Context-Aware Computing

$Sim\left(C,C\text{'}\right)=\sqrt{\frac{1}{n}{\displaystyle \sum _{i=1}^{n}si{m}^2\left(A_i,c_i,c_i^{\text{'}}\right)}}\left(13.1\right)$

Example 46. For two 2-dimensional context instances C = (2010-10-1, New York) and C' = (2010-10-3, New York) in Figure 13.4, the similarity between C and C' is: $Sim\left(C,C\text{'}\right)=\sqrt{\frac{1}{2}\times \left({0.72}^2+1\right)}=\mathrm{0.87.}$

Definition 41. Assume context is an n-dimensional vector (A1, A2, ⋅⋅ ⋅ , An). Let C = (c1, c2, ⋅⋅ ⋅ , cn) and $C\text{'}=\left(c_1^{\text{'}},c_2^{\text{'}},\mathrm{..},c_n^{\text{'}}\right)$ be two context instances.

–C is equal to C', denoted as C' = C, if and only if ∀i ∈ {1, 2, ⋅⋅ ⋅ , n} $\left(c_i^{\text{'}}=c_i\right).$

–C is more general than C', denoted as C' ≺ C, if and only if ...