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Conditional Fuzzy Entropy of Maps in Fuzzy Systems

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Abstract

The fuzzy entropy was investigated as an isomorphism invariant in the last decade. The aim of this paper is to define and study a new invariant called conditional fuzzy entropy which is an extension of fuzzy entropy on fuzzy dynamical systems. This new invariant possesses some basic properties, such as isomorphic invariant, power rule, affinity, and generator. The analysis used in the proof of these properties relies on more techniques of ergodic theory and topological dynamics.

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  1. Department of Applied Mathematics, Chinese Culture University, Yangmingshan, 11114, Taipei, Taiwan

    Wen-Chiao Cheng

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  1. Wen-Chiao Cheng
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Correspondence to Wen-Chiao Cheng.

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Cheng, WC. Conditional Fuzzy Entropy of Maps in Fuzzy Systems. Theory Comput Syst 48, 767–780 (2011). https://doi.org/10.1007/s00224-010-9268-5

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  • DOI: https://doi.org/10.1007/s00224-010-9268-5

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