## Animated Fuzzy Logic (1993)

Venue: | Journal of Functional Programming |

Citations: | 1 - 0 self |

### BibTeX

@ARTICLE{Meehan93animatedfuzzy,

author = {Gary Meehan and Mike Joy},

title = {Animated Fuzzy Logic},

journal = {Journal of Functional Programming},

year = {1993},

volume = {8}

}

### OpenURL

### Abstract

In this paper we aim to give an introduction to fuzzy logic using the language Haskell to implement our solutions. We shall see how the high-level, declarative nature of a functional language allows us to implement easily and efficiently solutions to problems using fuzzy logic and, in particular, how the presence of functions as first-class values allows us to model the key concept of the fuzzy subset in a natural way. 1 Introduction Fuzzy logic, developed by Lotfi Zadeh (Zadeh, 1965; Zadeh, 1973), is a form of multivalued logic which has its grounds in / Lukasiewicz's work on such logics (/Lukasiewicz, 1967a; / Lukasiewicz, 1967b). It finds many applications in expert systems (in particular control problems) (Cox, 1994; Mamdani & Assilian, 1975; Ross, 1995; Wang, 1994), neural nets (Eklund & Kwalonn, 1992), formal reasoning (Negoita, 1985; Tanaka, 1997), decision making (Cox, 1994; Negoita, 1985; Zimmermann, 1991), database enquiries (Negoita, 1985) and many other areas. The use of f...

### Citations

3867 |
Fuzzy sets
- Zadeh
- 1965
(Show Context)
Citation Context ... and, in particular, how the presence of functions as first-class values allows us to model the key concept of the fuzzy subset in a natural way. 1 Introduction Fuzzy logic, developed by Lotfi Zadeh (=-=Zadeh, 1965-=-; Zadeh, 1973), is a form of multivalued logic which has its grounds in / Lukasiewicz's work on such logics (/Lukasiewicz, 1967a; / Lukasiewicz, 1967b). It finds many applications in expert systems (i... |

667 |
Outline of a new approach to the analysis of complex systems and decision processes
- Zadeh
- 1973
(Show Context)
Citation Context ...icular, how the presence of functions as first-class values allows us to model the key concept of the fuzzy subset in a natural way. 1 Introduction Fuzzy logic, developed by Lotfi Zadeh (Zadeh, 1965; =-=Zadeh, 1973-=-), is a form of multivalued logic which has its grounds in / Lukasiewicz's work on such logics (/Lukasiewicz, 1967a; / Lukasiewicz, 1967b). It finds many applications in expert systems (in particular ... |

619 | Artificial Intelligence. A Modern Approach, 2nd edition - Russel, Norvig |

512 | An Experiment in Linguistic Synthesis with a Fuzzy Logic - Mamdani, Assilian - 1975 |

317 | Fuzzy preference modelling and multicriteria decision support, in: Theory and Decision - Fodor, Roubens - 1994 |

279 |
Fuzzy Logic with Engineering Applications
- Ross
- 2004
(Show Context)
Citation Context ...in / Lukasiewicz's work on such logics (/Lukasiewicz, 1967a; / Lukasiewicz, 1967b). It finds many applications in expert systems (in particular control problems) (Cox, 1994; Mamdani & Assilian, 1975; =-=Ross, 1995-=-; Wang, 1994), neural nets (Eklund & Kwalonn, 1992), formal reasoning (Negoita, 1985; Tanaka, 1997), decision making (Cox, 1994; Negoita, 1985; Zimmermann, 1991), database enquiries (Negoita, 1985) an... |

191 |
Adaptive Fuzzy Systems and Control: Design and Stability Analysis
- Wang
- 1994
(Show Context)
Citation Context ...wicz's work on such logics (/Lukasiewicz, 1967a; / Lukasiewicz, 1967b). It finds many applications in expert systems (in particular control problems) (Cox, 1994; Mamdani & Assilian, 1975; Ross, 1995; =-=Wang, 1994-=-), neural nets (Eklund & Kwalonn, 1992), formal reasoning (Negoita, 1985; Tanaka, 1997), decision making (Cox, 1994; Negoita, 1985; Zimmermann, 1991), database enquiries (Negoita, 1985) and many other... |

