Tsallis Entropy and Conditional Tsallis Entropy of Fuzzy Partitions

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Zarenezhad m.h.; EBRAHIMZADEH A.

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ISSN: 2588-4824

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Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2019 | Volume:5 | Issue:19 Page(s): 5-18

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Title

Tsallis Entropy and Conditional Tsallis Entropy of Fuzzy Partitions

Author(s)

Zarenezhad m.h. | EBRAHIMZADEH A. | Issue Writer Certificate

Keywords

fuzzy partitionQ1

Tsallis entropyQ1

conditional Tsallis entropyQ1

Abstract

The purpose of this study is to define the concepts of Tsallis entropy and conditional Tsallis entropy of fuzzy partitions and to obtain some results concerning this kind entropy. We show that the Tsallis entropy of fuzzy partitions has the subadditivity and concavity properties. We study this information measure under the refinement and zero mode subset relations. We check the chain rules for this information measure and prove some properties about the entropy of independent fuzzy partitions. Some results of the relationship between the Tsallis entropy and conditional Tsallis entropy of fuzzy partitions are obtained and, by using conditional Tsallis entropy of fuzzy partitions, we show that the subadditivity property for Tsallis entropy of fuzzy partitions is not established in the case that the parameter of this entropy is smaller than one. In general, the Tsallis entropy of fuzzy partitions has similar properties to the shannon entropy, where the parameter of this entropy is larger than one, and therefore can be used in addition to the Shannon entropy, to measure the amount of information to be extracted from a fuzzy experiment.

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APA: Copy

Zarenezhad, m.h., & EBRAHIMZADEH, A.. (2019). Tsallis Entropy and Conditional Tsallis Entropy of Fuzzy Partitions. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 5(19 ), 5-18. SID. https://sid.ir/paper/257338/en

Vancouver: Copy

Zarenezhad m.h., EBRAHIMZADEH A.. Tsallis Entropy and Conditional Tsallis Entropy of Fuzzy Partitions. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2019;5(19 ):5-18. Available from: https://sid.ir/paper/257338/en

IEEE: Copy

m.h. Zarenezhad, and A. EBRAHIMZADEH, “Tsallis Entropy and Conditional Tsallis Entropy of Fuzzy Partitions,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 5, no. 19 , pp. 5–18, 2019, [Online]. Available: https://sid.ir/paper/257338/en

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