Multivariate models for the triangular and duo-trio methods are described, and theoretical methods are compared to a Monte Carlo simulation. Implications are discussed for a new theory of multidimensional scaling which challenges the traditional assumption that proximity measures and perceptual distances are monotonically related. (Author/GDC)

Description of management games continues a previous article's discussion of how mathematical modeling and microeconomic concepts can be used by players. Highlights include an initial condition simulating a profit-maximizing monopoly; simulating the transition from monopoly to oligopoly; and how mathematical properties of the model affect final…

Compares and expands upon two approaches to dealing with fuzzy relational databases. The proposed similarity measure is based on a fuzzy Hausdorff distance and estimates the mismatch between two possibility distributions using a reduction process. The consequences of the reduction process on query evaluation are studied. (Author/EM)

Relations on a finite set V are viewed as weighted graphs. Using the language of graph theory, two methods of partitioning V are examined: selecting threshold values and applying them to a maximal weighted spanning forest, and using a parametric linear program to obtain a most adhesive partition. (Author/EM)

A binomial test for hierarchical dependency is presented. The null hypothesis is that all members of a population who possess a certain skill are a subset of the members who possess another skill. The model, assumptions, formula derivations, and procedures for the test are explained. An illustrative hypothesis is provided. (Author/LMO)

The application of the theory of fuzzy sets to the description of information retrieval systems makes it possible (1) to take into account the fact that the degree of importance of the particular terms is of a continuous character, (2) to formalize the relations between terms describing documents and information requests (fuzzy thesaurus).…

This paper describes a model that integrates an item response theory (IRT) Rasch model and a hierarchical linear model and presents a method of estimating model parameter values that does not rely on large-sample theory and normal approximations. The model resulting from the integration of a hierarchical linear model and the Rasch model allows one…

The feature that makes item response theory (IRT) models the models of choice for many psychometric data analysts is parameter invariance, the equality of item and examinee parameters from different populations. Using the well-known fact that item and examinee parameters are identical only up to a set of linear transformations specific to the…

This paper describes the graded response model. The graded response model represents a family of mathematical models that deal with ordered polytomous categories, such as: (1) letter grading; (2) an attitude survey with "strongly disagree, disagree, agree, and strongly agree" choices; (3) partial credit given in accord with an…

Using abstract models of thesaurus-based and multi-attribute retrieval systems a correspondence between the two systems is established so that equivalent transformation of problem statements expressed by notions developed for one system into problem statements expressed by notions pretaining to the other one may be effectively constructed. (5…

A probabilistic model for interactive retrieval is presented. Bayesian statistical decision theory principles are applied: use of prior and sample information about the relationship of document descriptions to query relevance; maximization of expected value of a utility function, to the problem of optimally restructuring search strategies in an…

The theoretical model of a document retrieval system is described by giving logical meaning to the vagueness and the similarity characteristic to such systems, with the frequency of occurrences of keywords and the relations among them taken into consideration. (6 references) (Author/SJ)

A formula for the ratio of the variance of the pooled transformed data under departure from the binomial assumption to the variance of the pooled transformed data when the binomial assumption holds is given. (Authors)

This paper attempts to analyze the problem of congestion, using a mathematical model shown to be of value in other similar applications. Three criteria of congestion are considered, and it is found that the conclusion one can draw is sensitive to which of these criteria is paramount. (8 references) (Author/NH)

Authors demonstrate that a simple algebraic analysis renders previous interpretations superfluous, making overlap" a tautology and not a hypothesis. (Authors/MB)