Modeling Uncertainty with Fuzzy Logic

This book presents an uncertainty modeling approach using a new type of fuzzy system model via "Fuzzy Functions". It also reviews standard tools of fuzzy system modeling approaches to demonstrate the novelty of the structurally different fuzzy function.

The world we live in is pervaded with uncertainty and imprecision. Is it likely to rain this afternoon? Should I take an umbrella with me? Will I be able to find parking near the campus? Should I go by bus? Such simple questions are a c- mon occurrence in our daily lives. Less simple examples: What is the probability that the price of oil will rise sharply in the near future? Should I buy Chevron stock? What are the chances that a bailout of GM, Ford and Chrysler will not s- ceed? What will be the consequences? Note that the examples in question involve both uncertainty and imprecision. In the real world, this is the norm rather than exception. There is a deep-seated tradition in science of employing probability theory, and only probability theory, to deal with uncertainty and imprecision. The mon- oly of probability theory came to an end when fuzzy logic made its debut. H- ever, this is by no means a widely accepted view. The belief persists, especially within the probability community, that probability theory is all that is needed to deal with uncertainty. To quote a prominent Bayesian, Professor Dennis Lindley, The only satisfactory description of uncertainty is probability.

Introduces the formation of type-2 fuzzy functions to capture uncertainties associated with system behaviour Presents an uncertainty modeling approach using a new type of fuzzy system model via Fuzzy Functions

Klappentext

The objective of this book is to present an uncertainty modeling approach using a new type of fuzzy system model via "Fuzzy Functions". Since most researchers on fuzzy systems are more familiar with the standard fuzzy rule bases and their inference system structures, many standard tools of fuzzy system modeling approaches are reviewed to demonstrate the novelty of the structurally different fuzzy functions, before we introduced the new methodologies. To make the discussions more accessible, no special fuzzy logic and system modeling knowledge is assumed. Therefore, the book itself may be a reference for some related methodologies to most researchers on fuzzy systems analyses. For those readers, who have knowledge of essential fuzzy theories, Chapter 1, 2 should be treated as a review material. Advanced readers ought to be able to read chapters 3, 4 and 5 directly, where proposed methods are presented. Chapter 6 demonstrates experiments conducted on various datasets.

Zusammenfassung
From the reviews: "The present book has as goal the representation and utilization of uncertainty by means of fuzzy functions. ... The book begins with a very good overview of the basic notions and principles related to fuzzy sets and systems ... . The fuzzy models proposed in this book can be used with success by researchers from various domains of activity: engineering, economics, biology, sociology etc., in order to model complex systems." (Ion Iancu, Zentralblatt MATH, Vol. 1168, 2009)

Inhalt
Fuzzy Sets and Systems.- Improved Fuzzy Clustering.- Fuzzy Functions Approach.- Modeling Uncertainty with Improved Fuzzy Functions.- Experiments.- Conclusions and Future Work.