<p>I wouldn't consider fuzzy logic dead. For control systems, I don't know. However, there's been a lot of activity in fuzzy logics for proof theorists for the last several years: look for papers by Ciabattoni, Olivetti, Fermüller, Metcalfe, and Baaz for starters.</p>

<p><strong>Edit:</strong> Some specific references from my BibTeX file:</p>

<ul>
<li>D. Galmiche and Y. Sahli, Labelled Calculi for Łukasiewicz Logics, Int. Workshop on Logic, Language, Information and Computation, WoLLIC'08, Edinburgh, LNAI 5110, 2008.</li>
<li>M. Baaz and G. Metcalfe, Proof Theory for First Order Łukasiewicz Logic. TABLEAUX 2007.</li>
<li>D. Galmiche and D. Larchey-Wendling and Y. Salhi, Provability and Countermodels in Gödel-Dummett Logics, DISPROVING'07: Workshop on Disproving Non-Theorems, Non-Validity, and Non-Provability, 2007.</li>
<li>S. Bova and F. Montagna, Proof search in Häjek's Basic Logic, ACM Trans. Comput. Log., 2007. </li>
<li>D.M. Gabbay and G. Metcalfe, Fuzzy logics based on [0,1)-continuous uninorms, AML 46(5), 2007.</li>
<li>G. Metcalfe and F. Montagna, Substructural fuzzy logics. JSL 72(3), 2007.</li>
<li>R. Dyckhoff and S. Negri, Decision methods for linearly ordered {H}eyting algebras. AML 45, 2006.</li>
<li>G. Metcalfe and N. Olivetti and D. Gabbay, Sequent and Hypersequent calculi for Abelian and Łukasiewicz Logics. ACM Trans. Comput. Log. 6(3), 2005.</li>
<li>M. Baaz and A. Ciabattoni and F. Montagna, Analytic calculi for monoidal t-norm based logic, Fund. Inf. 59(4), 2004.</li>
<li>S. Negri and J. van Plato, Proof systems for lattice theory, Math. Struct. in Comp. Science 14(4), 2004.</li>
<li>A. Ciabattoni and
           C.G. Fermüller and
           G. Metcalfe, Uniform Rules and Dialogue Games for Fuzzy Logics. LPAR 2004.</li>
<li>A. Ciabattoni, Automated Generation of Analytic Calculi for Logics with
           Linearity. CSL 2004.</li>
<li>F. Montagna and L. Saccetti, Kripke-style semantics for many-valued logics, Math. Log. Q. 49(6), 2003. Correction in MLQ 50(1), 2004.</li>
<li>D. Larchey-Wendling, Countermodel search in Gödel-Dummett logics, IJCAR 2004, LNAI 3097, Springer, 2004.</li>
<li>G. Metcalfe, Proof Theory for Propositional Fuzzy Logics, PhD Thesis, Department of Computer Science, King's College, 2004.</li>
<li>D. Gabbay and G. Metcalfe and N. Olivetti, Hypersequents and Fuzzy Logic, Revista de la Real Academia de Ciencias 98(1), 2004.</li>
<li>A. Ciabattoni and G. Metcalfe, Bounded Łukasiewicz Logics. TABLEAUX 2003.</li>
<li>M. Baaz and
           A. Ciabattoni and
           C. G. Fermüller, ypersequent Calculi for Gödel Logics---a Survey. JLC 13(6), 2003.</li>
<li>M. Baaz and
           A. Ciabattoni and
           C. G. Fermüller, Sequent of Relations Calculi: A Framework for Analytic Deduction in Many-Valued Logics. Beyond Two: Theory and Applications of Multiple-Valued Logic, M. Fitting and E. Orlowska, eds., Physica-Verlag, 2003.</li>
<li>N. Olivetti, Tableaux for Łukasiwicz Infinite Valued Logic. Studia Logica  73(1), 2003.</li>
<li>G. Metcalfe and N. Olivetti and D. Gabbay, Analytic Sequent Calculi for Abelian and Łukasiewicz Logics. TABLEAUX 2002.</li>
<li>A. Ciabattoni and C. G. Fermüller, Hypersequents as a Uniform Framework for Urquhart's C, MTL and Related Logics.Proceedings of the 31th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2001), 2001.</li>
<li>F. Esteva and L. Godo, Monoidal t-norm based logic: towards a logic for
       left-continuous t-norms, Fuzzy Sets and Systems 124(3), 2001.</li>
<li>M. Baaz and R. Zach, Hypersequent and the Proof Theory of Intuitionistic Fuzzy
           Logic. CSL 2000.</li>
<li>A. Avron, A Tableau System for Gödel-Dummett Logic Based on a
           Hypersequent Calculus. TABLEAUX 2000, LNAI 1847, 2000.</li>
<li>A. Ciabattoni and M. Ferrari, Hypertableau and Path-Hypertableau Calculi for some families of intermediate logics. TABLEAUX 2000, LNAI 1847, 2000.</li>
<li>R.L.O. Cignoli and I.M.L. D'Ottaviano and D. Mundici, Algebraic Foundations of Many-Valued Reasoning, Kluwer, London, 2000.</li>
<li>S. Aguzzoli and A. Ciabattoni, Finiteness in Infinite-Valued Łukasiewicz Logic. J. Logic, Language and Information 9, 2000.</li>
<li>R. Dyckhoff, A Deterministic Terminating Sequent Calculus for Gödel-Dummett logic, IGPL 7(3), 1999.</li>
<li>M. Baaz and
           A. Ciabattoni and
           C. G. Ferm{\"u}ller and
           H. Veith, Proof Theory of Fuzzy Logics: Urquhart's C and Related Logics. Mathematical Foundations of Computer Science 1998, 23rd
           International Symposium, MFCS'98, Brno, Czech Republic,
           August 24-28, 1998, Proceedings, 1998.</li>
<li>P. Häjek, Metamathematics of Fuzzy Logics, Kluer, 1998.</li>
<li>R. Hähnle, Proof theory of many-valued logic--linear optimization--logic
           design: connections and interactions. Soft Comput. 1(3), 1997.</li>
</ul>

