Algebraic Techniques and Their Use in Describing and Processing Uncertainty

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.

Presents a wide range of algebraic techniques and their use in describing and processing uncertainty Features papers dedicated to Elbert Walker (19302018) and commemorating his work Written by experts in the field

Klappentext

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.

Inhalt
Specker Algebras: A Survey.- Least Square Approximations and Linear Values of Cooperative Game.- Elementary Divisor Domains as Endomorphism Rings.- A Topos View of the Type-2 Fuzzy Truth Value Algebra.- A Symmetry-Based Explanation of the Main Idea Behind Chubanov's Linear Programming Algorithm.- Why Bohmian Approach to Quantum Econometrics: An Algebraic Explanation.- Direct Decompositions of Matrices.