Journal of Data Science Research by Xianrong Zheng

Author:Xianrong Zheng [Zheng, Xianrong]
Language: eng
Format: azw3
Published: 2017-05-01T04:00:00+00:00

4 THE DEFINITION OF “SET CODE” AND ITS OPERATION RULES

To improve the efficiency of set operations, the elements in a set need to be formalized. We introduce the binary to the set computing process, and form a comparatively complete, formalized “set code” system. Below, we first propose the concept of “set code”, and then define the operation rules of “set code”.

4.1 The Definitions of “Set Code”

Suppose that there are n elements in a set A, and that we sort its n elements, where an element occupies one bit. Each subset X of the entire set A corresponds to a string, which is composed of 0 and 1 (also called a Boolean vector). The “set code” of X is represented as C(X), which is composed of 0 and 1. The corresponding rule is the following: If A’s ith element appears in the subset X, then the C(X)’s ith element is 1, otherwise it is 0.

According to the definition of “set code” and Table 2, we can obtain the “set code” of the entire set E, and the subsets A, B, C, I, J, K, P, Q, and R.

C(E) = 11111111111

C(A) = 10100001000

C(B) = 00000110011

C(C) = 01011000100

C(I) = 10000010010

C(J) = 01010101001

C(K) = 00101000100

C(P) = 11000110001

C(Q) = 00101001010

C(R) = 00010000100

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