Readings in Fuzzy Sets for Intelligent Systems - 1st Edition - ISBN: 9781483214504

Readings in Fuzzy Sets for Intelligent Systems

1st Edition

Editors: Didier Dubois Henri Prade Ronald R. Yager
eBook ISBN: 9781483214504
Imprint: Morgan Kaufmann
Published Date: 12th May 2014
Page Count: 928
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Readings in Fuzzy Sets for Intelligent Systems is a collection of readings that explore the main facets of fuzzy sets and possibility theory and their use in intelligent systems. Basic notions in fuzzy set theory are discussed, along with fuzzy control and approximate reasoning. Uncertainty and informativeness, information processing, and membership, cognition, neural networks, and learning are also considered.

Comprised of eight chapters, this book begins with a historical background on fuzzy sets and possibility theory, citing some forerunners who discussed ideas or formal definitions very close to the basic notions introduced by Lotfi Zadeh (1978). The reader is then introduced to fundamental concepts in fuzzy set theory, including symmetric summation and the setting of fuzzy logic; uncertainty and informativeness; and fuzzy control. Subsequent chapters deal with approximate reasoning; information processing; decision and management sciences; and membership, cognition, neural networks, and learning. Numerical methods for fuzzy clustering are described, and adaptive inference in fuzzy knowledge networks is analyzed.

This monograph will be of interest to both students and practitioners in the fields of computer science, information science, applied mathematics, and artificial intelligence.

Table of Contents


Chapter 1 Introduction

Chapter 2 Basic Notions in Fuzzy Set Theory

Fuzzy Sets

Representation Theorems for Fuzzy Concepts

On Some Logical Connectives for Fuzzy Sets Theory

Symmetric Summation: A Class of Operations on Fuzzy Sets

On Ordered Weighted Averaging Aggregation Operators in Multicriteria Decisionmaking

Fuzzy Power Sets and Fuzzy Implication Operators

On Implication and Indistinguishability in the Setting of Fuzzy Logic

A Theorem on Implication Functions Defined from Triangular Norms

Fuzzy Numbers: An Overview

A Review of Some Methods for Ranking Fuzzy Subsets

Solutions in Composite Fuzzy Relation Equations: Application to Medical Diagnosis in Brouwerian Logic

Fuzzy Relation Equation under a Class of Triangular Norms: A Survey and New Results

Chapter 3 Uncertainty and Informativeness

A Definition of a Nonprobabilistic Entropy in the Setting of Fuzzy Sets Theory

On the Specificity of a Possibility Distribution

Measures of Uncertainty and Information Based on Possibility Distributions

Conditional Possibility Measures and a Note on Defining Conditional Probability

On Modeling of Linguistic Information Using Random Sets

On the Concept of Possibility-Probability Consistency

Fuzzy Measures and Fuzzy Integrals—A Survey

Properties of the Fuzzy Expected Value and the Fuzzy Expected Interval in Fuzzy Environment

Fuzzy Random Variables

The Strong Law of Large Numbers for Fuzzy Random Variables

Chapter 4 Fuzzy Control

An Experiment in Linguistic Synthesis with a Fuzzy Logic Controller

Analysis of a Fuzzy Logic Controller

Selection of Parameters for a Fuzzy Logic Controller

Modelling Controllers Using Fuzzy Relations

The Use of Fuzzy Sets for the Treatment of Fuzzy Information by Computer

A Linguistic Self-Organizing Process Controller

Some Properties of Fuzzy Feedback Systems

Control of a Cement Kiln by Fuzzy Logic

Fuzzy Control for Automatic Train Operation System

Fuzzy Controlled Robot Arm Playing Two-Dimensional Ping-Pong Game

A Fuzzy Logic Programming Environment for Real-Time Control

A Reinforcement Learning-Based Architecture for Fuzzy Logic Control

Characterization of a Class of Fuzzy Optimal Control Problems

Fuzzy Identification of Systems and Its Applications to Modeling and Control

Fuzzy Modeling of Complex Systems

Chapter 5 Approximate Reasoning

The Logic of Inexact Concepts

Fuzzy Logic and the Resolution Principle

Fundamentals of Fuzzy Prolog

Epistemic Entrenchment and Possibilistic Logic

Fuzzy and Probability Uncertainty Logics

Possibility Theory and Soft Data Analysis

Axiomatic Approach to Implication for Approximate Reasoning with Fuzzy Logic

An Approach to Fuzzy Reasoning Method

Some Considerations on Fuzzy Conditional Inference

A Fuzzy System Model Based on the Logical Structure

On Mode and Implication in Approximate Reasoning

Fuzzy Inferences and Conditional Possibility Distributions

Fuzzy Modus Ponens: A New Model Suitable for Applications in Knowledge-Based Systems

Using Approximate Reasoning to Represent Default Knowledge

Fuzzy Set Simulation Models in a Systems Dynamics Perspective

Chapter 6 Information Processing

Numerical Methods for Fuzzy Clustering

A Physical Interpretation of Fuzzy ISODATA

Convex Decompositions of Fuzzy Partitions

New Results in Fuzzy Clustering Based on the Concept of Indistinguishability Relation

The Fuzzy Geometry of Image Subsets

Fuzzy Confidence Measures in Midlevel Vision

Fuzzy Sets and Generalized Boolean Retrieval Systems

A Fuzzy Representation of Data for Relational Databases

FREEDOM-0: A Fuzzy Database System

Weighted Fuzzy Pattern Matching

Fuzzy Querying with SQL: Extensions and Implementation Aspects

FILIP: A Fuzzy Intelligent Information System with Learning Capabilities

Chapter 7 Decision and Systems Science

Decision-Making with a Fuzzy Preference Relation

Structure of Fuzzy Binary Relations

Some Properties of Choice Functions Based on Valued Binary Relations

A New Methodology for Ordinal Multiobjective Decisions Based on Fuzzy Sets

Decision Making under Uncertainty with Various Assumptions about Available Information

A Linguistic Approach to Decisionmaking with Fuzzy Sets

Group Decision Making with Fuzzy Majorities Represented by Linguistic Quantifiers

Applications of Fuzzy Set Theory to Mathematical Programming

Fuzzy Versus Stochastic Approaches to Multicriteria Linear Programming under Uncertainty

Fuzzy Sets in Few Classical Operational Research Problems

Fuzzy Zero-Base Budgeting

The Fuzzy Mathematics of Finance

Chapter 8 Membership, Cognition, Neural Networks, and Learning

Reconciliation of the Yes-No Versus Grade of Membership Dualism in Human Thinking

A Model for the Measurement of Membership and the Consequences of Its Empirical Implementation

The Concept of Grade of Membership

Adaptive Inference in Fuzzy Knowledge Networks

A Formulation of Fuzzy Automata and Its Application as a Model of Learning Systems

Learning of Fuzzy Production Rules for Medical Diagnosis



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© Morgan Kaufmann 1993
Morgan Kaufmann
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About the Editor

Didier Dubois

Affiliations and Expertise

Directeur de Recherches CNRS, Paris, Laboratoire IRIT and Université Paul Sabatier, Toulouse, France

Henri Prade

Ronald R. Yager

Affiliations and Expertise

Iona College, Machine Intelligence Institute, New York, U.S.A.