• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.4
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• pp.269-274
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• 2009

Measuring uncertainty for fuzzy sets has been carried out by calculating fuzzy entropy. Fuzzy entropy of fuzzy set is derived with the help of distance measure. The distance proportional value between the fuzzy set and the corresponding crisp set is designed as the fuzzy entropy. The usefulness is verified by proving the proposed entropy. Generally, fuzzy entropy contains the complementary characteristics that the fuzzy entropies of fuzzy set and complementary fuzzy set have the same entropies. Discrepancy that low fuzzy entropy did not guarantee the data certainty was overcome by modifying fuzzy entropy formulation. Obtained fuzzy entropy is analyzed and discussed through simple example.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.4
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• pp.259-262
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• 2010

Study about fuzzy entropy and similarity measure on intuitionistic fuzzy sets (IFSs) were proposed, and analyzed. Unlike fuzzy set, IFSs contains uncertainty named hesistancy, which is contained in fuzzy membership function itself. Hence, designing fuzzy entropy is not easy because of ununified entropy definition. By considering different fuzzy entropy definitions, fuzzy entropy is designed and discussed their relation. Similarity measure was also presented and verified its usefulness to evaluate degree of similarity.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2004.04a
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• pp.349-352
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• 2004

In this literature, the selection of data set among the universe set is carried out with the fuzzy entropy function. By the definition of fuzzy entropy, we have proposed the fuzzy entropy function and the proposed fuzzy entropy function is proved through the definition. The proposed fuzzy entropy function calculate the certainty or uncertainty value of data set, hence we can choose the data set that satisfying certain bound or reference. Therefore the reliable data set can be obtained by the proposed fuzzy entropy function. With the simple example we verify that the proposed fuzzy entropy function select reliable data set.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.5
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• pp.655-659
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• 2004

In this literature, the selection of data set among the universe set is carried out with the fuzzy entropy function. By the definition of fuzzy entropy, the fuzzy entropy function is proposed and the proposed fuzzy entropy function is proved through the definition. The proposed fuzzy entropy function calculate the certainty or uncertainty value of data set, hence we can choose the data set that satisfying certain bound or reference. Therefore the reliable data set can be obtained by the proposed fuzzy entropy function. With the simple example we verify that the proposed fuzzy entropy function select reliable data set.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.5 no.4
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• pp.367-371
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• 2005

The similarity measure is derived using fuzzy entropy and distance measure. By the elations of fuzzy entropy, distance measure, and similarity measure, we first obtain the fuzzy entropy. And with both fuzzy entropy and distance measure, similarity measure is obtained., We verify that the proposed measure become the similarity measure.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.1
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• pp.4-9
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• 2009

Fuzzy entropy is designed for non convex fuzzy membership function using well known Hamming distance measure. Design procedure of convex fuzzy membership function is represented through distance measure, furthermore characteristic analysis for non convex function are also illustrated. Proof of proposed fuzzy entropy is discussed, and entropy computation is illustrated.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2008.04a
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• pp.21-22
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• 2008

Fuzzy entropy is designed for non-convex fuzzy membership function using well known Hamming distance measure. Design procedure of convex fuzzy membership function is represented through distance measure, furthermore characteristic analysis for non-convex function are also illustrated. Proof of proposed fuzzy entropy is discussed, and entropy computation is illustrated.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.12a
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• pp.1-4
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• 2002

There have been several tipical methods being used to measure the fuzziness (entropy) of fuzzy sets. Pedrycz is the original motivation of this paper. This paper studies the entropy variation on the fuzzy numbers with arithmetic operations(addition, subtraction, multiplication) and the relationship between entropy and information energy. It is shown that through the arithmetic operations, the entropy of the resultant fuzzy number has the arithmetic relation with the entropy of each original fuzzy number. Moreover, the information energy variation on the fuzzy numbers is also discussed. The results generalize earlier results of Pedrycz [FSS 64(1994) 21-30] and Wang and Chiu [FSS 103(1999) 443-455].

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.5
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• pp.642-647
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• 2004

The relations of fuzzy entropy, distance measure, and similarity measure are discussed in this paper. For the purpose of reliable signal selection, the fuzzy entropy is proposed by a distance measure. Properness of the proposed entropy is verified by the definition of the entropy measure. Fourier and Wavelet transform are applied to the stator current signal to obtain the fault features of an induction motor. Membership functions for 3-phase currents are obtained by the Bootstrap method and Central Limit Theorem. Finally, the proposed entropy is applied to measure the fault signal of an induction machine, and the fuzzy entropy values of phase currents are illustrated.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.4
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• pp.275-280
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• 2010

Verification of efficiency in data management fuzzy entropy and similarity measure were discussed and verified by applying reliable data selection problem and numerical data similarity evaluation. In order to calculate the certainty or uncertainty fuzzy entropy and similarity measure are designed and proved. Designed fuzzy entropy and similarity are considered as dissimilarity measure and similarity measure, and the relation between two measures are explained through graphical illustration. Obtained measures are useful to the application of decision theory and mutual information analysis problem. Extension of data quantification results based on the proposed measures are applicable to the decision making and fuzzy game theory.