Open AccessEntropic Explanation of Power Set
Author(s) -
Yutong Song,
Yong Deng
Publication year - 2021
Publication title -
international journal of computers, communications and control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.422
H-Index - 33
eISSN - 1841-9844
pISSN - 1841-9836
DOI - 10.15837/ijccc.2021.4.4413
Subject(s) - power set , set function , set (abstract data type) , mathematics , discrete mathematics , entropy (arrow of time) , combinatorics , event (particle physics) , power function , finite set , infinite set , computer science , physics , mathematical analysis , quantum mechanics , programming language
A power set of a set S is defined as the set of all subsets of S, including set S itself and empty set, denoted as P(S) or 2S. Given a finite set S with |S|=n hypothesis, one property of power set is that the amount of subsets of S is |P(S)| = 2n. However, the physica meaning of power set needs exploration. To address this issue, a possible explanation of power set is proposed in this paper. A power set of n events can be seen as all possible k-combination, where k ranges from 0 to n. It means the power set extends the event space in probability theory into all possible combination of the single basic event. From the view of power set, all subsets or all combination of basic events, are created equal. These subsets are assigned with the mass function, whose uncertainty can be measured by Deng entropy. The relationship between combinatorial number, Pascal's triangle and power set is revealed by Deng entropy quantitively from the view of information measure.