ldo@waikato.ac.nz (Lawrence D'Oliveiro, Waikato University) (03/29/91)
This is a novice question. I've read precisely one article on "fuzzy logic" so far that was at all informative, and the understanding I got from it goes like this: * Traditional feedback systems are analog in implementation. Their control signals can be characterized as analytic functions of their present and past error inputs (e g the classic example of the engine governor). Sophisticated control algorithms require more complex analytic functions, which rapidly become unmanageable in an analog-only implementation. * With computers, it becomes possible to have control outputs which are arbitrary combinatorial functions of present and past error inputs. * "Fuzzy logic" lies somewhere between a purely analytic and an arbitrarily combinatorial form; control functions are now _piecewise analytic_ (a hybrid digital/analog approach). A combinatorial decision procedure selects a different analytic function, depending on the ranges of the error inputs. The resulting compound function is continuous across the decision boundaries. Does this agree with what other people understand by "fuzzy logic"? If so, there isn't really anything in it that can be described as "fuzzy". Please correct me if I'm wrong. Lawrence D'Oliveiro fone: +64-71-562-889 Computer Services Dept fax: +64-71-384-066 University of Waikato electric mail: ldo@waikato.ac.nz Hamilton, New Zealand 37^ 47' 26" S, 175^ 19' 7" E, GMT+12:00 $ show node %DCL-W-ABKEYW, ambiguous qualifier or keyword - supply more characters \NODE\
ah314368@longs.LANCE.ColoState.EDU (Vincent Huffaker) (03/30/91)
>This is a novice question. I've read precisely one article on >"fuzzy logic" so far that was at all informative, and the >understanding I got from it goes like this: >* Traditional feedback systems are analog in implementation. Their >control signals can be characterized as analytic functions of their... >* With computers, it becomes possible to have control outputs >which are arbitrary combinatorial functions of present and... >* "Fuzzy logic" lies somewhere between a purely analytic and >an arbitrarily combinatorial form; control functions are now.... >Does this agree with what other people understand by "fuzzy logic"? >If so, there isn't really anything in it that can be described >as "fuzzy". Please correct me if I'm wrong. Recently, I've also been wondering about fuzzy logic and just what it is. There's been an incredible amount of hype about it. If a reporter doesn't understand the logic behind something, it suddenly becomes "fuzzy-logic". According to all the sources, Japan loves it and America doesn't care about it (so, of course, America is behind). There's supposed to be new cameras coming out that use "fuzzy-logic" for their auto-focusing mechanisms. As for your description, I've never heard of fuzzy logic being described as a analog-digital hybrid before. But then again, I've never heard any satisfactory descriptions of fuzzy-logic (I'm still thinking about yours). All the times I've heard about it, its description has sounded like conditional logic (or probabilistic logic). All the reports talk about how now you can define "fuzzy" sets like (short, medium, tall, very tall) rather being restricted to two-valued sets (true, false). In normal logic, if you have a set (say a set of tall people), then a person is either in the set or not in the set. There is no in-between. Conditional logic allows you to assign probabilities to statements. A person can be in the set with a certain probability. The complications begin when you start to apply operators like 'and' or 'or'. In normal logic, this is easy (true 'and' true) = true. In conditional logic, you might have multiple probabilistic dependencies that have to be calculated in a reasonable manner. If I recall right, the expert system Mycin used a simplistic method to apply those operators. If you had three statements with probabilities of 0.2,0.4, and 0.8, then the 'OR' of those three statements was simply the greatest value (0.8) and the 'AND' of those three statements was simply the lowest value (0.2). So, in order to give something that people can respond to (I'm really curious about what fuzzy-logic really is), I make the following claim: Fuzzy-logic is essentially conditional logic but with a well-defined method (I don't know what it is) for applying operators (like 'and' or 'or') to statements with multiple probabilistic dependencies. Any comments? (I hope so.) -Vincent Huffaker e-mail = ah314368@longs.lance.colostate.edu ------------------------------------------------------------------- No, I haven't made my .sig file yet and thanks so much for reminding me.
