### Abstract

The paper covers partly the first author's plenary talk at the Fuzzy Systems '94 Workshop held in Munich, Germany, and was partly written during a visiting appointment at the Dept. of Computer and Management Science, University of Trento, Italy. The basic motivation of using fuzzy rule-based systems especially for control purposes is to deduce simple and fast approximations of the unknown or too complicated models. Fuzzy rule-based systems have become very popuar because of their transparency and easiness of tuning and modification. Recently, some results concerning the explicit functions implemented by realistic fuzzy controllers presented the class of functions that could be implemented in this way. Some parallel results, on the other hand, attempted to prove that the main advantage of using fuzzy systems was the suitability for approximation with arbitrary accuracy in their universality. The explicit formulas and some very recent theoretical results made it clear however that fuzzy systems were not really good approximators, as realistic fuzzy controllers could generate only very rough approximations of given transference functions. In connection with approximation the question can be asked, whether there is an optimal fineness/roughness of a fuzzy rule-base that controls a certain action with roughness gives minimal time complexity. As an example, a target tracking problem was chosen ("Cat and Mouse", or "Hawk and Sparrow" problem) where the antagonistic criteria of minimizing inference time by the given rule-base and minimizing action time (search for the target, with given uncertainty provided by the rule model) were examined. Under certain assumptions the solution of this optimization problem leads to nontrivial rule-base sizes. These results have also practical applicability since if a fine enough model of the system is known it is always possible to generate a rougher version of the same, by applying the model transformation technique offered by rule interpolation with α-levels.

Original language | English |
---|---|

Pages (from-to) | 203-222 |

Number of pages | 20 |

Journal | Fuzzy Sets and Systems |

Volume | 85 |

Issue number | 2 |

Publication status | Published - 1997 |

### Fingerprint

### Keywords

- Approximate reasoning
- Control theory
- Model transformation
- Rule-based models
- Target tracking
- Time complexity minimization
- Universal approximators

### ASJC Scopus subject areas

- Artificial Intelligence
- Computer Science Applications
- Computer Vision and Pattern Recognition
- Information Systems and Management
- Statistics, Probability and Uncertainty
- Electrical and Electronic Engineering
- Statistics and Probability

### Cite this

*Fuzzy Sets and Systems*,

*85*(2), 203-222.

**Fuzzy systems and approximation.** / Kóczy, L.; Zorat, Alessandro.

Research output: Contribution to journal › Article

*Fuzzy Sets and Systems*, vol. 85, no. 2, pp. 203-222.

}

TY - JOUR

T1 - Fuzzy systems and approximation

AU - Kóczy, L.

AU - Zorat, Alessandro

PY - 1997

Y1 - 1997

N2 - The paper covers partly the first author's plenary talk at the Fuzzy Systems '94 Workshop held in Munich, Germany, and was partly written during a visiting appointment at the Dept. of Computer and Management Science, University of Trento, Italy. The basic motivation of using fuzzy rule-based systems especially for control purposes is to deduce simple and fast approximations of the unknown or too complicated models. Fuzzy rule-based systems have become very popuar because of their transparency and easiness of tuning and modification. Recently, some results concerning the explicit functions implemented by realistic fuzzy controllers presented the class of functions that could be implemented in this way. Some parallel results, on the other hand, attempted to prove that the main advantage of using fuzzy systems was the suitability for approximation with arbitrary accuracy in their universality. The explicit formulas and some very recent theoretical results made it clear however that fuzzy systems were not really good approximators, as realistic fuzzy controllers could generate only very rough approximations of given transference functions. In connection with approximation the question can be asked, whether there is an optimal fineness/roughness of a fuzzy rule-base that controls a certain action with roughness gives minimal time complexity. As an example, a target tracking problem was chosen ("Cat and Mouse", or "Hawk and Sparrow" problem) where the antagonistic criteria of minimizing inference time by the given rule-base and minimizing action time (search for the target, with given uncertainty provided by the rule model) were examined. Under certain assumptions the solution of this optimization problem leads to nontrivial rule-base sizes. These results have also practical applicability since if a fine enough model of the system is known it is always possible to generate a rougher version of the same, by applying the model transformation technique offered by rule interpolation with α-levels.

AB - The paper covers partly the first author's plenary talk at the Fuzzy Systems '94 Workshop held in Munich, Germany, and was partly written during a visiting appointment at the Dept. of Computer and Management Science, University of Trento, Italy. The basic motivation of using fuzzy rule-based systems especially for control purposes is to deduce simple and fast approximations of the unknown or too complicated models. Fuzzy rule-based systems have become very popuar because of their transparency and easiness of tuning and modification. Recently, some results concerning the explicit functions implemented by realistic fuzzy controllers presented the class of functions that could be implemented in this way. Some parallel results, on the other hand, attempted to prove that the main advantage of using fuzzy systems was the suitability for approximation with arbitrary accuracy in their universality. The explicit formulas and some very recent theoretical results made it clear however that fuzzy systems were not really good approximators, as realistic fuzzy controllers could generate only very rough approximations of given transference functions. In connection with approximation the question can be asked, whether there is an optimal fineness/roughness of a fuzzy rule-base that controls a certain action with roughness gives minimal time complexity. As an example, a target tracking problem was chosen ("Cat and Mouse", or "Hawk and Sparrow" problem) where the antagonistic criteria of minimizing inference time by the given rule-base and minimizing action time (search for the target, with given uncertainty provided by the rule model) were examined. Under certain assumptions the solution of this optimization problem leads to nontrivial rule-base sizes. These results have also practical applicability since if a fine enough model of the system is known it is always possible to generate a rougher version of the same, by applying the model transformation technique offered by rule interpolation with α-levels.

KW - Approximate reasoning

KW - Control theory

KW - Model transformation

KW - Rule-based models

KW - Target tracking

KW - Time complexity minimization

KW - Universal approximators

UR - http://www.scopus.com/inward/record.url?scp=0030784126&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030784126&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0030784126

VL - 85

SP - 203

EP - 222

JO - Fuzzy Sets and Systems

JF - Fuzzy Sets and Systems

SN - 0165-0114

IS - 2

ER -