Showing papers on "Pairwise comparison published in 1987"
TL;DR: In this article, the authors explore various methods for reducing the complexity of the preference eliciting process in a group decision-making session, where the group structures the problem in a hierarchical framework and pairwise comparisons are elicited from the group for each level of the hierarchy.
406 citations
TL;DR: In this paper, a generalization of regret theory is suggested and is compared and contrasted with Fishburn's generalisation of SSB utility theory, and it is shown that under this generalization an individual with non-transitive pairwise preferences with not be caught in a never-ending cycle and is not vulnerable to being “money-pumped” into bankruptcy.
400 citations
TL;DR: A set of questionnaires was prepared to compare four elicitation methods: point estimation, interval estimation, membership function exemplification, and pairwise comparison.
109 citations
TL;DR: The idea of collective rationality is a well established one in social choice theory as mentioned in this paper, and it is a defining property of the social welfare functions of Bergson (1938) and Samuelson (1947), and of Arrow (1951).
Abstract: THE PRINCIPLE of pairwise comparisons is a well established one in social choice theory. The idea of collective rationality-that social decisions be made consistently with the maximization of some ordering of the alternatives-is the most familiar application of this principle, and indeed, is a defining property of the social welfare functions of Bergson (1938) and Samuelson (1947), and of Arrow (1951). As is well known, the idea of collective rationality involves comparing every social state to every other social state in terms of the welfare assigned by those states to a given group of individuals, and declaring a social state to be fair or good if it is good when considering all such pairwise comparisons with other social states. Alternatively, one could imagine a social decision process based on comparing every individual to every other individual in terms of the welfare assigned to those individuals by a given social state, and declaring a social state to be good or fair if it is fair when considering all such pairwise comparisons of individuals. A social decision process in this spirit has been suggested by Harsanyi (1959),
71 citations
TL;DR: It is proved that the obvious necessary conditions on the existence of pairwise balanced designs are also sufficient, with two exceptions, corresponding to the non-existence of Nearly Kirkman Triple Systems of orders 6 and 12.
50 citations
TL;DR: In this article, a heuristic procedure based on pairwise exchange of subfacilities is developed to generate the efficient solution associated with a given set of objective weights, and a paired comparison method based on the strength of preference among alternatives is developed.
Abstract: In this paper, we formulate the quadratic assignment problem through multiple objective programming in which we can have several objectives. In the facility layout problem, the objectives can be materials handling cost, production rate, and flexibility. We define efficiency and describe how efficient alternatives can be generated. A heuristic procedure based on pairwise exchange of subfacilities is developed to generate the efficient solution associated with a given set of objective weights. Our approach could just as easily implement the graph theoretic or other approaches to solve the quadratic assignment problem and generate efficient points associated with given weights. A paired comparison method based on the strength of preference among alternatives is developed. The paired comparison method generates the decision maker's weights of an assumed unknown utility function. The method asks simple questions and uses linear programming to solve the problem. An experiment with the developed computer package...
43 citations
TL;DR: A useful approach to solving the problem of evaluating individual alternatives, derive importance weights of criteria, construct the overall ranking of alternatives and identify the best alternative is proposed by T.L. Saaty.
36 citations
TL;DR: In this paper, a method to reduce the number of pairwise comparisons by using the derivatives of the right Perron vector and the graph-theoretic interpretation of a positive reciprocal matrix is presented.
16 citations
01 Nov 1987
TL;DR: Within the framework of the vector space models, a statistical similarity measure between document and query is proposed, which provides a natural and consistent interpretation of term occurrence frequencies obtained from autoindexing.
Abstract: Within the framework of the vector space models, a statistical similarity measure between document and query is proposed. In this approach the assumption that term (or atomic) vectors are pairwise orthogonal is not required. In addition, it provides a natural and consistent interpretation of term occurrence frequencies obtained from autoindexing.
14 citations
TL;DR: In this paper, the relationship between the reciprocal property and preference relations with and without the axiom of transitivity is explored, and some important distinctions between utility theory and the Analytic Hierarchy Process are made.
10 citations
01 Jul 1987
TL;DR: A new mathematical interpretation of alternative pairwise comparisons for a recently developed model of single-stage multiattribute decisionmaking and trade-off weight determination under uncertainty is presented, guaranteeing that more precise lowest level attribute utility scores will not increase the imprecision of the trade-offs.
Abstract: A new mathematical interpretation of alternative pairwise comparisons for a recently developed model of single-stage multiattribute decisionmaking and trade-off weight determination under uncertainty is presented. This model includes the following key features: 1) parameter values, i.e., lowest level attribute utility scores and trade-off weights, are described by set membership, and 2) use is made of directly expressed preferences among pairs of alternatives. The original mathematical interpretation of pairwise comparisons produced the following undesirable result: more precise lowest level attribute utility scores produce a more imprecise description of the trade-off weights. The new more conservative interpretation guarantees that more precise lowest level attribute utility scores will not increase the imprecision of the trade-off weights.
01 Dec 1987
TL;DR: The analytical hierarchical process (AH P) of Saaty and Vargas is an ideal decision analysis technique for this application as discussed by the authors, where evaluation criteria which may be both quantitative and qualitative are numerically combined, and the results are combined by matrix perturbation resulting in a normalized vector of priorities among the alternatives.
