Algebraic Techniques and Their Use in Describing and Processing Uncertainty

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

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. 

• Fuzzy Systems
• Fuzzy Techniques
• Algebraic Methods to Fuzzy techniques
• Uncertainty
• Elbert Walker

• 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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