Hello Fernandez,
Zadeh has a definition of fuzzy entropy in eq.(28) of the paper
@article{zfuzzyevent,
author = {Zadeh, L.A.},
title = {Probability Measures of Fuzzy Events},
journal = {Journal of Mathematical Analysis and Applications},
year = {1968},
volume = {23},
ignored = {footnote p. 31. Use of multiplication instead of min for AND.
Mentioned in my book in file intro.tex, sect. 1.7.3.},
pages = {421-427} }
Another definition of a fuzzy entropy is given in
Deluca & Termini (1972) Information and Control, 301-312.
Both of the above two definitions differ from Shannon's definition of
an entropy.
A discussion of these two definitions, and
a definition of a fuzzy entropy which cannot go wrong (because it
makes direct use of Shannon's formula) is given in
@techreport{inf1p4,
author = {Hisdal, E.},
title = {Infinite-Valued Logic Based on Two-Valued Logic and
Probability, Part~1.4. {T}he {TEE} Model},
institution = {Institute of Informatics, University of Oslo, Box
1080 Blindern, 0316 Oslo 3, Norway},
year = {1988,1990},
type = {Research Report},
note = {ISBN~82-7368-054-1} }
This paper can also be found on the internet under
http://www.ifi.uio.no/~ftp/publications/research-reports/Hisdal-4.ps ,
(see eqs (28)-(36) for entropy).
Some of the foundations for this paper are described in
@techreport{inf1p3,
author = {Hisdal, E.},
title = {Infinite-Valued Logic Based on Two-Valued Logic and
Probability, Part~1.3. {Reference Experiments and Label Sets},
institution = {Institute of Informatics, University of Oslo, Box
1080 Blindern, 0316 Oslo 3, Norway},
year = {1988,1990},
type = {Research Report},
note = {ISBN~82-7368-053-3} }
The latter paper can also be found on the internet under
http://www.ifi.uio.no/~ftp/publications/research-reports/Hisdal-3.ps .
Best greetings,
Ellen
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