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1) Give an example where the law of transitivity for similarity does not hold (transitivity means: if a is similar to b and b is similar to c than a is similar to c). What is the explanation?

2) For  the vectors

 u = (1, 1, 0)
 v = (0, 1, 1)
 w = (1, 0, 1)

define two similarity measures sim1 and sim2  such that

 sim1 (u, v)  <  sim1 (u, w)
and
 sim2 (u, w)  < sim2 (u, v)
is true.

3) Define in detail a sequential search algorithm (in linear time) for finding the m most similar objects..  
Use the following data structures:

Types:
  SimObject = RECORD 
    object: object;    
    similarity: [0..1]  
         END;
  SimOjectQueue = ARRAY[1..m] OF SimObject;

Variables:
  scq: SimObjectQueue  (* m most similar objects *)
  cb: ARRAY [1..n] OF object (* Object base *)

4) You want to sell cars to all types of customers (business, private, single, married., no children, children).  Describe an example for the increased flexibility using catalogues, static and dynamic forms.

5) You own a large supermarket. For each customer it is counted at the cashier which goods he has bought. You are interested in three subclasses of the class of regular customers: Those who buy fames branda, those who buy no name goods and those who buy ecological goods.
Describe customers by an attribute-value vector and describe a method to determine the membership to the (vague) customer classes. 
Observe: The values of the attributes must be described by the information about the customer obtained at the cashier.