Principles of Imprecise-Information Processing: A New Theoretical and Technological System

The book showcases cutting-edge concepts and methods, and presents the principle of imprecise-information processing. It also proposes a new theory and technology for imprecise-information processing that differs from fuzzy technology, thus providing a platform for related applications and laying the theoretical basis for further research.

Imprecise-information processing – a type of processing based on flexible linguistic values and quantifiable rigid linguistic values – is an important component of intelligence science and technology. This book offers an easy-to-understand overview of the basic principles and methods of imprecise-information processing, allowing readers to develop related applications or pursue further research.

Table of Contents

Chapter 1 Overview of Imprecise-Information Processing
Chapter 2 Flexible Concepts and Flexible Linguistic Values and Their Mathematical Models
Chapter 3 Multidimensional Flexible Concepts and Flexible Linguistic Values and Their Mathematical Models
Chapter 4 Modeling of Flexible Concepts
Chapter 5 Flexible Sets and Operations on Flexible Sets
Chapter 6 Flexible Linguistic Values and Operations on Flexible Linguistic Values
Chapter 7 Superposition, Quantification, Conversion, and Generalization of Flexible Linguistic Values
Chapter 8 Relatively Opposite Flexible Linguistic Values and Relatively Opposite Flexible Sets
Chapter 9 Correspondence Between Flexible Sets, and Flexible Linguistic Functions
Chapter 10 Flexible Numbers and Flexible Functions
Chapter 11 Truth-Degreed Logic and Corresponding Inference
Chapter 12 Flexible-Linguistic-Truth-Valued Logic and Corresponding Inference
Chapter 13 Flexible Linguistic Rules and Their Numerical Model
Chapter 14 Adjoint Functions of a Flexible Linguistic Rule
Chapter 15 Reasoning and Computation with Flexible Linguistic Rules
Chapter 16 Approximate Evaluation of Flexible Linguistic Functions
Chapter 17 Approximate Reasoning and Computation Based on the Approximate Evaluation Principle of Flexible Linguistic Functions
Chapter 18 Imprecise-Problem Solving, and Anthropomorphic Computer Application Systems
Chapter 19 Imprecise-Knowledge Discovery
Chapter 20 Several Measures of Sets and Flexible Sets
Chapter 21 Quantifiable Rigid Linguistic Values and Related Theories
Chapter 22 Methodology of Imprecise-Information Processing and Some Other Application Problems
Chapter 23 Probabilities of Random Flexible Events
Chapter 24 Degrees of Believability of Flexible Propositions and Reasoning with Believability-Degrees
Chapter 25 Some Discussions About Possibly-Type Modal Propositions and Rules
Chapter 26 Several Further Research Directions and Topics