# Re: References on fuzzy entropy

Ellen Hisdal (ellen@ifi.uio.no)
Wed, 17 Mar 1999 23:36:11 +0100 (MET)

> Date: Sat, 6 Mar 1999 00:54:36 +0100 (MET)
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> From: Alvaro Fernandez <alvaro@rice.edu>
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> My apologies if this is covered in the FAQ somewhere - could someone
> recommend references where the concept of fuzzy entropy is explained? I
> lurked for a while, hoping someone would start a thread on it, but to no
> avail. :-(
>
> As to my mathematical background, I am a mechanical engineer, which
> means I have good multivariate calculus and real analysis skills, but
> little probability or formal logic. (I did take a course in digital
> circuit design, though, so I know Boolean logic OK).
>
>
>
> Alvaro Fernandez
> Research Assistant
> Rice University
>
>
>
> ############################################################################

Hello Fernandez,

Zadeh has a definition of fuzzy entropy in eq.(28) of the paper

@article{zfuzzyevent,
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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