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Modal Interval Analysis

New Tools for Numerical Information

  • Miguel A. Sainz
  • Joaquim Armengol
  • Remei Calm
  • Pau Herrero
  • Lambert Jorba
  • Josep Vehi

Part of the Lecture Notes in Mathematics book series (LNM, volume 2091)

Table of contents

  1. Front Matter
    Pages i-xvi
  2. Miguel A. Sainz, Joaquim Armengol, Remei Calm, Pau Herrero, Lambert Jorba, Josep Vehi
    Pages 1-16
  3. Miguel A. Sainz, Joaquim Armengol, Remei Calm, Pau Herrero, Lambert Jorba, Josep Vehi
    Pages 17-37
  4. Miguel A. Sainz, Joaquim Armengol, Remei Calm, Pau Herrero, Lambert Jorba, Josep Vehi
    Pages 39-72
  5. Miguel A. Sainz, Joaquim Armengol, Remei Calm, Pau Herrero, Lambert Jorba, Josep Vehi
    Pages 73-120
  6. Miguel A. Sainz, Joaquim Armengol, Remei Calm, Pau Herrero, Lambert Jorba, Josep Vehi
    Pages 121-141
  7. Miguel A. Sainz, Joaquim Armengol, Remei Calm, Pau Herrero, Lambert Jorba, Josep Vehi
    Pages 143-158
  8. Miguel A. Sainz, Joaquim Armengol, Remei Calm, Pau Herrero, Lambert Jorba, Josep Vehi
    Pages 159-183
  9. Miguel A. Sainz, Joaquim Armengol, Remei Calm, Pau Herrero, Lambert Jorba, Josep Vehi
    Pages 185-228
  10. Miguel A. Sainz, Joaquim Armengol, Remei Calm, Pau Herrero, Lambert Jorba, Josep Vehi
    Pages 229-264
  11. Miguel A. Sainz, Joaquim Armengol, Remei Calm, Pau Herrero, Lambert Jorba, Josep Vehi
    Pages 265-305
  12. Back Matter
    Pages 307-318

About this book

Introduction

This book presents an innovative new approach to interval analysis. Modal Interval Analysis (MIA) is an attempt to go beyond the limitations of classic intervals in terms of their structural, algebraic and logical features. The starting point of MIA is quite simple: It consists in defining a modal interval that attaches a quantifier to a classical interval and in introducing the basic relation of inclusion between modal intervals by means of the inclusion of the sets of predicates they accept. This modal approach introduces interval extensions of the real continuous functions, identifies equivalences between logical formulas and interval inclusions, and provides the semantic theorems that justify these equivalences, along with guidelines for arriving at these inclusions. Applications of these equivalences in different areas illustrate the obtained results. The book also presents a new interval object: marks, which aspire to be a new form of numerical treatment of errors in measurements and computations.

Keywords

65G40, 65G50, 03B10, 26A24, 65F10 Intervals Marks Quantifiers

Authors and affiliations

  • Miguel A. Sainz
    • 1
  • Joaquim Armengol
    • 2
  • Remei Calm
    • 3
  • Pau Herrero
    • 4
  • Lambert Jorba
    • 5
  • Josep Vehi
    • 6
  1. 1.Informática, Matemática Aplicada y EstadísticaEscola Politecnica Superior, University of GironaGironaSpain
  2. 2.Enginyeria Elèctrica, Electrònica i AutomàticaEscola Politecnica Superior, University of GironaGironaSpain
  3. 3.Informática, Matemática Aplicada y EstadísticaEscola Politecnica Superior, University of GironaGironaSpain
  4. 4.Imperial College LondonLondonUnited Kingdom
  5. 5.Matemática Económica, Financiera y ActuarialFacultad de Economia y Empresa, Universitat de BarcelonaBarcelonaSpain
  6. 6.Enginyeria Elèctrica, Electrònica i AutomàticaEscola Politecnica Superior, University of GironaGironaSpain

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-01721-1
  • Copyright Information Springer International Publishing Switzerland 2014
  • Publisher Name Springer, Cham
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-319-01720-4
  • Online ISBN 978-3-319-01721-1
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
  • Buy this book on publisher's site
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