Modeling Uncertainty with Fuzzy Logic

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.

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.

Introduces the formation of type-2 fuzzy functions to capture uncertainties associated with system behaviour

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