<p>These are largely proof-theory and automated deduction references, though,</p>

CC BY-SA 2.5
2011-04-06T17:40:21.660Z
How about some more details Rob?
Dave Clarke
CC BY-SA 2.5
2011-04-06T19:50:35.000Z
Edited reply with specific references.
Rob
CC BY-SA 2.5
2011-04-06T19:52:42.867Z
Wow. That's quite a list.
Dave Clarke
CC BY-SA 3.0
2011-04-08T08:40:20.680Z
Rob, this is an interesting answer. I think most of these results are not dealing with Zadeh's fuzzy logic (as is used in control systems, $\land$ being interpreted as min) but with the more general notion.
Kaveh
CC BY-SA 3.0
2011-04-08T09:03:06.203Z
Most fuzzy logics interpret $\land$ as min and $\lor$ as max. Been a while, but I recall that Zadeh's logic is the same as Łukasiewicz w.r.t. implication. (I might be wrong on that.)
Rob
CC BY-SA 2.5
2011-04-06T17:20:37.350Z
2011-04-06T19:50:10.023Z
2011-04-06T19:50:10.023Z
Rob
<p>I am reviewing the <a href="http://www.springer.com/computer/ai/book/978-0-387-40532-2" rel="nofollow">Handbook of Nature-Inspired and Innovative Computing</a> for SIGACT News.  It's a very interesting read.  Each chapter, though, has the flavor, "This is my research area, and damn it's awesome!"  So part of what I am trying to do is to separate out the hype, and make a sober assessment of the book's contents.</p>

<p>One chapter is on fuzzy logic and fuzzy systems, and how frikkin awesome they are.  And maybe they are, I frankly don't know.  The intuitive sense I've gotten from hanging around computer scientists is that fuzzy logic and fuzzy modeling of control systems, etc., are "dead."  I don't know if that's true, though -- and, even if it is true, I don't know if it's true for a "good reason."</p>

<p>Would anyone like to weigh in here?  What's the current status of research into fuzzy systems?  Does fuzzification see real-world applications?  Did it used to and people moved away because of problems?  Or do people "in the trenches" use it all the time, and it's just that theorists have moved away from it?  Or... something else?  (I have no idea what is true.)</p>

<p>I will probably cite answers to this question in the book review, unless an answerer specifically asks me not to.</p>

