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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.
Table of Contents
Introduction 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
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CHOICE – Outstanding Academic Title – Award Winner
CHOICE – 2018 Outstanding Academic Title – Award Winner
Shingo Research and Professional Publication Award Winner
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