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Algebraic Techniques and Their Use in Describing and Processing Uncertainty

To the Memory of Professor Elbert A. Walker

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  • © 2020

Overview

Editors:
  1. Hung T. Nguyen

    1. Department of Mathematical Sciences, New Mexico State University, Las Cruces, USA

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    You can also search for this editor in PubMed   Google Scholar

  2. Vladik Kreinovich

    1. Department of Computer Science, The University of Texas at El Paso, El Paso, USA

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    You can also search for this editor in PubMed   Google Scholar

  • Presents a wide range of algebraic techniques and their use in describing and processing uncertainty
  • Features papers dedicated to Elbert Walker (1930–2018) and commemorating his work
  • Written by experts in the field

Part of the book series: Studies in Computational Intelligence (SCI, volume 878)

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Table of contents (13 chapters)

  1. Front Matter

    Pages i-viii
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  2. Specker Algebras: A Survey

    • G. Bezhanishvili, P. J. Morandi, B. Olberding
    Pages 1-19

  3. Least Square Approximations and Linear Values of Cooperative Games

    • Ulrich Faigle, Michel Grabisch
    Pages 21-32

  4. Elementary Divisor Domains as Endomorphism Rings

    • László Fuchs
    Pages 33-40

  5. A Topos View of the Type-2 Fuzzy Truth Value Algebra

    • John Harding, Carol Walker
    Pages 41-54

  6. A Symmetry-Based Explanation of the Main Idea Behind Chubanov’s Linear Programming Algorithm

    • Olga Kosheleva, Vladik Kreinovich, Thongchai Dumrongpokaphan
    Pages 55-64

  7. Why Bohmian Approach to Quantum Econometrics: An Algebraic Explanation

    • Vladik Kreinovich, Olga Kosheleva, Songsak Sriboonchitta
    Pages 65-75

  8. Direct Decompositions of Matrices

    • Adolf Mader, Otto Mutzbauer
    Pages 77-87

  9. Generators of Fuzzy Logical Operations

    • Mirko Navara, Milan Petrík
    Pages 89-112

  10. An Enjoyable Journey of Research Collaboration with Elbert A. Walker

    • Hung T. Nguyen
    Pages 113-121

  11. In Memory of Dr. Elbert A. Walker

    • Nadipuram R. Prasad
    Pages 123-128

  12. Duality via Truth for Some Fuzzy Modal Logic

    • Anna Maria Radzikowska, Etienne E. Kerre
    Pages 129-149

  13. Me and Elbert

    • Fred Richman
    Pages 151-156

  14. Fuzzy Bigraphs

    • Apostolos Syropoulos
    Pages 157-170
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Keywords

About this book

This book discusses heuristic methods – methods lacking a solid theoretical justification – which are ubiquitous in numerous application areas, and explains techniques that can make heuristic methods more reliable. Focusing on algebraic techniques, i.e., those that use only a few specific features of a situation, it describes various state-of-the-art applications, ranging from fuzzy methods for dealing with imprecision to general optimization methods and quantum-based methods for analyzing economic phenomena. The book also includes recent results from leading researchers, which could (and hopefully will) provide the basis for future applications. As such, it is a valuable resource for mathematicians interested in potential applications of their algebraic results and ideas, as well as for application specialists wanting to discover how algebraic techniques can help in their domains. 

Editors and Affiliations

  • Department of Mathematical Sciences, New Mexico State University, Las Cruces, USA

    Hung T. Nguyen

  • Department of Computer Science, The University of Texas at El Paso, El Paso, USA

    Vladik Kreinovich

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