cpshelley@violet.uwaterloo.ca (cameron shelley) (03/30/91)
In article <13842@ccncsu.ColoState.EDU> ah314368@longs.LANCE.ColoState.EDU (Vincent Huffaker) writes: [...] >Recently, I've also been wondering about fuzzy logic and just what it is. >There's been an incredible amount of hype about it. If a reporter doesn't >understand the logic behind something, it suddenly becomes "fuzzy-logic". >According to all the sources, Japan loves it and America doesn't care about >it (so, of course, America is behind). There's supposed to be new >cameras coming out that use "fuzzy-logic" for their auto-focusing mechanisms. [...] >So, in order to give something that people can respond to (I'm really >curious about what fuzzy-logic really is), I make the following claim: > >Fuzzy-logic is essentially conditional logic but with a well-defined >method (I don't know what it is) for applying operators (like 'and' or 'or') >to statements with multiple probabilistic dependencies. > >Any comments? (I hope so.) I don't have any more insight than you on this, but I can tell you what I surmised from a talk Lofti Zadeh ("Mr. Fuzzy Logic") gave here a few weeks ago. It seems that fuzzy logic is an ontological go-between from `classical' logic and probability. Classical logic is (among other things) a system for dealing with objects by assigning them values from a discrete set (usually two --- binary logic). Probability is a system which deals with objects by assigning them values from a continuous set (bounded between real values 0 and 1). From what Dr. Zadeh said, fuzzy logic is an attempt at a system to deal with objects by assigning them values from a `large' discrete set but without a well-definable order relation (such as "<" in probability). If this sounds obscure, then I can at least say I've accurately communicated my current mental state on the subject. :-) Cam -- Cameron Shelley | "Belladonna, n. In Italian a beautiful lady; cpshelley@violet.waterloo.edu| in English a deadly poison. A striking example Davis Centre Rm 2136 | of the essential identity of the two tongues." Phone (519) 885-1211 x3390 | Ambrose Bierce
ttoupin@diana.cair.du.edu (Tory Toupin) (03/30/91)
While we are on the subject, what is the significance of the term "first order predicate calculus"? What is "nth other predicate calculus"? Perchance "fuzzy-logic"? -- Tory S. Toupin | ttoupin@diana.cair.du.edu | Existence toward perfection... Unversity of Denver | Life of mediocrity. Undergraduate: Math & Computer Sciences| Denver, CO 80208 | -Tory Toupin ----- C'est ne pas un fichier de <<.signature>>
epstein@sunc4.cs.uiuc.edu (Milt Epstein) (03/30/91)
In <1991Mar30.030729.15540@mercury.cair.du.edu> ttoupin@diana.cair.du.edu (Tory Toupin) writes: >While we are on the subject, what is the significance of the term "first order >predicate calculus"? What is "nth other predicate calculus"? Perchance >"fuzzy-logic"? First-order means you can only quantify over objects in the domain of discourse -- that is, variables can only represent objects. In second-order, you can quantify over functions and predicates, such as: (forall (P) (P A) ==> (P B)) (everything that is true of A is true of B). I guess I had never dealt with anything beyond second-order, but I found something about higher-order logics in "The Computer Modelling Of Mathematical Reasoning" by Alan Bundy. It talks about the ideas of "functionals", "lambda abstractions" and "omega order logic", which I have not really heard of before (except lambda abstractions). Fuzzy logic, as some other people have pointed out, is something of a cross between classical (two-valued) logic and probability (where you have continuous values between 0 and 1). -- Milt Epstein Department of Computer Science University of Illinois epstein@cs.uiuc.edu
yee@edison.seas.ucla.edu (John Yee) (03/30/91)
While we are all asking questions about fuzzy logic (my understanding being that it allows for more uncertainty that true/false), can someone tell me how it is actually implemented on a computer. Being but an ignoramus in all languages newer than Fortran, I naively think that in making a decision, a computer has to execute as statement like "if x > 10 then [do something]". How would a computer decide whether an object is "tall" without something like "if x > 999 then (x in tall)"? Thanks, yee@seas.ucla.edu
wido@isgtec.uucp (Wido Menhardt) (03/31/91)
In article <13842@ccncsu.ColoState.EDU> ah314368@longs.LANCE.ColoState.EDU (Vincent Huffaker) writes: > Recently, I've also been wondering about fuzzy logic and just what it is. I would recommend to take a dive into literature. There is nothing fuzzy about Fuzzy Logic, and that's the way to find out. [stuff deleted] > Fuzzy-logic is essentially conditional logic but with a well-defined > method (I don't know what it is) for applying operators (like 'and' or 'or') > to statements with multiple probabilistic dependencies. Now, this *IS* fuzzy!
