Foundations of Measurement Geometrical, Threshold, and Probabilistic Representations

Name: Foundations of Measurement Geometrical, Threshold, and Probabilistic Representations
Price: 4.55 USD
Availability: InStock
ISBN: 9780486453156

ISBN-10: 0486453154

ISBN-13: 9780486453156

Edition: 2007

Authors: Patrick Suppes, R. Duncan Luce, David H. Krantz, Amos Tversky

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Description:

A classic series in the field of quantitative measurement,Volume Iintroduces the distinct mathematical results that serve to formulate numerical representations of qualitative structures.Volume IIextends the subject in the direction of geometrical, threshold, and probabilistic representations, andVolume IIIexamines representation as expressed in axiomatization and invariance. 1989 edition.

Book details

List price: $29.95
Copyright year: 2007
Publisher: Dover Publications, Incorporated
Publication date: 12/15/2006
Binding: Paperback
Pages: 512
Size: 6.34" wide x 8.46" long x 1.06" tall
Weight: 1.122
Language: English



Preface


Acknowledgments



Overview



Geometry Unit



Geometrical Representations (Chapter 12)



Axiomatic Synthetic Geometry (Chapter 13)



Proximity Measurement (Chapter 14)



Color and Force Measurement (Chapter 15)



Threshold and Error Unit



Representations with Thresholds (Chapter 16)



Representations of Choice Probabilities (Chapter 17)



Geometrical Representations



Introduction



Vector Representations



Vector Spaces



Analytic Affine Geometry



Analytic Projective Geometry



Analytic Euclidean Geometry



Meaningfulness in Analytic Geometry



Minicowski Geometry



General Projective Metrics



Metric Representations



General Metrics with Geodesies



Elementary Spaces and the Helmholtz-Lie Problem



Riemannian Metrics



Other Metrics


Exercises



Axiomatic Geometry and Applications



Introduction



Order on the Line



Betweenness: Affine Order



Separation: Projective Order



Proofs



Projective Planes



Projective Spaces



Affine and Absolute Spaces



Ordered Geometric Spaces



Affine Spaces



Absolute Spaces



Euclidean Spaces



Hyperbolic Spaces



Elliptic Spaces



Double Elliptic Spaces



Single Elliptic Spaces



Classical Space-Time



Space-Time of Special Relativity



Other Axiomatic Approaches



Perceptual Spaces



Historical Survey through the Nineteenth Century



General Considerations Concerning Perceptual Spaces



Experimental Work before Luneburg's Theory



Luneburg Theory of Binocular Vision



Experiments Relevant to Luneburg's Theory



Other Studies


Exercises



Proximity Measurement



Introduction



Metrics with Additive Segments



Collinearity



Constructive Methods



Representation and Uniqueness Theorems



Proofs



Theorem 2



Reduction to Extensive Measurement



Theorem 3



Theorem 4



Multidimensional Representations



Decomposability



Intradimensional Subtractivity



Interdimensional Additivity



The Additive-Difference Model



Additive-Difference Metrics



Proofs



Theorem 5



Theorem 6



Theorem 7



Theorem 9



Preliminary Lemma



Theorem 10



Experimental Tests of Multidimensional Representations



Relative Curvature



Translation Invariance



The Triangle Inequality



Feature Representations



The Contrast Model



Empirical Applications



Comparing Alternative Representations



Proofs



Theorem 11


Exercises



Color and Force Measurement



Introduction



Grassmann Structures



Formulation of the Axioms



Representation and Uniqueness Theorems



Discussion of Proofs of Theorems 3 and 4



Proofs



Theorem 3



Theorem 4



Color Interpretations



Metameric Color Matching



Tristimulus Colorimetry



Four Ways to Misunderstand Color Measurement



Asymmetric Color Matching



The Dimensional Structure of Color and Force



Color Codes and Metamer Codes



Photopigments



Force Measurement and Dynamical Theory



Color Theory in a Measurement Framework



The Konig and Hurvich-Jameson Color Theories



Representations of 2-Chromatic Reduction Structures



The Konig Theory and Alternatives



Codes Based on Color Attributes



The Cancellation Procedure



Representation and Uniqueness Theorems



Tests and Extensions of Quantitative Opponent-Colors Theory



Proofs



Theorem 6



Theorem 9



Theorem 10


Exercises



Representations with Thresholds



Introduction



Three Approaches to Nontransitive Data



Idea of Thresholds



Overview



Ordinal Theory



Upper, Lower, and Two-Sided Thresholds



Induced Quasiorders: Interval Orders and Semiorders



Compatible Relations



Biorders: A Generalization of Interval Orders



Tight Representations



Constant-Threshold Representations



Interval and Indifference Graphs



Proofs



Theorem 2



Lemma 1



Theorem 6



Theorem 9



Theorem 10



Theorem 11



Theorems 14 and 15



Ordinal Theory for Families of Orders



Finite Families of Interval Orders and Semiorders



Order Relations Induced by Binary Probabilities



Dimension of Partial Orders



Proofs



Theorem 16



Theorem 17



Theorem 18



Theorem 19



Semiordered Additive Structures



Possible Approaches to Semiordered Probability Structures



Probability with Approximate Standard Families



Axiomatization of Semiordered Probability Structures



Weber's Law and Semiorders



Proof of Theorem 24



Random-Variable Representations



Weak Representations of Additive Conjoint and Extensive Structures



Variability as Measured by Moments



Qualitative Primitives for Moments



Axiom System for Qualitative Moments



Representation Theorem and Proof


Exercises



Representation of Choice Probabilities



Introduction



Empirical Interpretations



Probabilistic Representations



Ordinal Representations for Pair Comparisons



Stochastic Transitivity



Difference Structures



Local Difference Structures



Additive Difference Structures



Intransitive Preferences



Proofs



Theorem 2



Theorem 3



Theorem 4



Constant Repmsentations for Multiple Choice



Simple Scalabihty



The Strict-Utility Model



Proofs



Theorem 5



Theorem 7



Random Variable Representations



The Random-Utility Model



The Independent Double-Exponential Model



Error Tradeoff



Proofs



Theorem 9



Theorem 12



Theorem 13



Markovian Elimination Processes



The General Model



Elimination by Aspects



Preference Trees



Proofs



Theorem 15



Theorem 16



Theorem 17


Exercises


References


Author Index


Subject Index