Showing papers on "Pairwise comparison published in 1980"

A Tradeoff Cut Approach to Multiple Objective Optimization

Abstract: There is a need to develop user-oriented math programming techniques for resolution of decision problems in which several objectives must be considered. One approach, the Geoffrion-Dyer-Feinberg algorithm, allows interaction between the computer and the decision maker during the solution process. The interactive approach is adopted in this paper. However, our approach focuses on reducing the feasible region of the decision space rather than improving the stored image of the overall preference function. In so doing, the problem is reduced to a series of pairwise tradeoffs between the objectives. This obviates the need for any type of choice among vectors on the part of the decision maker and stays reasonably within his capability to supply necessary information for problem solution.

Towards a unified definition of maximum likelihood

Abstract: A unified definition of maximum likelihood (ml) is given. It is based on a pairwise comparison of probability measures near the observed data point. This definition does not suffer from the usual inadequacies of earlier definitions, i.e., it does not depend on the choice of a density version in the dominated case. The definition covers the undominated case as well, i.e., it provides a consistent approach to nonparametric ml problems, which heretofore have been solved on a more less ad hoc basis. It is shown that the new ml definition is a true extension of the classical ml approach, as it is practiced in the dominated case. Hence the classical methodology can simply be subsumed. Parametric and nonparametric examples are discussed.

The joint analysis of direct ratings, pairwise preferences, and dissimilarities

Abstract: In studies involving judgments of similarity or dissimilarity, a variety of other variables may also be measured. Examples might be direct ratings of the stimuli, pairwise preference judgments, and physical measurements of the stimuli with respect to various properties. In such cases, there are important advantages to joint analyses of the dissimilarity and collateral variables. A variety of models are described for relating these and algorithms described for fitting these to data. A number of hypothesis tests are developed and an example offered.

Number of observations required for the comparison of two correlated proportions

Abstract: Previous sample size tables for studies with pairwise matching of experimental units and all-or-none responses have relied upon asymptotic results for the power function given the effective sample size of the experiment. In this paper the exact power function is employed to construct detailed sample size tables for such studies.

Lower bounds for the number of pairwise orthogonal symmetric Latin squares

Abstract: 3. When a map, drawing or chart, etc., is part of the material being photo­ graphed the photographer has followed a definite method in “sectioning” the material. It is customary to begin filming at the upper left hand comer of a large sheet and to continue from left to right in equal sections with small overlaps. If necessary, sectioning is continued again—beginning below the first row and continuing on until complete.

A model to support the assessment of subjective probabilities

Abstract: The purpose of this article has been to provide a new method for the determination of subjective probabilities. The kind of support which is suggested for the assessment process has several interesting properties. Constructed in accordance with the Savage theory the procedure considers a preference structure on the space of the possible actions A or on a suitably chosen space A* as its basis. This structure will be attained by pairwise comparison of the elements ai eA (or ai*eA*). It may be incomplete and inconsistent. A linear programming approach will use this information to derive numerical probabilities which are in accordance with the stated preference judgments. Therefore, it avoids the difficulties which arise when the judge has to assign the numerical values to the possible states of nature. On the other hand, this method presents the advantage of taking into consideration all relevant a priori information because of its systematic judgment process. Another important element is given by the use of coefficients which express the judge's confidence in the stated comparisons. Further relevance is added to the procedure by the relatively small consumption of time and work to report the judgments even in complex situations, and by the renunciation of any methodological knowledge on the part of the judges.