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Fuzzy Decisions

Fuzzy Decisions. Decision-Making with Fuzzy Rules. Human Control. Many of the problems that humans face and deal with easily are very difficult to handle computationally. The main reason is that we use fuzzy control, and it works well for us. A classic example is parking a car:

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Fuzzy Decisions

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  1. Fuzzy Decisions Decision-Making with Fuzzy Rules

  2. Human Control • Many of the problems that humans face and deal with easily are very difficult to handle computationally. • The main reason is that we use fuzzy control, and it works well for us. • A classic example is parking a car: • Parking a car is a difficult task. • Humans can park a car relatively well. • It is extremely difficult to program a robot to park a car, even in strictly controlled cases.

  3. Driving (Miss Daisy?) • Driving a car is an excellent example of fuzzy decision making. • We can describe the process by a set of fuzzy rules, some of which are: • IF traffic is heavy THEN drive slowly • IF police are close THEN drive legally • IF cars are slowing THEN slow down • IF it is dark THEN switch on lights • IF light is yellow THEN consider stopping

  4. Fuzzy Rules • Some rules are fuzzier than others. • We know that we should drive slowly in heavy traffic, but both terms are fuzzy • Driving “legally” is technically crisp, but in practice it is a fuzzy term (maybe not in Germany, but in most countries!) • Turning on the lights is a crisp action, they are either on or off, but deciding if it is dark is certainly fuzzy.

  5. Yellow Lights • The action we take at a yellow light is a good example of fuzzy decision making. • We consider the following factors: • Are we driving fast? • Is there a car close behind us? • Are there nearby cars in the cross traffic? • Is our passenger nervous? • And all this has to be determined in a fraction of a second. • It’s a big computing job!

  6. Decision Making • An extension of fuzzy control is fuzzy decision making. • Decision making uses inputs in human terms to decide on a course of action. • Because humans think in fuzzy terms, it is natural to use fuzzy rules in designing decision support systems (DSS).

  7. Crisp Decisions • The housing office lists apartments • You pick a price bracket, they give you a folder to look through • You are offered several choices: under €300, €300-500, over €500 • If you pick < €300 you may lose out on a great place that costs €302! • If your budget is €250-350, you may really miss out no matter which bracket you choose.

  8. Fuzzy Decisions • A fuzzy DSS would let you specify “cheap”, “moderate”, or “expensive” apartments, with room for qualifiers like “moderately expensive” or “very cheap”. • Instead of putting each apartment in one of the three folders (i.e., sets), each apartment could be a partial member of two sets, such as both “moderate” and “expensive”.

  9. Design of the DSS • To implement a DSS for the housing office, each apartment has its memberships assigned - a rent of €460 qualifies as moderately expensive, say 70% moderate and 30% expensive. • Requests are classified in terms of ranges of membership in the three sets, µC in cheap, µM in moderate, and µE in expensive. You see all apartments in this range.

  10. Using the DSS • Your request for a “moderately expensive” apartment translates to membership ranges µC = 0, µM between 0.5 and 0.9 and µE between 0.1 and 0.5 (for example). • However the apartments with highest membership in this set have µM close to 0.7 and µE close to 0.3 so you would see those first. • So you start around €460.

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