This paper systematically investigates the properties of six kinds of entropy-based risk measures: Information Entropy and Cumulative Residual Entropy in the probability space, Fuzzy Entropy, Credibility Entropy and Sine Entropy in the fuzzy space, and Hybrid Entropy in the hybridized uncertainty of both fuzziness and randomness. We discover that none of the risk measures satisfy all six of the...

After generalization of Shannon‘s entropy measure by Renyi in 1961, many generalized versions of Shannon measure were proposed by different authors. Shannon measure can be obtained from these generalized measures asymptotically. A natural question arises in the parametric generalization of Shannon‘s entropy measure. What is the role of the parameter(s) from application point of view? In the pre...

The entropy of intuitionistic fuzzy sets is used to indicate the degree of fuzziness of an interval-valued intuitionistic fuzzy set(IvIFS). In this paper, we deal with the entropies of IvIFSs. Firstly, we propose a set of entropies on IvIFSs with a parameter λ ∈ [0,+∞), which generalizes the entropy measure defined by Gao, for IvIFSs, and then we prove that the new entropy is an increasing func...

Brain tumor is the most deadly disease that affects human life span. To segment the brain tumor part, many segmentation techniques have been emerged in image processing like region based Segmentation, Boundary based segmentation. In this paper, several entropies based methods and several cluster techniques are compared and analyzed for brain tumor segmentation. Several entropies such as rough e...

The main attribution of this paper is to propose two methods to construct entropy of interval valued fuzzy sets (IVFSs). First, we use an IVFS to construct two FSs and define entropy by similarity measure of the two FSs; then we use an IVFS to construct two IVFSs and also define entropy by similarity measure of the two IVFSs. At the same time, we give two examples to show that our methods are e...

The present paper introduces a parametric generalized exponential measure of fuzzy divergence of order α with the proof of its validity. A particular case of proposed fuzzy divergence measure is studied. Some properties of the new divergence measure between different fuzzy sets are proved. We establish a relation between exponential fuzzy entropy of order α and our fuzzy divergence measure. Fur...

The information-theoretical entropy is an effective measure of uncertainty connected with an information source. Its transfer from the classical probabilistic information theory models to the fuzzy set theoretical environment is desirable and significant attempts were realized in the existing literature. Nevertheless, there are some open topics for analysis in the suggested models of fuzzy entr...

This paper presents an efficient fuzzy classifier with the ability of feature selection based on a fuzzy entropy measure. Fuzzy entropy is employed to evaluate the information of pattern distribution in the pattern space. With this information, we can partition the pattern space into nonoverlapping decision regions for pattern classification. Since the decision regions do not overlap, both the ...