Showing papers on "Pairwise comparison published in 2002"

A fuzzy ahp approach to the determination of importance weights of customer requirements in quality function deployment

Abstract: Quality function deployment (QFD) is an important tool in product planning that could contribute to increase in customer satisfaction and shorten product design and development time During the QFD process, determination of the importance weights of customer requirements is a crucial and essential step The analytic hierarchy process (AHP) has been used in weighting the importance However, due to the vagueness and uncertainty existing in the importance attributed to judgement of customer requirements, the crisp pairwise comparison in the conventional AHP seems to be insufficient and imprecise to capture the degree of importance of customer requirements In this paper, fuzzy number is introduced in the pairwise comparison of AHP An AHP based on fuzzy scales is proposed to determine the importance weights of customer requirements The new approach can improve the imprecise ranking of customer requirements which is based on the conventional AHP Finally, an example of bicycle splashguard design is used to illustrate the proposed approach

Fuzzy analytical approach to partnership selection in formation of virtual enterprises

Abstract: The main objective of this paper is to present a new fuzzy approach to partnership selection in the formation of virtual enterprises. The phases of the virtual enterprise life cycle are briefly described and it is shown that the partnership selection is a key factor in the formation of such complex organisations. It is justified that the partnership selection process should be formulated as a multiple criteria decision-making problem under uncertainty. A new fuzzy programming method is proposed for assessment of uncertain weights of partnership selection criteria and uncertain scores of alternative partners, in the basic framework of the Analytic Hierarchy Process. The proposed fuzzy prioritisation method uses interval pairwise comparison judgements rather than exact numerical values of the comparison ratios and transforms the initial prioritisation problem into a linear program. The method can derive priorities from inconsistent interval comparison matrices, thus eliminating the drawbacks of the existing interval prioritisation methods. Moreover, the method generalises the known prioritisation methods, since it can be used for deriving priorities from exact, interval or mixed comparison matrices, regardless of their consistency. A numerical example, illustrating the application of this method to partnership selection process is given.

A Microeconometric Test of Alternative Stochastic Theories of Risky Choice

Abstract: The random preference, Fechner (or ‘white noise’), and constant error (or ‘tremble’) models of stochastic choice under risk are compared. Various combinations of these approaches are used with expected utility and rank-dependent theory. The resulting models are estimated in a random effects framework using experimental data from two samples of 46 subjects who each faced 90 pairwise choice problems. The best fitting model uses the random preference approach with a tremble mechanism, in conjunction with rank-dependent theory. As subjects gain experience, trembles become less frequent and there is less deviation from behaviour consistent with expected utility theory.

A Theory of Diversity

Abstract: How can diversity be measured? What does it mean to value biodiversity? Can we assist Noah in constructing his preferences? To address these questions, we propose a multi-attribute approach under which the diversity of a set of species is the sum of the values of all attributes possessed by some species in the set. We develop the basic intuitions and requirements for a theory of diversity and show that the multi-attribute approach satisfies them in a flexible yet tractable manner. A natural starting point is to think of the diversity of a set as an aggregate of the pairwise dissimilarities between its elements. The multi-attribute framework allows one to make this program formally precise. It is shown that the program can be realized if and only if the family of relevant attributes is well-ordered (“acyclic”). Moreover, there is a unique functional form aggregating dissimilarity into diversity, the length of a minimum spanning tree. Examples are taxonomic hierarchies and lines representing uni-dimensional qualities. In multi-dimensional settings, pairwise dissimilarity information among elements is insufficient to determine their diversity. By consequence, the qualitative and quantitative behavior of diversity differs fundamentally.

Permutation tests for equality of distributions in high‐dimensional settings

Abstract: Motivated by applications in high-dimensional settings, we suggest a test of the hypothesis H-0 that two sampled distributions are identical. It is assumed that two independent datasets are drawn from the respective populations, which may be very general. In particular, the distributions may be multivariate or infinite-dimensional, in the latter case representing, for example, the distributions of random functions from one Euclidean space to another. Our test uses a measure of distance between data. This measure should be symmetric but need not satisfy the triangle inequality, so it is not essential that it be a metric. The test is based on ranking the pooled dataset, with respect to the distance and relative to any fixed data value, and repeating this operation for each fixed datum. A permutation argument enables a critical point to be chosen such that the test has concisely known significance level, conditional on the set of all pairwise distances.