wido@isgtec.uucp (Wido Menhardt) (03/31/91)
In article <27F41DFC.3E0E@ibma0.cs.uiuc.edu> epstein@sunc4.cs.uiuc.edu (Milt Epstein) writes: [..] > Fuzzy logic, as some other people have pointed out, is something of a > cross between classical (two-valued) logic and probability (where you > have continuous values between 0 and 1). Fuzzy logic is simply a multi-valued logic; and it is not the only one, although quite popular (and successful) in a number of fields, like pattern recognition, vision, XPS, NN, process control.... Fuzzy logic has nothing to do with probability, except for the fact that the range of truth values are usually taken from the interval [0,1]. On the contrary, it is _dangerous_ to think of fuzzy variables as of random variables, because both the concepts and the operators are quite different. It seems like somebody should post a tutorial.... so little time.
kadie@herodotus.cs.uiuc.edu (Carl M. Kadie) (04/01/91)
In <13842@ccncsu.ColoState.EDU> ah314368@longs.LANCE.ColoState.EDU (Vincent Huffaker) writes: [...] >Fuzzy-logic is essentially conditional logic but with a well-defined >method (I don't know what it is) for applying operators (like 'and' or 'or') >to statements with multiple probabilistic dependencies. [...] When Dr. Zadeh spoke here last semester, he was asked if Fuzzy Logic provided (required) a particular combination function. He said no; you should use whatever combination function worked. Likewise it does not provide (require) any particular possibility distribution; you should use whatever works. -- Carl Kadie -- kadie@cs.uiuc.edu -- University of Illinois at Urbana-Champaign
ah314368@longs.LANCE.ColoState.EDU (Anthony Huffaker) (04/02/91)
> > I would recommend to take a dive into literature. There is nothing > fuzzy about Fuzzy Logic, and that's the way to find out. > Are there any reports in particular that you feel give a good introduction (not too "fuzzy") to Fuzzy Logic? -Vincent Huffaker e-mail = ah314368@longs.lance.colostate.edu ----------------------------------------------------------------- No, I don't have a .sig file yet, and thanks so much for reminding me!
mcovingt@athena.cs.uga.edu (Michael A. Covington) (04/02/91)
In fuzzy logic, truth values range from 0 to 1. The logical functions "and", "or", etc., are floating-point functions that combine two truth-values to get another truth-value. So "if Joe is tall and gangly" might be rendered in FORTRAN as IF (AND(TALL(JOE),GANGLY(JOE))>0.5) ... That is: If the AND function, applied to TALL(JOE) and GANGLY(JOE), yields a value greater than 0.5, then... (where TALL(JOE) and GANGLY(JOE) would each give a floating-point value between 0 and 1). -- ------------------------------------------------------- Michael A. Covington | Artificial Intelligence Programs The University of Georgia | Athens, GA 30602 U.S.A. -------------------------------------------------------
ken@aiai.ed.ac.uk (Ken Johnson) (04/02/91)
In article <1991Apr1.205421.8079@athena.cs.uga.edu> mcovingt@athena.cs.uga.edu (Michael A. Covington) writes: >In fuzzy logic, truth values range from 0 to 1. In some versions, truth varies from -1 to +1, with -1 meaning `certainly false', +1 meaning `certainly true' and 0 meaning `don't know'. E.g. ``It is raining now in Los Angeles'' has a truth value of 0 (for me) because I have no evidence one way or the other, but ``It is raining now in Edinburgh'' has a truth value of -1 because I can see the sun shining. The version implemented in the `Fril' language goes a step further, and a truth value is indicated as a range. E.g. the truth value of some statement might be written as (0.5 0.7) meaning that its certainty lies somewhere between 0.5 and 0.7 inclusive. A probability can also be attached to a rule as a probability of implication. ``It is raining --> the sidewalk is wet'' has a certainty of +1 since the sidewalk always gets wet when it rains, but ``It is raining --> Louise is wet'' has a certainty of around 0.2 as Louise doesn't usually go out in the rain. Ken Johnson, AIAI This is the Earth. No-one gets out of here alive 80 South Bridge, Edinburgh PAY NO ROOF TAX! PAY NO RATES! E-mail ken@aiai.ed.ac.uk 031-650 2756 direct line Muslims say: Hands Off Shoplifters
