Affiliations: [a] Department of Mathematics, Soochow University, Suzhou, Jiangsu, P.R. China | [b] Department of Applied Mathematics, Chinese Culture University, Taipei, Taiwan
Correspondence:
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Corresponding author. Chih-Chang Ho, Department of Applied Mathematics, Chinese Culture University, Taipei 11114, Taiwan. E-mail: hzc3@faculty.pccu.edu.tw.
Abstract: Shannon entropy is an important tool in the study of information theory. A new fuzzy entropy was introduced by Dumitrescu [5, 6] in the context of fuzzy sets or messages. From the perspective of the fuzzy version, this paper defines the conditional fuzzy entropy of a sequence of fuzzy process, and studies the commutativity behavior of sequential fuzzy entropy in the fuzzy process. Moreover, the commutativity behavior of functions and invariant measures is discussed in those different fuzzy processes. However, our demonstration needs more techniques of topological dynamics and fuzzy analysis.
Keywords: Fuzzy entropy, fuzzy dynamical systems, power rule, commutativity
