Invariance and Structural Dependence
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Invariance and Structural Dependence: (380 Lecture Notes in Economics and Mathematical Systems)

Invariance and Structural Dependence: (380 Lecture Notes in Economics and Mathematical Systems)


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About the Book

This book deals with the notices of structural dependenceand independence, which are used in many applications ofmathematics to science. For instance, a physical law statesthat one physical aspect is structurally dependent on one ormore other aspects. Structural dependence is closely relatedto the mathematical idea of functional dependence. However, functional dependence expresses a kind of completedependence while structural dependence includes partialdependence. Further, structural dependence is primarilythought of as a relation holding between aspects rather thanbetween their measures. In this book, the traditional way oftreating aspects within measurement theory is modified. Anaspect is not viewed as a set-theoretical structure but as afunction which has sets as arguments and set-theoreticalstructures as values. This way of regardingaspects isillustrated with an application to social choice and groupdecision theory. Structural dependence is connected with theidea of concomitant variations and the mathematical notionof invariance. A distinction between dependence in the senseof determination and in the sense of relevance is drawn. Structural dependence both in the sense of determination andof relevance can be found in degrees from completedetermination and relevance to complete undetermination andirrelevance. The possibility of different "scales" ofdetermination and relevance is considered. One chapter ofthe book is devoted to a study of the dependence relationbetween the social ordering and the individual orderings insocial choice and group decision theory.

Table of Contents:
1. Problem Area and Basic Formal Apparatus.- 1. The Concept of Dependence in Applied Mathematics; a First Account.- 2. Basic Formal Concepts and Terminology.- 2. An Informal Presentation of the Main Themes.- 3. Relationals.- 4. Subordination, Uncorrelation and Derivation.- 5. An Example: Social Choice.- 6. Conformity and Measures.- 3. Formal Treatment of Basic Topics.- 7. Transitions Between Systems of Relationals.- 8. The Structure of Subordination.- 9. Isomorphic Mappings and Invariance.- Final remarks.- References.


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Product Details
  • ISBN-13: 9783540552604
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
  • Publisher Imprint: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • Height: 244 mm
  • No of Pages: 245
  • Returnable: N
  • Width: 170 mm
  • ISBN-10: 354055260X
  • Publisher Date: 15 Apr 1992
  • Binding: Paperback
  • Language: English
  • Returnable: N
  • Series Title: 380 Lecture Notes in Economics and Mathematical Systems


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