あいまい情報処理の原理（第２版） Principles of Imprecise-Information Processing〈Second Edition 2025〉 : A New Theoretical and Technological System on Flexible Linguistic Information（2）

著者名：Lian, Shiyou

Springer（2024/11/02発売）

• 言語：ENG
• ISBN：9789819764242
• eISBN：9789819764259

Description

This book reveals the origin of imprecise information and establishes the mathematical models of flexible words and related mathematical and logical theories. It presents a set of models and algorithms of reasoning and computation, thus building a platform for related applications and laying a foundation for further research.

Applying the theories and technologies in the book builds flexible AI systems to solve corresponding clustering, classification, judging, recognition, control, prediction, regression, etc., problems, and to enhance the Agent’s and Robot’s abilities to perceive environment and control behavior. Combine large language models (LLMs) with flexible linguistic information technologies in the book to enhance and extend the capability of natural language processing, and to realize understanding and generation of flexible words.

This book differentiates imprecision from the uncertainty of information and explicitly treats imprecise-information processing as an independent subject. Imprecise-information processing is an indispensable research topic and branch field of artificial intelligence. With a new perspective and idea, the book starts from the origin of imprecise information, comprehensively and systematically expounds the principles, methods, and applications of imprecise-information processing, and establishes a new theoretical and technological system different from fuzzy technology on flexible linguistic information.

The audience of this book includes scholars, engineers, teachers, Ph.D. candidates, postgraduates, and advanced undergraduates in the fields of artificial intelligence, natural language processing, Agent, Robot, automation, information, computer, logics, mathematics, language, as well as brain and cognitive science, etc.

Table of Contents

Overview of Imprecise-Information Processing.- Flexible Concepts and Flexible Linguistic Values and Their Mathematical Models.- Modeling of Flexible Concepts.- Flexible Sets and Operations on Flexible Sets.- Flexible Linguistic Values, and Operations on Flexible Linguistic Values.- Superposition, Quantification, Conversion and Generalization of Flexible Linguistic Values.- Relatively-Opposite Flexible Linguistic Values and Relatively-Opposite Flexible Sets.- Correspondence between Flexible Sets, and Flexible Linguistic Functions.- Flexible Numbers and Flexible Functions.- Truth Degreed Logic and Corresponding Inference.- Flexible Linguistic Truth-Valued Logic and Corresponding Inference.- Adjoint Functions of a Flexible Linguistic Rule.- Reasoning and Computation with Flexible Linguistic Rules.- Approximate Evaluation of Flexible Linguistic Functions.- Approximate Reasoning and Computation Based on the Approximate Evaluation Principle of Flexible Linguistic Functions.- Imprecise-Problem Solving and Flexible Intelligent Systems.- Imprecise-Knowledge Discovery.- Several Measures of Sets and Flexible Sets.- Quantifiable Rigid Linguistic Values and Related Theories.- Methodology of Imprecise-Information Processing, and Some Other Application Problems.- Probabilities of Random Flexible Events.- Degrees of Believability of Flexible Propositions and Reasoning with Believability-Degrees.- Some Discussions about Possibly-Type Modal Propositions and Rules.- Several Further Research Directions and Topics.