Abstract
Negation operation is important in intelligent information processing. Different 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, and we find that the fix point is the uniform probability distribution, which reaches the maximum entropy. 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.
Highlights
Knowledge representation and uncertainty measure are important issues in artificial intelligence [21,13,51,9]
Applying the proposed exponential negation to the probability distribution causes it to converge to the maximum entropy state
The entropy in the proposed exponential negation will converge to a uniform distribution in this special binary case which is common in the real world
Summary
Knowledge representation and uncertainty measure are important issues in artificial intelligence [21,13,51,9]. Yager proposed an important method of negation which has the maximum entropy allocation [53]. Inspired by Yager’s negation, the negation of joint and marginal probability distributions in the binary case is proposed [40]. Combining the negative distribution of probability with evidence theory is a popular application direction According to this idea, a method for determining the weight of the sum of probability distribution based on MCDM is proposed recently [41]. All the existing negation methods have the similar structure with Yager’s negation, whose aim is to achieve the maximum entropy in the final status. None of existing methods can achieve the maximum entropy To address this issue, an exponential negation is proposed in this article.
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