical variables. The use of B splines for estimating the transformation functions is discussed and it is shown how B splines can be generalized to the multivariate case by using as basis functions tensor products of the univariate basis functions. A maximum likelihood estimation procedure for the Thurstone Case V model with spline transformation is described and applied for illustrative purposes to various artificial and real data sets. Finally, the model is extended using a latent class approach to the case where there are unreplicated paired comparisons data from a relatively large number of subjects drawn from a heterogeneous population. An EM algorithm for estimating the parameters in this extended model is outlined and illustrated on some real data.
01 Jan 1993
TL;DR: Any positive reciprocal matrix with a large CR can be so corrected that the modified matrix can both tally with the consistency requirement and reserve the most information that the original matrix contains.
Abstract: This paper presents a theorem, on which an approximation method of modifying comparison matrices is offered. By this method any positive reciprocal matrix with a large CR can be so corrected that the modified matrix can both tally with the consistency requirement and reserve the most information that the original matrix contains. Two criteria of evaluating modificatory effectiveness are also presented.
01 Jan 1993
TL;DR: This correspondence investigates a penalty function approach for solving the concomitant nonlinear programs that may be necessary to solve in order to determine an accurate partial order on the alternatives.
Abstract: In imprecisely specified multiattribute utility theory (ISMAUT), a pairwise comparison of two alternatives produces a bilinear inequality, composed of trade-off weights and value scores. This correspondence investigates a penalty function approach for solving the concomitant nonlinear programs that may be necessary to solve in order to determine an accurate partial order on the alternatives. >
Journal Article•
01 Jul 1993
TL;DR: In this paper, the analytical hierarchy process (AHP) and the French collection of ELECTRE systems, typically based on pairwise comparison methods, are concerned with category judgement of ratio magnitudes, whereas the Simple Multi-Attribute Rating Technique (SMART) essentially uses the orders of magnitude of these ratios.
Abstract: Since decisions are invariably made within a given context, we model relative preferences as ratios of increments or decrements in an interval on the axis of desirability. Next, we sort the ratio magnitudes into a small number of categories, represented by numerical values on a geometric scale. We explain why the Analytic Hierarchy Process (AHP) and the French collection of ELECTRE systems, typically based on pairwise -- comparison methods, are concerned with category judgement of ratio magnitudes, whereas the Simple Multi-Attribute Rating Technique (SMART) essentially uses the orders of magnitude of these ratios. This phenomenon, well-known in psycho-physics, provides a common basis for the analysis of the methods in question and for a cross-validation of their results. Throughout the paper, we illustrate the approach via a well-known case study, the choice of a location for a nuclear power plant.
TL;DR: The purpose of the study is to examine the expected likelihood with which subjects will have transitive responses in agreement with May's model as this degree of precision is varied, and the impact that the imposition of the assumption of single peaked preferences on the ordinal information on attributes has on this expected likelihood.
20 Dec 1993
TL;DR: In this paper, a logarithmic least squares method or a geometric mean method for estimating the relative weight of alternatives when some entries of the pairwise comparisons matrix are missing is described.
Abstract: This paper describes a logarithmic least squares method or a geometric mean method for estimating the relative weight of alternatives when some entries of the pairwise comparisons matrix are missing.
Dissertation•
01 Jan 1993
TL;DR: In this paper, the authors study individual choice behavior from various angles, including voting behavior in mass elections using data from the 1968 and 1980 presidential elections, and explore the methodological treatment of voter heterogeneity.
Abstract: This dissertation consists of three relatively independent chapters that study individual choice behavior from various angles. Chapter 1 is aimed at improving the existing discrete choice models. Of the commonly used models, the probit class is computationally infeasible for problems with more than a few alternatives, and the GEV class, including the widely used logit and nested logit models, suffers from the restriction of homoscedastic disturbances. We relax the homoscedasticity restriction on the GEV class to achieve both functional flexibility and computational feasibility. The heteroscedastic logit/nested logit models are of particular practical interest. Chapter 2 studies voting behavior in mass elections using data from the 1968 and 1980 presidential elections. We discuss theoretical and methodological issues in the specification, comparative study, and empirical testing of the rational voter models, and explore the methodological treatment of voter heterogeneity. While the standard models do not predict voting turnout well, we obtain clear evidence
of strategic voting in the candidate choice decision in three candidate elections. The data suggest voter information as one source of voter heterogeneity which introduces heteroscedasticity. The heteroscedastic logit model developed in Chapter 1 is therefore applied and is shown to outperform the standard logit model and to reveal strong effects of voter information on the turnout decision. Chapter 3 studies choice behavior in congressional career decisions. Previous research largely focuses on the binary choices of retiring vs. seeking reelection or
seeking higher office vs. seeking reelection. Using data from the 80th through the 99th congresses, we rigorously explore the congressmen's choice from all available
career options, and discuss the effects of variables on both pairwise comparisons of the alternatives and on the unconditional probabilities of choosing the congressional
career options. Our findings suggest that formal positions held and previous vote margins do not figure into House members' career decisions, and being a Republican per se does not encourage progressive ambition. We also see
that a number of factors previously identified as predisposing House members to seek higher office also affect retirement decision.
TL;DR: An optimal sequential rule has been derived and its efficiency with the bost fixed sample size rule is considered at the common least favourable configuration.
Abstract: Scores of k players have been observed. Tho problem of selecting the player with highest expected wins is considered. An optimal sequential rule has been derived in this context, Its efficiency with the bost fixed sample size rule is considered at the common least favourable configuration.AMS 1980 Subject Classification: 62F07.
01 Jan 1993
TL;DR: In this article, a penalty function approach for solving the concomitant nonlinear program is proposed, which may be necessary to solve in order to determine an accurate partid order on the alternatives.
Abstract: Abstmct-hh ISMAUT, a pahvk comparison of two alternatives produces a bilinear inequality, composed of trade-off weights and value scores. This correspondence investigates a penalty function approach for solving the concomitant nonlinear program ,that may be necessary to solve in order to determine an accurate partid order on the alternatives.
01 Jan 1993
TL;DR: Two threads: reduction of the number of alternatives and generation of the proposal for the DM’s most preferred alternative are distinguished in the process of decision support.
Abstract: Two threads: reduction of the number of alternatives and generation of the proposal for the DM’s most preferred alternative are distinguished in the process of decision support. Presented approach is based on pairwise comparisons of alternatives.