Rank Ordering Engineering Designs: Pairwise Comparison Charts and Borda Counts

Abstract: Designers routinely rank alternatives in a variety of settings using a staple of comparison, the pairwise comparison. In recent years questions have been raised about the use of such comparisons as a means of calculating and aggregating meaningful preference or choice data. Results on voting have been used to argue that the positional procedure known as the Borda count is the best pairwise voting procedure, or at least the only one that is not subject to a number of demonstrable problems. We show here that pairwise comparison charts (PCC) provide results that are identical to those obtained by the Borda count, and that the PCC is thus not subject to the arguments used against non-Borda count methods. Arrow's impossibility theorem has also been invoked to cast doubt upon any pairwise procedure, including the Borda count. We discuss the relevance of the Arrow property that is lost in the Borda count, the independence of irrelevant alternatives (IIA). While the theoretical consequences of IIA are devastating, it is not clear that the same is true of its practical consequences. Examples are presented to illustrate some primary objections to pairwise methods.

An overview on predicting the subcellular location of a protein.

Abstract: The present paper overviews the issue on predicting the subcellular location of a protein. Five measures of extracting information from the global sequence based on the Bayes discriminant algorithm are reviewed. 1) The auto-correlation functions of amino acid indices along the sequence; 2) The quasi-sequence-order approach; 3) the pseudo-amino acid composition; 4) the unified attribute vector in Hilbert space, 5) Zp parameters extracted from the Zp curve. The actual performance of the predictive accuracy is closely related to the degree of similarity between the training and testing sets or to the average degree of pairwise similarity in dataset in a cross-validated study. Many scholars considered that the current higher predictive accuracy still cannot ensure that some available algorithms are effective in practice prediction for the higher pairwise sequence identity of the datasets, but some of them declared that construction of the dataset used for developing software should base on the reality determined by the Mother Nature that some subcellular locations really contain only a minor number of proteins of which some even have a high percentage of sequence similarity. Owing to the complexity of the problem itself, some very sophisticated and special programs are needed for both constructing dataset and improving the prediction. Anyhow finding the target information in mature protein sequence and properly cooperating it with sorting signals in prediction may further improve the overall predictive accuracy and make the prediction into practice.

Going Metric: Denoising Pairwise Data

Abstract: Pairwise data in empirical sciences typically violate metricity, either due to noise or due to fallible estimates, and therefore are hard to analyze by conventional machine learning technology. In this paper we therefore study ways to work around this problem. First, we present an alternative embedding to multi-dimensional scaling (MDS) that allows us to apply a variety of classical machine learning and signal processing algorithms. The class of pair-wise grouping algorithms which share the shift-in variance property is statistically invariant under this embedding procedure, leading to identical assignments of objects to clusters. Based on this new vectorial representation, denoising methods are applied in a second step. Both steps provide a theoretically well controlled setup to translate from pairwise data to the respective denoised metric representation. We demonstrate the practical usefulness of our theoretical reasoning by discovering structure in protein sequence data bases, visibly improving performance upon existing automatic methods.

Convergence Properties of Pairwise NQD Random Sequences

Abstract: In this paper, we extend the Kolmogorov-type inequality to the case of pairwise NQD random sequences. Moreover, we study the convergence properties of pairwise NQD random sequences. As a result, we extend Baum and Katz complete convergence, the three series theorem, Marcinkiewicz strong law of large number to the case pairwise NQD of random sequences.

A conceptual framework for evaluation of information technology investments

Abstract: The decision to acquire a new information technology poses a number of serious evaluation and selection problems to technology managers, because the new system must not only meet current information requirements of the organisation, but also the needs for future expansion. Tangible and intangible benefits factors, as well as risks factors, must be identified and evaluated. The paper provides a review of ten major evaluation categories and available models, which fall under each category, showing their advantages and disadvantages in handling the above difficulties. This paper describes strategic implications involved in the selection decision, and the inherent difficulties in: (1) choosing or developing a model, (2) obtaining realistic inputs for the model, and (3) making tradeoffs among the conflicting factors. It proposes a conceptual framework to help the decision maker in choosing the most appropriate methodology in the evaluation process. It also offers a new model, called GAHP, for the evaluation problem combining integer goal linear programming and Analytic Hierarchy Process (AHP) in a single hybrid multiple objective multi-criteria model. A goal programming methodology, with zero-one integer variables and mixed integer constraints, is used to set goal target values against which information technology alternatives are evaluated and selected. AHP is used to structure the evaluation process providing pairwise comparison mechanisms to quantify subjective, nonmonetary, intangible benefits and risks factors, in deriving data for the model. A case illustration is provided showing how GAHP can be formulated and solved.

A method for improving the consistency of judgements

Abstract: 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.

