why do we refer to the feedback process as ' fuzzy logic' Why fuzzy?

Answer 1

G'day Raja S.

Thanks for your question.

Fuzzy logic comes from fuzzy set theory dealing with reasoning which is approximate or fuzzy rather than precisely deducted from classical logic.

Fuzzy logic is derived from fuzzy set theory dealing with reasoning that is approximate rather than precisely deduced from classical predicate logic. It can be thought of as the application side of fuzzy set theory dealing with well thought out real world expert values for a complex problem. (Klir 1997).

Degrees of truth are often confused with probabilities. However, they are conceptually distinct; fuzzy truth represents membership in vaguely defined sets, not likelihood of some event or condition. To illustrate the difference, consider this scenario: Bob is in a house with two adjacent rooms: the kitchen and the dining room. In many cases, Bob's status within the set of things "in the kitchen" is completely plain: he's either "in the kitchen" or "not in the kitchen". What about when Bob stands in the doorway? He may be considered "partially in the kitchen". Quantifying this partial state yields a fuzzy set membership. With only his little toe in the dining room, we might say Bob is 99% "in the kitchen" and 1% "in the dining room", for instance. No event (like a coin toss) will resolve Bob to being completely "in the kitchen" or "not in the kitchen", as long as he's standing in that doorway. Fuzzy sets are based on vague definitions of sets, not randomness.

Fuzzy logic allows for set membership values between and including 0 and 1, shades of gray as well as black and white, and in its linguistic form, imprecise concepts like "slightly", "quite" and "very". Specifically, it allows partial membership in a set. It is related to fuzzy sets and possibility theory. It was introduced in 1965 by Prof. Lotfi Zadeh at the University of California, Berkeley.

Fuzzy logic is controversial in some circles, despite wide acceptance and a broad track record of successful applications. It is rejected by some control engineers for validation and other reasons, and by some statisticians who hold that probability is the only rigorous mathematical description of uncertainty. Critics also argue that it cannot be a superset of ordinary set theory since membership functions are defined in terms of conventional sets.

If you would like to know more about fuzzy logic, I would recommend the following books:

# Von Altrock C., Fuzzy Logic and NeuroFuzzy Applications Explained (2002), ISBN 0-13-368465-2
# Cox E., The Fuzzy Systems Handbook (1994), ISBN 0-12-194270-8
# Elkan C.. The Paradoxical Success of Fuzzy Logic. November 1993. Available from Elkan's home page.
# Hájek P., Metamathematics of fuzzy logic. Kluwer 1998.
# Hájek P., Fuzzy logic and arithmetical hierarchy, Fuzzy Sets and Systems, 3, (1995), 359-363.
# Höppner F., Klawonn F., Kruse R. and Runkler T., Fuzzy Cluster Analysis (1999), ISBN 0-471-98864-2.
# Klir G. and Folger T., Fuzzy Sets, Uncertainty, and Information (1988), ISBN 0-13-345984-5.
# Klir G. , UTE H. St.Clair and Bo Yuan Fuzzy Set Theory Foundations and Applications,1997.
# Klir G. and Bo Yuan, Fuzzy Sets and Fuzzy Logic (1995) ISBN 0-13-101171-5
# Bart Kosko, Fuzzy Thinking: The New Science of Fuzzy Logic (1993), Hyperion. ISBN 078688021X
# Yager R. and Filev D., Essentials of Fuzzy Modeling and Control (1994), ISBN 0-471-01761-2
# Zimmermann H., Fuzzy Set Theory and its Applications (2001), ISBN 0792374355.
# Kevin M. Passino and Stephen Yurkovich, Fuzzy Control, Addison Wesley Longman, Menlo Park, CA, 1998.
# Zadeh L.A., Fuzzy algorithms, Information and Control, 5,(1968), 94-102.

I have attached some sources for your reference.

Answer 2

Because it uses inductive rather than deductive logic to reach conclusions.

The difference:

Deductive logic is used to reach conclusions based on premises you know to be true.

Inductive logic is used to reach conclusions based on premises you ASSUME to be true.

How the premises are ASSUMED to be true is the essential problem with implementing "fuzzy logic" models. Some models use statistics. Some use chaos theory. Some use a mix.

Basically, the goal of implementing "fuzzy logic" models in, say, computers, is to simulate "educated guessing" that works, for the most part.

Feedback processes, e.g. "feedback control loops", are just one type of implementation of fuzzy logic models. In this case the information fed back to the processor during a control loop is ASSUMED to describe the operation of a complicated system as accurately as possible. Once the assumption is fine-tuned, the feedback loop proceeds and a number of corrections are applied to the system. On the next pass, residual errors or other operational characteristics are selectively ASSUMED to be true, while others are ASSUMED to be false, and a new set of corrections is applied.

This is a pretty complicated topic for a BBS like this, and for the limited space available for discussion and argument - and I'm sure there are dissenting opinions of what I've just said, since "fuzzy logic" itself has a "fuzzy" definition.

You're better off going to Wikipedia and searching as many of the cited references on this topic as possible. If you can come to a definitive answer to your question, fine.

But I'm GUESSING you won't!!!

Answer 3

Fuzzy logic is a system not just a random term, or term for randomness.

Bob is in a house with two adjacent rooms: the kitchen and the dining room. In many cases, Bob's status within the set of things "in the kitchen" is completely plain: he's either "in the kitchen" or "not in the kitchen". What about when Bob stands in the doorway? He may be considered "partially in the kitchen". Quantifying this partial state yields a fuzzy set membership. With only his little toe in the dining room, we might say Bob is 99% "in the kitchen" and 1% "in the dining room", for instance. No event (like a coin toss) will resolve Bob to being completely "in the kitchen" or "not in the kitchen", as long as he's standing in that doorway. Fuzzy sets are based on vague definitions of sets, not randomness.


http://en.wikipedia.org/wiki/Fuzzy_logic

Answer 4

I think "fuzzy processes" contain a random element which make the results indeterminate