Accession Number : AD0676640

Title :   ON THE COMPATIBILITY BETWEEN A GRAPH AND A SIMPLE ORDER,

Corporate Author : RAND CORP SANTA MONICA CALIF

Personal Author(s) : Roberts,Fred S.

Report Date : SEP 1968

Pagination or Media Count : 35

Abstract : A formal graph-theoretic approach to measurement problems, such as those occurring in psychology, sociology, and economics is given. The relation of indifference is represented by adjacency in a graph. Since indifference is symmetric, the graph is unoriented (preference relations are asymmetric and result in oriented graphs). The psychological notion of threshold, or just noticeable difference (jnd), suggests a problem in which numbers are assigned to points so that indifference exists relative to the two objects represented (i.e., so that the two points are adjacent) if and only if the numbers are close. The present study generalizes the problem to that of ordering the points of a graph (rather than numbering them) so that two nonadjacent points cannot be included between two adjacent points. This notion of compatible ordering turns out to be more general than numbering because it permits theorems to be proved for graphs with an arbitrarily large (infinite) number of points. (Author)

Descriptors :   (*GRAPHICS, MEASUREMENT), ECONOMICS, SOCIOLOGY, PSYCHOLOGY, SET THEORY, COMBINATORIAL ANALYSIS, MATHEMATICAL LOGIC, THEOREMS, THESES

Subject Categories : Theoretical Mathematics

Distribution Statement : APPROVED FOR PUBLIC RELEASE