http://www.eoht.info/page/Fuzzy+entropy

"In science, fuzzy entropy is the entropy of a fuzzy set, loosely representing the information of uncertainty. [1] The fuzzy entropy is peculiar to mathematics, information theory, and computer science, tracing to the fuzzy set (1965) and fuzzy logic (1973) theories of Iranian-born American electrical engineer and computer scientist Lotfi Zadeh, who extended the Claude Shannon entropy theory to be applied as a fuzzy entropy of a fuzzy subset for a finite set. [2] The conception of fuzzy entropy, in some publications, seems to find crude overlap, carrying thermodynamic connotations into other fields, although mostly baseless."

However, there is no fuzzy entropy in thermodynamics. Such a thing does not exists in thermodynamics.

There is no fuzzy set in thermodynamics. Thermodynamics deals with well defined thermodynamic systems, using defined content and borders since Clausius.

So this fuzzy entropy (whatever it means) cannot carry any thermodynamic connotations.

In thermodynamics there are two types of entropies. 

1. Thermodynamic entropy S and

2. Residual entropy So or sometime in literature Ro

You may conclude that fuzzy entropy is absolutely not related to thermodynamic concept raised by Clausius 150 years ago. 

http://www.eoht.info/page/Fuzzy+entropy

"In science, fuzzy entropy is the entropy of a fuzzy set, loosely representing the information of uncertainty. [1] The fuzzy entropy is peculiar to mathematics, information theory, and computer science, tracing to the fuzzy set (1965) and fuzzy logic (1973) theories of Iranian-born American electrical engineer and computer scientist Lotfi Zadeh, who extended the Claude Shannon entropy theory to be applied as a fuzzy entropy of a fuzzy subset for a finite set. [2] The conception of fuzzy entropy, in some publications, seems to find crude overlap, carrying thermodynamic connotations into other fields, although mostly baseless."

However, there is no fuzzy entropy in thermodynamics. Such a thing does not exists in thermodynamics.

There is no fuzzy set in thermodynamics. Thermodynamics deals with well defined thermodynamic systems, using defined content and borders since Clausius.

So this fuzzy entropy (whatever it means) cannot carry any thermodynamic connotations.

In thermodynamics there are two types of entropies. 

1. Thermodynamic entropy S and

2. Residual entropy So or sometime in literature Ro

You may conclude that fuzzy entropy is absolutely not related to thermodynamic concept raised by Clausius 150 years ago. 

Entropy: A concept that is not a physical quantity

https://www.researchgate.net/publication/230554936_Entropy_A_concept_that_is_not_a_physical_quantity

Fuzzy entropy can be deterministic or stochastic.

A fuzzy entropy is a function on fuzzy sets that becomes smaller when the sharpness of its argument fuzzy set is improved [1]. This definition is more appropriate in image processing domain.

[1] W. Tao, J. Tian, and J. Liu, “Image segmentation by three-level threshold- ing based on maximum fuzzy entropy and genetic algorithm”, J. Pattern Recognition Letters, vol. 24, pp. 3069-â ˘

A¸ S3078, 2003.