184 | A system of constructor classes: overloading and implicit higherorder polymorphism
- Jones
- 1995
(Show Context)
Citation Context ... operators &&, ------, etc. so that they work on fuzzy values as well as boolean ones. This is done by shadowing the connectives (see above) and placing the connectives in a class (Hall et al., 1996; =-=Jones, 1995-=-; Peyton Jones et al., 1997): class Logic a where true, false :: a (&&), (------) :: a -? a -? a not :: a -? a The functions and, or, etc. are then also overloaded so that they now operate on instance... |

128 | Type Classes in Haskell
- Hall, Hammond, et al.
- 1996
(Show Context)
Citation Context ... by overloading the operators &&, ------, etc. so that they work on fuzzy values as well as boolean ones. This is done by shadowing the connectives (see above) and placing the connectives in a class (=-=Hall et al., 1996-=-; Jones, 1995; Peyton Jones et al., 1997): class Logic a where true, false :: a (&&), (------) :: a -? a -? a not :: a -? a The functions and, or, etc. are then also overloaded so that they now operat... |

107 | Haskell: The Craft of Functional Programming
- Thompson
- 1999
(Show Context)
Citation Context ...s. Section 4 introduces fuzzy systems and gives several examples. Section 5 concludes. Throughout the paper we shall give examples of using the programs we develop using the Haskell interpreter Hugs (=-=Thompson, 1996-=-). The programs in question can be downloaded off the WWW from: http://www.dcs.warwick.ac.uk/people/research/Gary.Meehan/funcprog/research.html Hugs is available from: http://haskell.systemsz.cs.yale.... |

101 | Type classes: an exploration of the design space
- Jones, Jones, et al.
- 1997
(Show Context)
Citation Context ...-, etc. so that they work on fuzzy values as well as boolean ones. This is done by shadowing the connectives (see above) and placing the connectives in a class (Hall et al., 1996; Jones, 1995; Peyton =-=Jones et al., 1997-=-): class Logic a where true, false :: a (&&), (------) :: a -? a -? a not :: a -? a The functions and, or, etc. are then also overloaded so that they now operate on instances of the Logic class, rathe... |

89 |
Introduction to the theory of fuzzy subsets
- Kaufmann
- 1973
(Show Context)
Citation Context ...ion of . Of course, this is only an elementary introduction to fuzzy logic, and we have not mention more esoteric connectives such as averaging operators. For more information we refer the reader to (=-=Kaufmann, 1975-=-), (Zimmermann, 1991) and (Fodor & Roubens, 1994). From now on we shall presume that all fuzzy truth values lie in [0; 1]. We shall now set about implementing these ideas in Haskell. We shall place al... |

87 |
The fuzzy systems handbook
- Cox
- 1994
(Show Context)
Citation Context ...tivalued logic which has its grounds in / Lukasiewicz's work on such logics (/Lukasiewicz, 1967a; / Lukasiewicz, 1967b). It finds many applications in expert systems (in particular control problems) (=-=Cox, 1994-=-; Mamdani & Assilian, 1975; Ross, 1995; Wang, 1994), neural nets (Eklund & Kwalonn, 1992), formal reasoning (Negoita, 1985; Tanaka, 1997), decision making (Cox, 1994; Negoita, 1985; Zimmermann, 1991),... |

31 |
An introduction to Fuzzy for Logic Practical Applications
- Tanaka
- 1997
(Show Context)
Citation Context ...y applications in expert systems (in particular control problems) (Cox, 1994; Mamdani & Assilian, 1975; Ross, 1995; Wang, 1994), neural nets (Eklund & Kwalonn, 1992), formal reasoning (Negoita, 1985; =-=Tanaka, 1997-=-), decision making (Cox, 1994; Negoita, 1985; Zimmermann, 1991), database enquiries (Negoita, 1985) and many other areas. The use of fuzzy logic in such applications not only makes their solutions sim... |

