Exponential Negation of a Probability Distribution

Abstract

Negation operation is important in intelligent information processing. Different with existing arithmetic negation, an exponential negation is presented in this paper. The new negation can be seen as a kind of geometry negation. Some basic properties of the proposed negation are investigated, we find that the fix point is the uniform probability distribution. The proposed exponential negation is an entropy increase operation and all the probability distributions will converge to the uniform distribution after multiple negation iterations. The convergence speed of the proposed negation is also faster than the existed negation. The number of iterations of convergence is inversely proportional to the number of elements in the distribution. Some numerical examples are used to illustrate the efficiency of the proposed negation.

Maximum Entropy of Random Permutation Set

“…The maximum entropy principle states that the distribution with maximal entropy best represents the current state of a system based on given information, which is widely used in many fields, such as negation transformation (Wu, Deng, & Xiong, 2021;Yager, 2014), imprecise side-conditions (Buckley, 2005), fuzzy cognitive maps (Feng, Lu, Pedrycz, Yang, & Liu, 2019), decision making (Yager, 2009), and uncertainty theory (Ma, 2021). As for the maximum entropy principle of RPS entropy, two aspects should be handled.…”

Complex interval number‐based uncertainty modeling method with its application in decision fusion

“…And uncertainty are universal in reality and vital for fusion systems 2 . Therefore, various theories have been established to handle uncertainty, including Z number, 3 rough sets, 4,5 random permutation set, 6–8 intuitionistic fuzzy set, 9–11 and so on 12,13 . Moreover, these theories have been applied in various fields, including data fusion, 14,15 decision making, 16–19 casual inference 20 community detection, 21,22 risk assessment, 23,24 reliability analysis, 25,26 social network analysis, 27 classification, 28,29 fault diagnosis, 30 medical diagnosis, 31,32 and so on.…”