Pairwise classification as an ensemble technique

Abstract: In this paper we investigate the performance of pairwise (or round robin) classification, originally a technique for turning multi-class problems into two-class problems, as a general ensemble technique. In particular, we show that the use of round robin ensembles will also increase the classification performance of decision tree learners, even though they can directly handle multi-class problems. The performance gain is not as large as for bagging and boosting, but on the other hand round robin ensembles have a clearly defined semantics. Furthermore, we show that the advantage of pairwise classification over direct multi-class classification and one-against-all binarization increases with the number of classes, and that round robin ensembles form an interesting alternative for problems with ordered class values.

Pairwise Classification as an Ensemble Technique

Abstract: In this paper we investigate the performance of pairwise (or round robin) classification, originally a technique for turning multi-class problems into two-class problems, as a general ensemble technique. In particular, we show that the use of round robin ensembles will also increase the classification performance of decision tree learners, even though they can directly handle multi-class problems. The performance gain is not as large as for bagging and boosting, but on the other hand round robin ensembles have a clearly defined semantics. Furthermore, we show that the advantage of pairwise classification over direct multi-class classification and one-against-all binarization increases with the number of classes, and that round robin ensembles form an interesting alternative for problems with ordered class values.

Generalization of pair correlation method (PCM) for non‐parametric variable selection

Abstract: The pair correlation method (PCM) has been developed for choosing between two correlated predictor variables (factors) provided that the scatter is caused not only by random effects. The distinction between two variables can be made using an arrangement into a 2 x 2 contingency table. Further on, suitable test statistics can be used to decide the significance of differences between factors. PCM can easily be generalized (GPCM) for variable selection purposes using more than two variables. The comparison of factors can be made pairwise in all possible combinations. If a given statistical test indicates a significant difference between the factors, the following terms are used for the overwhelming and subordinate factors: superior-inferior or winner-loser respectively. Every comparison can mark a factor as superior, inferior or no decision can be made. The following step is ranking of predictor variables. Three ways of ranking have been elaborated: (i) simple ranking, (ii) ranking based on differences and (iii) ranking according to probability-weighted differences. (Difference here means number of wins minus number of losses.) Suitable examples are presented to show the usefulness and applicability of the method in various conditions.

Weak consistency and Quasi-linear means imply the actual ranking

Abstract: It is known that in the Analytic Hierarchy Process (A.H.P.) a scale of relative importance for alternatives is derived from a pairwise comparisons matrix A = (aij). Priority vectors are basically provided by the following methods: the right eigenvector method, the geometric mean method and the arithmetic mean method. Antipriority vectors can also be considered; they are built by both the left eigenvector method and mean procedures applied to the columns of A. When the matrix A is inconsistent, priority and antipriority vectors do not indicate necessarily the same ranking. We deal with the problem of the reliability of quantitative rankings and we use quasi-linear means for providing a more general approach to get priority and antipriority vectors.

Machine decisions based on preferential voting techniques

Abstract: A method and apparatus for computing an overall or aggregate decision based on intermediate decisions as to which of a set of alternatives best characterize an object The alternatives are partitioned into at least two series of preferences corresponding to at least two intermediate rankings Various embodiments may base the intermediate rankings on: a machine learning technique; a decision tree; a belief network; a neural network; a static model; a program; or an evolutionary training method Based on the preferences, a weak alternative is selected and removed from the series The selection of the weak alternative may include identifying which alternatives lose pairwise to the other alternatives, are excluded from the first preferences, are included in the last preferences, or have a lowest average preference ranking The selecting and removing continue until the remaining alternatives are the aggregate decision Various embodiments may be applied to classification problems, prediction problems or selection problems

Modeling splicing sites with pairwise correlations.

Abstract: Motivation: A new method for finding subtle patterns in sequences is introduced. It approximates the multiple correlations among residuals with pair-wise correlations, with the learning cost where is the number of training sequences, each of length . The method suits to model splicing sites in human DNA, which are reported to have higher-order dependencies. Results: By computational experiments, the prediction accuracy of our model was shown to surpass that of previously reported Markov models for the prediction of acceptor sites in human. Availability: The C++ source code is available on request from the authors.

Comparison of closed testing procedures for pairwise testing of means.

Abstract: A Monte Carlo simulation was conducted to compare 9 pairwise multiple comparison procedures. Procedures were evaluated on the basis of any-pair power and all-pairs power. No procedure was found to be uniformly most powerful. A modification due to A. J. Hayter (1986) of Fisher's least significant difference was found to provide the best combination of ease of use and moderately high any-pair power in most cases. Pilot or exploratory studies can expect good power results with this relatively simple procedure. The greatest all-pairs power was usually provided by 1 of 2 partition-based versions of E. Peritz's (1970) procedure. Confirmatory studies will require such complex methods but may also need larger sample sizes than have been customary in psychological research.