20 | Neural fuzzy logic programming - Eklund, Klawonn - 1992 |

11 | Using Fuzzy Logic - Yan, Ryan, et al. - 1994 |

9 |
Expert systems and fuzzy systems. Benjamin/Cummings, nenlo Park
- Negoita
- 1985
(Show Context)
Citation Context ...). It finds many applications in expert systems (in particular control problems) (Cox, 1994; Mamdani & Assilian, 1975; Ross, 1995; Wang, 1994), neural nets (Eklund & Kwalonn, 1992), formal reasoning (=-=Negoita, 1985-=-; Tanaka, 1997), decision making (Cox, 1994; Negoita, 1985; Zimmermann, 1991), database enquiries (Negoita, 1985) and many other areas. The use of fuzzy logic in such applications not only makes their... |

8 |
Philosophical remarks on many-valued systems of propositional logic
- Lukasiewicz
- 1930
(Show Context)
Citation Context ...subset in a natural way. 1 Introduction Fuzzy logic, developed by Lotfi Zadeh (Zadeh, 1965; Zadeh, 1973), is a form of multivalued logic which has its grounds in / Lukasiewicz's work on such logics (/=-=Lukasiewicz, 1967-=-a; / Lukasiewicz, 1967b). It finds many applications in expert systems (in particular control problems) (Cox, 1994; Mamdani & Assilian, 1975; Ross, 1995; Wang, 1994), neural nets (Eklund & Kwalonn, 19... |

8 | The Implementation of Fprolog – A Fuzzy Prolog Interpreter. Fuzzy Sets and Systems - Martin, Baldwin, et al. - 1985 |

2 |
1967a, ‘On the Notion of Possibility/On Three-Valued Logic
- Lukasiewicz
(Show Context)
Citation Context ...subset in a natural way. 1 Introduction Fuzzy logic, developed by Lotfi Zadeh (Zadeh, 1965; Zadeh, 1973), is a form of multivalued logic which has its grounds in / Lukasiewicz's work on such logics (/=-=Lukasiewicz, 1967-=-a; / Lukasiewicz, 1967b). It finds many applications in expert systems (in particular control problems) (Cox, 1994; Mamdani & Assilian, 1975; Ross, 1995; Wang, 1994), neural nets (Eklund & Kwalonn, 19... |

1 | Focusing system. http://www.aptronix.com/fuzzynet/applnote/ focusing.htm - Ltd - 1992 |

1 | Washing machine. http://www.aptronix.com/fuzzynet/applnote/ wash.htm - Ltd - 1992 |

1 | Fuzzy java. http://www.aptronix.com/fuzzynet/applnote/java.htm - Ltd - 1996 |

1 |
A fuzzy set model of learning disability. Pages 345--382 of: Z'et'enyi, Tam'as (ed), Fuzzy sets in pyschology
- Horvath
- 1988
(Show Context)
Citation Context ... Chapter 2 of (Wang, 1994), or Chapter 3 of (Yan et al., 1994)). Fuzzy logic has been applied to many languages --- both in extending standard languages such as Prolog (Martin et al., 1987), Fortran (=-=Horvath, 1988-=-), APL (Negoita, 1985) and Java (Aptronix Ltd., 1996), and in custom-designed languages such as Fuzzy CLIPS (for Information Technology, 1996), FIL (Aptronix Ltd., 1992a; Aptronix Ltd., 1992b), and FL... |

1 |
Animated Fuzzy Logic 23
- Kosko
- 1994
(Show Context)
Citation Context ...ht is verytall then shoesize := verybig Here is serves as a membership test for height. These rules can be thought of as forming patches (see Figure 8) with the larger the patch the fuzzier the rule (=-=Kosko, 1994-=-). More input variables require more dimensions to the patches. As can be seen, these patches overlap, which in practical terms means that more than one rule can fire, i. e., we have more than one pos... |

1 | Logic Programming Associates - Ltd - 1997 |