Let n be the number of intervals ,x0 and xn be the lower and upper bounds of the universe of discourse U on historicaltime series dataset D(t), respectively.A particle is an array consisting of n−1 elements such as x1,x2,...,xi,...,xn−2 and xn−1,where 1 in−1 and xi−1Now based on these n−1 elements,define then intervals asI1=(x0,x1],I2=(x1,x2],...,Ii=(xi−1,xi],...,In−1=(xn−2,xn−1]andIn=(xn−1,xn], respectively.In case of movement of a particle from one position to another position,the elements of the corresponding new array always require to be adjusted in an ascending order such that x1x2···xn−1.The graphical representation of particle is shown in Fig.3.
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