mikeb@wdl35.wdl.loral.com (Michael H Bender) (04/03/91)
> kadie@herodotus.cs.uiuc.edu (Carl M. Kadie) writes: > ah314368@longs.LANCE.ColoState.EDU (Vincent Huffaker) writes: > [...] > >Fuzzy-logic is essentially conditional logic but with a well-defined > >method (I don't know what it is) for applying operators (like 'and' or 'or') > >to statements with multiple probabilistic dependencies. > [...] > > When Dr. Zadeh spoke here last semester, he was asked if Fuzzy Logic > provided (required) a particular combination function. He said no; you > should use whatever combination function worked. Likewise it does > not provide (require) any particular possibility distribution; you should > use whatever works. > > Carl Kadie -- kadie@cs.uiuc.edu -- University of Illinois at Urbana-Champaign I think there is legitimate reason for confusion here. It is my understanding that in Dr.Zadeh's originial work he DID specify various combination functions (e.g., how AND and OR would operate.) However, his specifications seemed to be arbitrary and did not stand up well to the force of criticism. As a result, many practicioners (myself included) have developed our own combination functions. It is my belief that Dr. Zadeh may have changed his mind over the years. By the way - Does anyone have information about what combination functions are designed into the "FUZZY CHIPS" which have been developed in Japan and in the United States? Mike Bender
ntm1169@dsac.dla.mil (Mott Given) (04/03/91)
From article <13842@ccncsu.ColoState.EDU>, by ah314368@longs.LANCE.ColoState.EDU (Vincent Huffaker): > Fuzzy-logic is essentially conditional logic but with a well-defined > method (I don't know what it is) for applying operators (like 'and' or 'or') > to statements with multiple probabilistic dependencies. Quoting from an article on page 32 of the March 18, 1991 issue of "Information Week", fuzzy logic is "a generalization of the mathematical notion of set membership, in which an element may have partial membership in a set." For more information I would suggest reading the papers and books of Lofti Zadeh. -- Mott Given @ Defense Logistics Agency Systems Automation Center, DSAC-TMP, Bldg. 27-1, P.O. Box 1605, Columbus, OH 43216-5002 INTERNET: mgiven@dsac.dla.mil UUCP: ...{osu-cis}!dsac!mgiven Phone: 614-238-9431 AUTOVON: 850-9431 FAX: 614-238-9928 I speak for myself
kadie@herodotus.cs.uiuc.edu (Carl M. Kadie) (04/03/91)
In <MIKEB.91Apr2090235@wdl35.wdl.loral.com> mikeb@wdl35.wdl.loral.com (Michael H Bender) writes: [...] >I think there is legitimate reason for confusion here. It is my >understanding that in Dr.Zadeh's originial work he DID specify various >combination functions (e.g., how AND and OR would operate.) However, his >specifications seemed to be arbitrary and did not stand up well to the >force of criticism. As a result, many practicioners (myself included) have >developed our own combination functions. It is my belief that Dr. Zadeh >may have changed his mind over the years. [...] Are these new combination functions less arbitrary? (Alternatively, do they show that any choice of combination function is arbitrary?) -- Carl Kadie -- kadie@cs.uiuc.edu -- University of Illinois at Urbana-Champaign
G.Moretti@massey.ac.nz (Giovanni Moretti) (04/03/91)
The easiest way I've found to think about fuzzy logic as related to
expert systems, is that you have rules with conditions and results in
the usual way, except that the conditions may have a modifier
attached to them so they're not BOOLEAN (ie TRUE or FALSE) but have
some degree of being TRUE or applicable.
How well the conditions are fulfilled affects how much significance
is given to the conclusion.