An Iterative Procedure for Evaluating Digraph Competitions

Abstract: A competition which is based on the results of (partial) pairwise comparisons can be modelled by means of a directed graph. Given initial weights on the nodes in such digraph competitions, we view the measurement of the importance (i.e., the cardinal ranking) of the nodes as an allocation problem where we redistribute the initial weights on the basis of insights from cooperative game theory. After describing the resulting procedure of redistributing the initial weights, an iterative process is described that repeats this procedure: at each step the allocation obtained in the previous step determines the new input weights. Existence and uniqueness of the limit is established for arbitrary digraphs. Applications to the evaluation of, e.g., sport competitions and paired comparison experiments are discussed.

On optimal pairwise linear classifiers for normal distributions: the two-dimensional case

Abstract: Optimal Bayesian linear classifiers have been studied in the literature for many decades. We demonstrate that all the known results consider only the scenario when the quadratic polynomial has coincident roots. Indeed, we present a complete analysis of the case when the optimal classifier between two normally distributed classes is pairwise and linear. We focus on some special cases of the normal distribution with nonequal covariance matrices. We determine the conditions that the mean vectors and covariance matrices have to satisfy in order to obtain the optimal pairwise linear classifier. As opposed to the state of the art, in all the cases discussed here, the linear classifier is given by a pair of straight lines, which is a particular case of the general equation of second degree. We also provide some empirical results, using synthetic data for the Minsky's paradox case, and demonstrated that the linear classifier achieves very good performance. Finally, we have tested our approach on real life data obtained from the UCI machine learning repository. The empirical results that we obtained show the superiority of our scheme over the traditional Fisher's discriminant classifier.

Hierarchical semi-numeric method for pairwise fuzzy group decision making

Abstract: Gradual improvements to a single-level semi-numeric method, i.e., linguistic labels preference representation by fuzzy sets computation for pairwise fuzzy group decision making are summarized. The method is extended to solve multiple criteria hierarchical structure pairwise fuzzy group decision-making problems. The problems are hierarchically structured into focus, criteria, and alternatives. Decision makers express their evaluations of criteria and alternatives based on each criterion by using linguistic labels. The labels are converted into and processed in triangular fuzzy numbers (TFNs). Evaluations of criteria yield relative criteria weights. Evaluations of the alternatives, based on each criterion, yield a degree of preference for each alternative or a degree of satisfaction for each preference value. By using a neat ordered weighted average (OWA) or a fuzzy weighted average operator, solutions obtained based on each criterion are aggregated into final solutions. The hierarchical semi-numeric method is suitable for solving a larger and more complex pairwise fuzzy group decision-making problem. The proposed method has been verified and applied to solve some real cases and is compared to Saaty's (1996) analytic hierarchy process (AHP) method.

Rejoinder to The Variety of an Assortment: An Extension to the Attribute-Based Approach

Abstract: Variety Perceptions Redux We comment on the paper by van Herpen and Pieters (2002, hereafter HP) and relate it to our earlier paper in this journal (Hoch, Bradlow, and Wansink 1999, hereafter HBW). The basic premise of HP is that people can engage in either a product or attribute-based approach when making variety perceptions. When people adopt a product approach they compare the products in an assortment on a pairwise basis and perceived variety is a function of dissimilarity or psychological distance between the pairs. When following an attribute approach, people engage in a bottom-up process where they focus on the entropy of the individual attributes and pairwise covariation between attributes. Young and Wasserman (2001) have shown that both people and pigeons rely on entropy when making variability discrimination judgments. HP suggest that the distinction between product versus attribute approaches to variety perception is similar in spirit to brand versus attribute processing in multiattribute choice (Bettman et al. 1998). Although we appreciate this conceptual distinction, we show that the two approaches are very similar mathematically. After appropriately standardizing our pairwise distance measures to control for differences in assortment size, we find that due to high collinearity, it is not possible to distinguish one approach from the other both in our (HBW) data and the data of HP. Finally, even though entropy and lambda are generally informative summary statistics, a couple of features render them less appropriate in some situations than others.

Diagnostics for Pairwise Extremal Dependence in Spatial Processes

Abstract: A measure of pairwise extremal dependence for spatial processes, that is marginally invariant, is introduced. This measure enables decisions to be made about whether a spatial process is asymptotically dependent, asymptotically independent or independent for any pair of locations, thus it provides fundamental diagnostic information for understanding or modeling the extreme values of a spatial process. We illustrate the properties and use of this measure through theoretical examples and applications in hydrology and oceanography.