A Fuzzy-Decision Based Approach for Composite Event Detection in Wireless Sensor Networks

Algorithm 2

Two-dimensional 𝜏-GAS algorithm.

Input: 𝐴_𝑗

output: 𝑥_𝑗

For (𝑖=1 to p)

   𝑥^𝑖_𝑗=𝜏-GAS(𝐴^𝑖_𝑗);

End for

 𝐴_𝑗={𝑥¹_𝑗,𝑥²_𝑗,…,𝑥^𝑝_𝑗};

 𝑥_𝑗=𝜏-GAS(𝐴_𝑗);

Function 𝜏-GAS ({𝑥₁,𝑥₂,…,𝑥_𝑘})

   Initialize:

      Sort the data of {𝑥₁,𝑥₂,…,𝑥_𝑘} from small to large 

      Choose ℜ₀={𝐶_𝑖={𝑥_𝑖},𝑙=1,2,…,𝑘} as the initial classification

       𝑡=0

   Repeat:

      𝑡=𝑡+1;

    𝑔(𝐶_𝑖,𝐶_𝑗)=min𝑔(𝐶_𝑛,𝐶_𝑞)(𝜓_𝐶𝑟≤𝜏_𝑗,𝐶_𝑟=𝐶_𝑛∪𝐶_𝑞);

    ℜ_𝑡=ℜ_𝑡−1−{𝐶_𝑖,𝐶_𝑗}+𝐶_𝑟;

   Until mergerofanytwoclasssatisfies𝜓_𝐶𝑟>𝜏_𝑗𝑜𝑟ℜ_𝑡=1

       𝐶_𝑒=𝐶_𝑖,𝐶_𝑖=max𝐶,𝐶∈ℜ_𝑡;

       1𝑥=𝐶_𝑒𝑥𝑖∑_∈𝐶𝑒𝑥_𝑖;

   Return 𝑥 ;

End function 𝜏-GAS