Beyond Traditional Probabilistic Data Processing Techniques: Interval, Fuzzy etc. Methods and Their Applications

Data processing has become essential to modern civilization. The original data for this processing comes from measurements or from experts, and both sources are subject to uncertainty. Traditionally, probabilistic methods have been used to process uncertainty. However, in many practical situations, we do not know the corresponding probabilities: in measurements, we often only know the upper bound on the measurement errors; this is known as interval uncertainty. In turn, expert estimates often include imprecise (fuzzy) words from natural language such as "small"; this is known as fuzzy uncertainty. In this book, leading specialists on interval, fuzzy, probabilistic uncertainty and their combination describe state-of-the-art developments in their research areas. Accordingly, the book offers a valuable guide for researchers and practitioners interested in data processing under uncertainty, and an introduction to the latest trends and techniques in this area, suitablefor graduate students.

This book is about going beyond traditional probabilistic data processing techniques, to pursue interval, fuzzy, etc. methods how to do it, and what the applications of the resulting non-traditional approaches are Dedicated to Vladik Kreinovich on the occasion of his 65th birthday Includes papers on constructive mathematics, fuzzy techniques, interval computations, uncertainty in general, and neural networks

Inhalt
Symmetries are Important.- Constructive Continuity of Increasing Functions.- A Constructive Framework for Teaching Discrete Mathematics.- Fuzzy Logic for Incidence Geometry.- Strengths of Fuzzy Techniques in Data Science.- Impact of Time Delays on Networked Control of Autonomous Systems.- Sets and Systems.- An Overview of Polynomially Computable Characteristics of Special Interval Matrices.- Interval Regularization for Inaccurate Linear Algebraic Equations.- Measurable Process Selection Theorem and Non-Autonomous Inclusions.- Handling Uncertainty When Getting Contradictory Advice from Experts.- Why Sparse?.- The Kreinovich Temporal Universe.- Integral Transforms induced by Heaviside Perceptrons.