<p>Thanks.</p>

CC BY-SA 2.5
2011-04-05T14:31:27.157Z
Verging on the border of subjective and argumentative with a fuzziness of 0.326.
Dave Clarke
CC BY-SA 2.5
2011-04-05T14:36:55.877Z
@Dave Clarke: :-)!!!  I know.  But there was even a question on this site, one of the "what research area should I go into" questions, where someone who answered said that fuzzy logic was not an active research area.  If you want to close this question, I won't be offended.  Still, I find the situation curious, and if there's a diplomatic way to find out about it, I'd like to.
Aaron Sterling
CC BY-SA 2.5
2011-04-05T14:38:34.433Z
This is a good question. Fuzzy logic is still used as a marketing term in washing machines, etc., which I find a bit amusing as I share your feeling: fuzzy logic sounds like a has-been. It would be nice to hear what fuzzy logic actually means in TCS in 2011.
Jukka Suomela
CC BY-SA 2.5
2011-04-05T14:40:21.147Z
Let's see what the consensus is. If someone sees this more black-and-white-ly then a meta thread will arise to discuss the issue.
Dave Clarke
CC BY-SA 2.5
2011-04-05T14:54:37.223Z
I changed the title to be closer to @Jukka's question, which is much better phrased.  Hopefully that will address most of @Dave's concern.
Aaron Sterling
CC BY-SA 2.5
2011-04-05T15:07:38.217Z
Thanks Aaron for raising this question. I'm not much familiar with fuzzy logic, but knowing if a field is dead or alive is interesting. You may also ask for "current trends in fuzzy logic" to make it even more interesting (if any!). I think the "Federated Logic Conference (FLoC)" is a good place to seek such trends (not sure).
Sadeq Dousti
CC BY-SA 2.5
2011-04-05T15:34:16.270Z
Thank you for changing the title.  The status of fuzzy logic may be a little broad, but I do not think that the current question (revision 3) is subjective.
Tsuyoshi Ito
CC BY-SA 2.5
2011-04-05T17:32:46.000Z
I think we should make sure that answers are factual and have relevant pointers. that will help keeping things civil. Preferably no self-promotion.
Suresh Venkat
CC BY-SA 2.5
2011-04-05T17:43:56.780Z
I have serious doubts that it *was* alive in CS at any point. My impression is that most researchers have negative feeling about it because of the hype surrounding it (though this should be taken with some caution since my knowledge of other CS area is limited, e.g. KR). On the other hand it was and it still might be interesting for people in EE/Control theory/... From a logician's point of view it is just *one* of many many-valued logics extending Hajek's basic logic, see Hajek's book "Metamathematics of Fuzzy Logic". Also see "Proof Theory for Fuzzy Logics" by Metcalfe, Olivetti, and Gabbay.
Kaveh
CC BY-SA 2.5
2011-04-05T17:47:04.500Z
Zadeh had a paper in 2008: [Is there a need for fuzzy logic?](http://linkinghub.elsevier.com/retrieve/pii/S0020025508000716)
Kaveh
CC BY-SA 2.5
2011-04-05T18:33:39.600Z
For whatever it's worth, the [2010 Australian conference rankings](http://core.edu.au/index.php/categories/conference%20rankings/1) gave the IEEE Conference on Fuzzy Systems an A (the same grade STOC and FOCS got), and the impact factor of the IEEE Transactions on Fuzzy Systems has [an impact factor of 3.343](http://www.bioxbio.com/if/html/IEEE-T-FUZZY-SYST.html), though I don't know what a good comparison would be for impact factor.  So superficially the area seems "healthy" outside of TCS.  Maybe it's like Genetic Algorithms, where very few theorists work on it, but it's used in practice.
Aaron Sterling
<soft-question>
What is the status of fuzzy logic for TCS in 2011?
Aaron Sterling
# What is the status of fuzzy logic for TCS in 2011?

(Asked by: username_0 on 2011-04-05)

I am reviewing the [Handbook of Nature-Inspired and Innovative Computing](http://www.springer.com/computer/ai/book/978-0-387-40532-2) for SIGACT News. It's a very interesting read. Each chapter, though, has the flavor, "This is my research area, and damn it's awesome!" So part of what I am trying to do is to separate out the hype, and make a sober assessment of the book's contents.

One chapter is on fuzzy logic and fuzzy systems, and how frikkin awesome they are. And maybe they are, I frankly don't know. The intuitive sense I've gotten from hanging around computer scientists is that fuzzy logic and fuzzy modeling of control systems, etc., are "dead." I don't know if that's true, though -- and, even if it is true, I don't know if it's true for a "good reason."

Would anyone like to weigh in here? What's the current status of research into fuzzy systems? Does fuzzification see real-world applications? Did it used to and people moved away because of problems? Or do people "in the trenches" use it all the time, and it's just that theorists have moved away from it? Or... something else? (I have no idea what is true.)

I will probably cite answers to this question in the book review, unless an answerer specifically asks me not to.

Thanks.

