### Abstract

A comparison is made of two approaches to approximate reasoning: Mamdani's interpolation method and the implication method. Both approaches are variants of Zadeh's compositional rule of inference. It is shown that the approaches are not equivalent. A correspondence between the approaches is established via the inverse of the implied fuzzy relation. The interpolation method has the lowest time-complexity, provided the minimum operator is chosen as t-norm. Otherwise, the time-complexity of both methods is the same. It is more efficient to first compile a set of fuzzy rules into a fuzzy relation, instead of aggregating inference results for each fuzzy rule separately.

Original language | Undefined |
---|---|

Title of host publication | EUSFLAT 2003 |

Editors | Michael Wagenknecht, Rainer Hampel |

Place of Publication | Zittau/Goerlitz, Germany |

Publisher | European Society for Fuzzy Logic and Technology |

Pages | 512-516 |

Number of pages | 5 |

ISBN (Print) | 3-9808089-4-7 |

Publication status | Published - Sep 2003 |

### Publication series

Name | |
---|---|

Publisher | European Society for Fuzzy Logic and Technology |

### Keywords

- Approximate reasoning
- IR-64088
- EWI-10085
- time-complexity
- compositional rule of inference
- SE-SC: Soft Computing applied to Software Engineering
- METIS-215015

## Cite this

van den Broek, P. M. (2003). Comparison of Two Approaches to Approximated Reasoning. In M. Wagenknecht, & R. Hampel (Eds.),

*EUSFLAT 2003*(pp. 512-516). Zittau/Goerlitz, Germany: European Society for Fuzzy Logic and Technology.