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assume that we have the points on l 1 and l 2 a but wish to deduce the relative ordering in between these two lines
...Definition 3 Thomsen condition
...Intuitively this can b e reasoned as follows
...The fourth condition is one concerned with the continuity of each component
...Definition 4 Restricted Solvability
...1 whenever R,R,R [[propersubset]]R and P,P [[propersubset]]P for which R,P >R,P >R,P then there exists R [[propersubset]]R s
...2 a similar condition holds on the second component
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| 169 |
The model We start by examining the structure which it is reasonable to assume for the measurement of effectiveness
...If R is the set of possible recall values and P is the set of possible precision values then we are interested in the set R x P with a relation on it
...Definition 1
...1 Connectedness:either e 1 >e 2 or e 2 >e 1 2 Transitivity:if e 1 >e 2 and e 2 >e 3 then e 1 >e 3 We insist that if two pairs can be ordered both ways then R 1,P 1 R 2,P 2,i
...We now turn to a second condition which is commonly called independence
...Definition 2
...All we are saying here is,given that at a constant recall precision we find a difference in effectiveness for two values of precision recall then this difference cannot be removed or reversed by changing the constant value
...We now come to a condition which is not quite as obvious as the preceding ones
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