**Tags:** soft-question

> **Comments:**
> **username_1**: Verging on the border of subjective and argumentative with a fuzziness of 0.326.  
> **username_0**: @username_1: :-)!!!  I know.  But there was even a question on this site, one of the "what research area should I go into" questions, where someone who answered said that fuzzy logic was not an active research area.  If you want to close this question, I won't be offended.  Still, I find the situation curious, and if there's a diplomatic way to find out about it, I'd like to.  
> **username_2**: This is a good question. Fuzzy logic is still used as a marketing term in washing machines, etc., which I find a bit amusing as I share your feeling: fuzzy logic sounds like a has-been. It would be nice to hear what fuzzy logic actually means in TCS in 2011.  
> **username_1**: Let's see what the consensus is. If someone sees this more black-and-white-ly then a meta thread will arise to discuss the issue.  
> **username_0**: I changed the title to be closer to @Jukka's question, which is much better phrased.  Hopefully that will address most of @Dave's concern.  
> **username_3**: Thanks Aaron for raising this question. I'm not much familiar with fuzzy logic, but knowing if a field is dead or alive is interesting. You may also ask for "current trends in fuzzy logic" to make it even more interesting (if any!). I think the "Federated Logic Conference (FLoC)" is a good place to seek such trends (not sure).  
> **username_4**: Thank you for changing the title.  The status of fuzzy logic may be a little broad, but I do not think that the current question (revision 3) is subjective.  
> **username_5**: I think we should make sure that answers are factual and have relevant pointers. that will help keeping things civil. Preferably no self-promotion.  
> **username_6**: I have serious doubts that it *was* alive in CS at any point. My impression is that most researchers have negative feeling about it because of the hype surrounding it (though this should be taken with some caution since my knowledge of other CS area is limited, e.g. KR). On the other hand it was and it still might be interesting for people in EE/Control theory/... From a logician's point of view it is just *one* of many many-valued logics extending Hajek's basic logic, see Hajek's book "Metamathematics of Fuzzy Logic". Also see "Proof Theory for Fuzzy Logics" by Metcalfe, Olivetti, and Gabbay.  
> **username_6**: Zadeh had a paper in 2008: [Is there a need for fuzzy logic?](http://linkinghub.elsevier.com/retrieve/pii/S0020025508000716)  
> **username_0**: For whatever it's worth, the [2010 Australian conference rankings](http://core.edu.au/index.php/categories/conference%20rankings/1) gave the IEEE Conference on Fuzzy Systems an A (the same grade STOC and FOCS got), and the impact factor of the IEEE Transactions on Fuzzy Systems has [an impact factor of 3.343](http://www.bioxbio.com/if/html/IEEE-T-FUZZY-SYST.html), though I don't know what a good comparison would be for impact factor.  So superficially the area seems "healthy" outside of TCS.  Maybe it's like Genetic Algorithms, where very few theorists work on it, but it's used in practice.  

---

## 1 answers

### Answer by username_7 on 2011-04-06. Score: 11 | Accepted answer

I wouldn't consider fuzzy logic dead. For control systems, I don't know. However, there's been a lot of activity in fuzzy logics for proof theorists for the last several years: look for papers by Ciabattoni, Olivetti, Fermüller, Metcalfe, and Baaz for starters.