Abstract: Anyone who needs to allocate a limited budget among proposed construction projects or facility improvements faces a difficult task. A logical and consistent prioritization method can ensure that the most needed projects receive funding and get accomplished. The Analytic Hierarchy Process (AH P) of Saaty and Vargas is an ideal decision analysis technique for this application. Evaluation criteria which may be both quantitative and qualitative are numerically combined. Data is collected in the form of pairwise comparisons of criteria (and then of alternatives with respect to the criteria) in a hierarchical structure. Inconsistencies in the form of violations of proportionality among pair preferences and even of transitivity are allowed (and measured for feedback to the decision-maker). A matrix is formed with all pairwise values, and the results are combined by matrix perturbation resulting in a normalized vector of priorities among the alternatives. The AHP methodology is applicable to problem size...
01 Apr 1987
TL;DR: This paper addresses the problem of choosing the best solution(s) from a set of interpretations of the same object (in this case a segment of text) using a notion of preference, based on pairwise comparisons of complete interpretations in order to obtain a partial order among the competing interpretations.
Abstract: In this paper we address the problem of choosing the best solution(s) from a set of interpretations of the same object (in our case a segment of text). A notion of preference is stated, based on pairwise comparisons of complete interpretations in order to obtain a partial order among the competing interpretations. An experimental implementation is described, which uses Prolog-like preference statements.
01 Jan 1987
TL;DR: A general strategy for the interpretation of twodimensional views of manufactured components is presented and an extension and generalisation of previous work on the matching of two-dimensional descriptions and complements work on low and intermediate level processing of the scene data, based on the use of the generalised Hough transformation.
Abstract: A general strategy for the interpretation of twodimensional views of manufactured components is presented. The model database contains as primitives parameterised two-dimensional shape descriptions including feature type, position, and orientation where appropriate. Depending on the extent of each feature either a point or a point vector is associated with each constituent feature within the model or scene. Attributed geometric pairwise relations are formed between relevant primitives. The complexity of the search space of possible scene-model feature correspondences is limited in two ways. Firstly, the pre-formed pairwise relations are used to indicate the probable occurrence of both specific components and specific features. Secondly, a measure of saliency is employed which directs the search to those features which most precisely determine particular components. This is an extension and generalisation of previous work on the matching of two-dimensional descriptions and complements work on low and intermediate level processing of the scene data, based on the use of the generalised Hough transformation.
TL;DR: A pragmatic pairwise group-decision approach is applied to compare two regions in order to select the more suitable one for construction of nuclear power plants in the Kingdom of Saudi Arabia as mentioned in this paper.
01 Jan 1987
TL;DR: A global rank-ordering is constructed which permits us to evaluate a given set of Pareto points and a modification of Saaty’s ratio scale method is given.
Abstract: In this paper we deal with polyoptimal decision making in chemical engineering Using information on the pairwise importance of the performance criteria we construct a global rank-ordering which permits us to evaluate a given set of Pareto points A modification of Saaty’s ratio scale method is given The case of fuzzy weights is discussed The developed method has been applied to the investigation of hydrocracking processes as well as to magnetic tape production
01 Jan 1987
TL;DR: Traditional procedures for clustering objects consist of two steps: measuring pairwise resemblance based on the attributes, and a clustering algorithm, which is generalized to multistate unordered and ordered attributes, to frequencies, and to directly obtained relational data.
Abstract: Traditional procedures for clustering objects consist of two steps: measuring pairwise resemblance based on the attributes, and a clustering algorithm. The use of pairwise resemblances can be avoided; a set of objects can be represented as a set of lists of attribute states; an application of the Laplace indifference principle then allows an estimate to be made of the probability of each list as representative of an association of objects. By use of set-covering procedures, the object associations having maximum joint probability are found. The procedure is generalized to multistate unordered and ordered attributes, to frequencies, and to directly obtained relational data.
TL;DR: This note is a response to an article by Zahedi that demonstrates that there is no need to calculate eigenvalues for consistent pairwise comparison matrices in order to calculate normalized values of attributes.
Abstract: This note is a response to an article by Zahedi [2] published in the Winter 1985 issue of Decision Sciences. It demonstrates that there is no need to calculate eigenvalues for consistent pairwise comparison matrices in order to calculate normalized values of attributes.
TL;DR: In this article, it was shown that this property cannot be derived from the usual set of axioms used to obtain order preserving value functions, but that they in turn are consequences of the reciprocal property.
01 Jan 1987
TL;DR: In this paper, the ambiguous interpretation of criteria weights commonly used in the Analytic Hierarchy Process is identified and a possible improvement is proposed and the results of a number of testing experiments are summarized.
Abstract: The paper refers to the literature which identifies the ambiguous interpretation of criteria weights commonly used in the Analytic Hierarchy Process. A possible improvement is proposed and the results of a number of testing experiments are summarized.
01 Jul 1987
TL;DR: It is found that significant gain in classification performance can be achieved by using the optimum sets of frequencies characterized by the parametric algorithms.
Abstract: : Three feature selection algorithms are investigated and applied to characterize optimum sets of frequencies for radar target identification. One algorithm is of the nonparametric discriminant analysis type, the other two algorithms, the pairwise exponential weight distance algorithm and the pairwise probability of error algorithm, are parametric and incorporate information about the measurement noise into the feature selection process. The utility of these feature selection algorithms for radar target identification is then evaluated through Monte-Carlo simulations. It is found that significant gain in classification performance can be achieved by using the optimum sets of frequencies characterized by the parametric algorithms.