1st Edition
Fuzzy Rule-Based Modeling with Applications to Geophysical, Biological, and Engineering Systems
This book presents in a systematic and comprehensive manner the modeling of uncertainty, vagueness, or imprecision, alias "fuzziness," in just about any field of science and engineering. It delivers a usable methodology for modeling in the absence of real-time feedback.
The book includes a short introduction to fuzzy logic containing basic definitions of fuzzy set theory and fuzzy rule systems. It describes methods for the assessment of rule systems, systems with discrete response sets, for modeling time series, for exact physical systems, examines verification and redundancy issues, and investigates rule response functions.
Definitions and propositions, some of which have not been published elsewhere, are provided; numerous examples as well as references to more elaborate case studies are also given. Fuzzy rule-based modeling has the potential to revolutionize fields such as hydrology because it can handle uncertainty in modeling problems too complex to be approached by a stochastic analysis. There is also excellent potential for handling large-scale systems such as regionalization or highly non-linear problems such as unsaturated groundwater pollution.
Basic Elements and Definitions
Fuzzy Sets: Definitions and Properties
Fuzzy Numbers
Assessment of the Membership Functions
Fuzzy Sets, Possibilities and Probabilities
Fuzzy Rules
The Structure of a Fuzzy Rule
Combination of Fuzzy Rule Responses
Defuzzification
Case of Fuzzy Premises
Rules with Multiple Responses
Rule Systems
Completeness and Redundancy
Variables to Be Used for Rule Systems
Rules and Continuous Functions
Membership Functions in Rule Systems
Sensitivity of the Response Functions
Rule Construction
Explicit Rule Specification
Deriving Rule Systems from Datasets
Known Rule Structure
Partially Explicit Rule Structures
Unknown Rule Structure
Deriving Rule Systems from Fuzzy Data
Rule Verification
Removing Unnecessary Rules
Fuzzy Rule-Based Modeling versus Fuzzy Control
Principles of Fuzzy Control
Examples of Fuzzy Control
Fuzzy Control and Fuzzy Rule-Based Modeling
Rule Systems with Discrete Responses
Combination of Discrete Consequence Type Rules
Rule Assessment
Application to Weather Classification
Application to Time Series
Rule Assessment
Example: Water Demand Forecasting
Example: Daily Mean Temperature
Application to Dynamical Physical Systems
Application to Soil Water Movement
Other Applications
Application to Medical Diagnosis
Sustainable Reservoir Operation
References
A Proofs of Selected Propositions
Biography
Andras Bardossy, Lucien Duckstein