**Edit:** Some specific references from my BibTeX file:

* D. Galmiche and Y. Sahli, Labelled Calculi for Łukasiewicz Logics, Int. Workshop on Logic, Language, Information and Computation, WoLLIC'08, Edinburgh, LNAI 5110, 2008.
* M. Baaz and G. Metcalfe, Proof Theory for First Order Łukasiewicz Logic. TABLEAUX 2007.
* D. Galmiche and D. Larchey-Wendling and Y. Salhi, Provability and Countermodels in Gödel-Dummett Logics, DISPROVING'07: Workshop on Disproving Non-Theorems, Non-Validity, and Non-Provability, 2007.
* S. Bova and F. Montagna, Proof search in Häjek's Basic Logic, ACM Trans. Comput. Log., 2007.
* D.M. Gabbay and G. Metcalfe, Fuzzy logics based on [0,1)-continuous uninorms, AML 46(5), 2007.
* G. Metcalfe and F. Montagna, Substructural fuzzy logics. JSL 72(3), 2007.
* R. Dyckhoff and S. Negri, Decision methods for linearly ordered {H}eyting algebras. AML 45, 2006.
* G. Metcalfe and N. Olivetti and D. Gabbay, Sequent and Hypersequent calculi for Abelian and Łukasiewicz Logics. ACM Trans. Comput. Log. 6(3), 2005.
* M. Baaz and A. Ciabattoni and F. Montagna, Analytic calculi for monoidal t-norm based logic, Fund. Inf. 59(4), 2004.
* S. Negri and J. van Plato, Proof systems for lattice theory, Math. Struct. in Comp. Science 14(4), 2004.
* A. Ciabattoni and
  C.G. Fermüller and
  G. Metcalfe, Uniform Rules and Dialogue Games for Fuzzy Logics. LPAR 2004.
* A. Ciabattoni, Automated Generation of Analytic Calculi for Logics with
  Linearity. CSL 2004.
* F. Montagna and L. Saccetti, Kripke-style semantics for many-valued logics, Math. Log. Q. 49(6), 2003. Correction in MLQ 50(1), 2004.
* D. Larchey-Wendling, Countermodel search in Gödel-Dummett logics, IJCAR 2004, LNAI 3097, Springer, 2004.
* G. Metcalfe, Proof Theory for Propositional Fuzzy Logics, PhD Thesis, Department of Computer Science, King's College, 2004.
* D. Gabbay and G. Metcalfe and N. Olivetti, Hypersequents and Fuzzy Logic, Revista de la Real Academia de Ciencias 98(1), 2004.
* A. Ciabattoni and G. Metcalfe, Bounded Łukasiewicz Logics. TABLEAUX 2003.
* M. Baaz and
  A. Ciabattoni and
  C. G. Fermüller, ypersequent Calculi for Gödel Logics---a Survey. JLC 13(6), 2003.
* M. Baaz and
  A. Ciabattoni and
  C. G. Fermüller, Sequent of Relations Calculi: A Framework for Analytic Deduction in Many-Valued Logics. Beyond Two: Theory and Applications of Multiple-Valued Logic, M. Fitting and E. Orlowska, eds., Physica-Verlag, 2003.
* N. Olivetti, Tableaux for Łukasiwicz Infinite Valued Logic. Studia Logica 73(1), 2003.
* G. Metcalfe and N. Olivetti and D. Gabbay, Analytic Sequent Calculi for Abelian and Łukasiewicz Logics. TABLEAUX 2002.
* A. Ciabattoni and C. G. Fermüller, Hypersequents as a Uniform Framework for Urquhart's C, MTL and Related Logics.Proceedings of the 31th IEEE International Symposium on Multiple-Valued Logic (ISMVL 2001), 2001.
* F. Esteva and L. Godo, Monoidal t-norm based logic: towards a logic for
  left-continuous t-norms, Fuzzy Sets and Systems 124(3), 2001.
* M. Baaz and R. Zach, Hypersequent and the Proof Theory of Intuitionistic Fuzzy
  Logic. CSL 2000.
* A. Avron, A Tableau System for Gödel-Dummett Logic Based on a
  Hypersequent Calculus. TABLEAUX 2000, LNAI 1847, 2000.
* A. Ciabattoni and M. Ferrari, Hypertableau and Path-Hypertableau Calculi for some families of intermediate logics. TABLEAUX 2000, LNAI 1847, 2000.
* R.L.O. Cignoli and I.M.L. D'Ottaviano and D. Mundici, Algebraic Foundations of Many-Valued Reasoning, Kluwer, London, 2000.
* S. Aguzzoli and A. Ciabattoni, Finiteness in Infinite-Valued Łukasiewicz Logic. J. Logic, Language and Information 9, 2000.
* R. Dyckhoff, A Deterministic Terminating Sequent Calculus for Gödel-Dummett logic, IGPL 7(3), 1999.
* M. Baaz and
  A. Ciabattoni and
  C. G. Ferm{\"u}ller and
  H. Veith, Proof Theory of Fuzzy Logics: Urquhart's C and Related Logics. Mathematical Foundations of Computer Science 1998, 23rd
  International Symposium, MFCS'98, Brno, Czech Republic,
  August 24-28, 1998, Proceedings, 1998.
* P. Häjek, Metamathematics of Fuzzy Logics, Kluer, 1998.
* R. Hähnle, Proof theory of many-valued logic--linear optimization--logic
  design: connections and interactions. Soft Comput. 1(3), 1997.

These are largely proof-theory and automated deduction references, though,

> **Comments:**
> **username_1**: How about some more details username_7?  
> **username_7**: Edited reply with specific references.  
> **username_1**: Wow. That's quite a list.  
> **username_6**: username_7, this is an interesting answer. I think most of these results are not dealing with Zadeh's fuzzy logic (as is used in control systems, $\land$ being interpreted as min) but with the more general notion.  
> **username_7**: Most fuzzy logics interpret $\land$ as min and $\lor$ as max. Been a while, but I recall that Zadeh's logic is the same as Łukasiewicz w.r.t. implication. (I might be wrong on that.)  

---

