Logarithmic Entropy Measures for Fuzzy Rough Set and their Application in Decision Making Problem

Decision-making is a critical problem in various circumstances where some vagueness and ambiguity is found in information. To handle these types of problems, entropy is an important measure of information theory which is exploited to evaluate the uncertain degree of any data. There are two methodologies to determine the entropy, one is probabilistic in nature and other is non-probabilistic. It is shown that for every probabilistic measure there is a corresponding non-probabilistic measure. In this article, some logarithmic non-probabilistic entropy measures have been proposed for the fuzzy rough set corresponding to existing probabilistic entropy measures. The proposed measures are employed in a decision-making problem, which is related to the agriculture. Finally, these proposed measures are compared with the existing trigonometric entropy measures for fuzzy rough sets.

Probabilistic Entropy EMD Thresholding for Periodic Fault Signal Enhancement in Rotating Machine

Since the slight fault feature of incipient fault is usually polluted by heavy background noise, it is difficult to extract the weak feature signal in rotating machine. As an adaptive decomposing technique, empirical mode decomposition (EMD) based denoising methods have a good effect on the feature separation and noise elimination. However, for rotating machine with poor working environment, the components attributed to noise might have higher amplitudes, which restrict the efficiency of noise reduction in current EMD-based denoising methods. Therefore, a probabilistic entropy EMD thresholding algorithm for periodic fault signal enhancement in rotating machine is proposed in this paper. In this method, the entropy threshold of each IMF is constructed instead of the threshold applied to N sampling points of each IMF directly, which overcomes the shortcoming of the denoising effect limited by larger amplitude noise reservation and smaller amplitude feature signal reduction in the current denoising methods. Meanwhile, in order to make the amplitudes of all the IMF reduce in a smooth way, a multiscale thresholding algorithm based on quantile statistics to provide probability indexes is presented. Engineering application demonstrates that the proposed method is effective in the noise reduction and fault feature enhancement in the rotating machine.

Towards a Semantic Theory of Information

Information can be understood as that which reduces uncertainty, no matter what origin it has. In the field of human communication, information is only meaningful if it is part of a finished or intentional action. Meaning should be gathered from the empirical perspective of the use of language. If we study the processing of signification through transmission of the normal use of language, we will see that it takes place communicating a set of prototype categories, the core or central facts, which defines meaning as empirical hypothesis. But if there are central facts showing the use of words, then other facts –more or less peripheral– should also exit, whose knowledge is necessary in order to communicate in contexts far away from the “denotative conceptual norm”. Hence meaning can be represented by a fuzzy subset of the universe of discourse partition set. This concept of meaning may be integrated in a formal model of semantic source and information may be measured by non-probabilistic entropy.

Towards a Semantic Theory of Information

Information can be understood as that which reduces uncertainty, no matter what origin it has. In the field of human communication, information is only meaningful if it is part of a finished or intentional action. Meaning should be gathered from the empirical perspective of the use of language. If we study the processing of signification through transmission of the normal use of language, we will see that it takes place communicating a set of prototype categories, the core or central facts, which defines meaning as empirical hypothesis. But if there are central facts showing the use of words, then other facts –more or less peripheral– should also exit, whose knowledge is necessary in order to communicate in contexts far away from the “denotative conceptual norm”. Hence meaning can be represented by a fuzzy subset of the universe of discourse partition set. This concept of meaning may be integrated in a formal model of semantic source and information may be measured by non-probabilistic entropy.