So, instead of the usual rules:
1) if HEATSINK_TEMP > HOT and AMBIENT_TEMPERATURE = HOT then FAN:= ON
2) if HEATSINK_TEMP < HOT Then FAN:= OFF
where Heatsink_temp is an integer and hot = 55
we could have in a fuzzy system
3) if HEATSINK_TEMP is HOT then INCREASE power_to_fan
4) if HEATSINK_TEMP is COLD then DECREASE power_to_fan
where Heatsink temperature is one of COLD, COOL, MODERATE, WARM and HOT
THIS is CRUCIAL
***********************************************************************
* ALL OF THE RULES AND THEIR CONCLUSIONS ARE EVALUATED EVERY TIME *
***********************************************************************
This means that:
-rule 3's conclusion will be evaluated even if the temperature is COLD
but the value of the increase will be very small.
However as the temperature increases,
the increase in fan power from rule 3 starts to dominate as the value
of HEATSINK_TEMP approaches HOT (the gradations of TEMPERATURE may be
COLD, COOL, MODERATE, WARM and HOT). The value of INCREASE or DECREASE
are related to how closely the conditions are met.
This would give much smoother control of the temperature with only
two rules than the brute force FULL-ON or FULL-OFF approach.
*** This evaluation of all of the rules all of the time means that the
system can easily handle conflicting rules and inputs.
*** The significance given to the conclusion is related to how well the
conditions are met, meaning that fewer rules are necessary.
There you have it - my understanding in a nutshell ...
I just wish it didn't sound so authoritative :-)
For more info:
REFERENCES:
Here's some of the articles I've found relating to Fuzzy Logic,
listed in order of ease of comprehension for a newcomer.
"Designing with Fuzzy Logic", Kevin Self, IEEE Spectrum, Nov 1990 p42 ..
Easy to read introduction - START HERE.
"Knowledge Representation in Fuzzy Logic" by Lofti Zaheh.
IEEE Transactions on Knowledge and Data Engineering, Vo1 No1 March
1989, p89.
This is a good article to go back to after you've read the one above
as it describes Knowledge Representation in fuzzy logic but not
particularly in terms of expert systems.
"Implementing Fuzzy Rule-Based Systems on Silicon Chips" by
Men-Hiot Lim and Yoshiyasu Takifuji. IEEE Expert, February 1990, p31
Building a chip to perform fuzzy inferencing using an example of
determining whether or not to grant a loan based on several financial
criteria. Takes some thinking about but covers a lot of ground and
does it quite well.
"Parallel Rule-based Fuzzy Inference on Mesh-connected Systolic Arrays"
by M.A. Eshera and S.C.Barash. IEEE Expert, Winter 1989 (Vol 4 no
4), p27...
I don't even understand the title and haven't tried to digest the article.
It's heavily into parallel processing, as you might expect from
the title :-).
Cheers
Giovanni
--
------------------------------------------------------------------------------
Giovanni Moretti, Consultant | G.Moretti@massey.ac.nz, Pkt-ZL2BOI@ZL2TCX
Computer Centre, Massey University| Ph 64 63 69099 x8398, FAX 64 63 505607
Palmerston North, New Zealand | QUITTERS NEVER WIN, WINNERS NEVER QUIT
------------------------------------------------------------------------------rlee@ADS.COM (Richard Lee) (04/04/91)
In article <kadie.670617272@herodotus.cs.uiuc.edu> kadie@herodotus.cs.uiuc.edu (Carl M. Kadie) writes: |In <MIKEB.91Apr2090235@wdl35.wdl.loral.com> mikeb@wdl35.wdl.loral.com (Michael H Bender) writes: | |>It is my understanding that in Dr.Zadeh's originial work he DID |>specify various combination functions (e.g., how AND and OR would |>operate.) However, his specifications seemed to be arbitrary and did |>not stand up well to the force of criticism. | |Are these new combination functions less arbitrary? | |(Alternatively, do they show that any choice of combination function |is arbitrary?) I strongly recommend reading "Foundations of Fuzzy Reasoning" by B.R. Gaines (Int'l Journal of Man-Machine Studies #8, 1976, pp 623-668). This paper provides an interesting introduction to fuzzy logic and fuzzy set theory. More to the point, it also has a lengthy discussion of the constraints one might want to impose on a fuzzy logic -- e.g. reducibility to classical logic, associativity, and certain intuitive properties -- and how various choices of functions for And, Or, Not, Implies, etc. meet those constraints. It is worth noting that what constitutes the "right" choice of functions may depend on what the logic is to be used for. The cognitive psychologist Greg Oden has written a number of papers which claim that different choices are appropriate for modelling human cognitive processing on different types of tasks.
