Fuzzy entropy: a brief survey

This paper presents a survey about different types of fuzzy information measures. A number of schemes have been proposed to combine the fuzzy set theory and its application to the entropy concept as a fuzzy information measurements. The entropy concept, as a relative degree of randomness, has been utilized to measure the fuzziness in a fuzzy set or system. However, a major difference exists between the classical Shannon entropy and the fuzzy entropy. In fact while the later deals with vagueness and ambiguous uncertainties, the former tackles probabilistic uncertainties (randomness).

[1]  Settimo Termini,et al.  Entropy of L-Fuzzy Sets , 1974, Inf. Control..

[2]  C. S. George Lee,et al.  Neural fuzzy systems: a neuro-fuzzy synergism to intelligent systems , 1996 .

[3]  Wolfgang Sander On measures of fuzziness , 1989 .

[4]  P.K Sahoo,et al.  A survey of thresholding techniques , 1988, Comput. Vis. Graph. Image Process..

[5]  Didier Dubois,et al.  Fuzzy sets and systems ' . Theory and applications , 2007 .

[6]  B. Kosko Fuzziness vs. probability , 1990 .

[7]  Tamaz Gachechiladze,et al.  Entropy of fuzzy events , 1997, Fuzzy Sets Syst..

[8]  M. T. Lamata,et al.  Entropy measures associated with a fuzzy basic probability assignment , 1997, Proceedings of 6th International Fuzzy Systems Conference.

[9]  R. Yager ON THE MEASURE OF FUZZINESS AND NEGATION Part I: Membership in the Unit Interval , 1979 .

[10]  Samuel D. Bedrosian,et al.  An information measure for fuzzy sets , 1984, IEEE Transactions on Systems, Man, and Cybernetics.

[11]  Tianxu Zhang,et al.  Local entropy-based transition region extraction and thresholding , 2003, Pattern Recognit. Lett..

[12]  J. J. Gerbrands Segmentation of noisy images , 1988 .

[13]  A. Ramer CONCEPTS OF FUZZY INFORMATION MEASURES ON CONTINUOUS DOMAINS , 1990 .

[14]  A. Kaufmann,et al.  Introduction to fuzzy arithmetic : theory and applications , 1986 .

[15]  Li-Xin Wang,et al.  A Course In Fuzzy Systems and Control , 1996 .

[16]  Okyay Kaynak,et al.  Entropy-based operations on fuzzy sets , 1998, IEEE Trans. Fuzzy Syst..

[17]  Sankar K. Pal,et al.  A review on image segmentation techniques , 1993, Pattern Recognit..

[18]  L. Zadeh Probability measures of Fuzzy events , 1968 .

[19]  Ute St. Clair,et al.  Fuzzy Set Theory: Foundations and Applications , 1997 .

[20]  L. Goddard Information Theory , 1962, Nature.

[21]  Sankar K. Pal,et al.  Higher order fuzzy entropy and hybrid entropy of a set , 1992, Inf. Sci..

[22]  Ronald R. Yager,et al.  On the Measure of Fuzziness and Negation. II. Lattices , 1980, Inf. Control..

[23]  Robert B. Ash,et al.  Information Theory , 2020, The SAGE International Encyclopedia of Mass Media and Society.

[24]  Settimo Termini,et al.  A Definition of a Nonprobabilistic Entropy in the Setting of Fuzzy Sets Theory , 1972, Inf. Control..

[25]  Dagmar Markechová,et al.  The entropy of fuzzy dynamical systems, general scheme and generators , 1998, Fuzzy Sets Syst..

[26]  Bart Kosko,et al.  Fuzzy entropy and conditioning , 1986, Inf. Sci..

[27]  Lefteri H. Tsoukalas,et al.  Fuzzy and neural approaches in engineering , 1997 .

[28]  Beloslav Riečan,et al.  The entropy of fuzzy dynamical systems , 1997 .

[29]  Xiu-Gang Shang,et al.  A note on fuzzy information measures , 1997, Pattern Recognit. Lett..