mikeb@wdl35.wdl.loral.com (Michael H Bender) (04/04/91)
> kadie@herodotus.cs.uiuc.edu (Carl M. Kadie) writes: > mikeb@wdl35.wdl.loral.com (Michael H Bender) writes: >> [...] >> I think there is legitimate reason for confusion here. It is my >> understanding that in Dr.Zadeh's originial work he DID specify various >> combination functions (e.g., how AND and OR would operate.) However, his >> specifications seemed to be arbitrary and did not stand up well to the >> force of criticism. As a result, many practicioners (myself included) have >> developed our own combination functions. It is my belief that Dr. Zadeh >> may have changed his mind over the years. >> [...] > Are these new combination functions less arbitrary? > (Alternatively, do they show that any choice of combination function > is arbitrary?) > Yes and no. It is my understanding of research conducted by Bonnissone (sp) and others on the class of functions called "T-Norms" that as long as the combination function belongs to this class it can be considered "consistent". I am not aware of any criteria for selecting a single function from this class. Further, I would argue that there are good grounds for selecting different functions, based on the individual application. I do not know if the Zadeh's original definitions fit into the family of T-Norms or not. Mike Bender
jagversm@cs.ruu.nl (Koen Versmissen) (04/04/91)
Talking about fuzzy logic, does any of you know a reference to the connection between fuzzy logic and topos theory? (I recall reading somewhere that toposes are well suited to define fuzzy logics, but are they of any real use?)> Koen. -- Koen Versmissen, Rijksuniversiteit Utrecht, Nederland. (jagversm@praxis.cs.ruu.nl).
spratt@hawk.cs.ukans.edu (Lindsey Spratt) (04/05/91)
I have spent some time working with fuzzy logic. There is an expert system shell I implemented to explore some issues in this area. MESS (Modest Expert System Shell, or My Expert System Shell) is a backward-chaining rule-based system built on top of the LPA MacProlog environment. In it, I use fuzzy truth values on the rules and the user can associate fuzzy truth values with her answers. That is, a truth value is a fuzzy set (or fuzzy data value) defined over the interval [0,1]. This is instead of simply having a truth value of some particular number (say 0.783)as the truth value associated with a rule or answer. The fuzzy truth values are named, for ease of reference in writing the rules and in answering questions. In this approach, one can represent the "unknown" truth value as the fuzzy set in which all truth values in the range [0,1] have a membership of 1. Some interesting problems in this approach include defining an ordering on fuzzy truth values and defining a similarity measure for fuzzy truth values, in addition to the perhaps obvious problems of defining the logical connectives and negation. The similarity measure is used to report results to the user. The processing of a query produces a result with some associated fuzzy truth value. This associated truth value may not have exactly the same membership function as any of the pre-defined (and named) fuzzy truth values. Rather than report the membership function to the user, the name of the most-similar predefined fuzzy truth value is reported instead. I'd like to add handling of fuzzy data values as well - so that one can use "linguistic values" in reporting data. Things like "big" vs "little". Lindsey
hanks@june.cs.washington.edu (Steve Hanks) (04/05/91)
Re. the discussion of fuzzy logic, combination functions, and the like: there's a paper by Bart Kosko, titled "Fuzziness vs. Probability", in Int. J. General Systems, Vol 17, 1990, pp. 211-240. First of all, it's a very lucid and interesting paper, although I can't evaluate the technical content since this isn't my area. Anyway, he makes the claim that if you define the entropy of a fuzzy set in a certain way, then min and max are unique among the T-norms (and dual C-norms) in that they maximize the entropy of the defining fuzzy system. Seemed pretty compelling to me, and a fun read regardless of whether you buy the technical point of view or not. Steve.