### Abstract

First, we make some remarks concerning the definition of connectives in fuzzy logic. We point out possible disadvantages of considering exclusively t-norms and t-conorms as proper models for the conjunction and disjunction. Coincidence of S- and It-implications is investigated by solving functional equations for conjunctions. Then, we suggest a constructive approach to axiomatics of the generalized modus ponens (GMP). Besides a special model, a particular class of conjunctions satisfying the axioms for GMP and based on the Hamacher family of t-norms is also characterized. On the other hand, the coincidence of R- and S-implications defined by the members of this class is verified.

Original language | English |
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Title of host publication | Fuzzy Logic in Artificial Intelligence - 8th Austrian Artificial Intelligence Conference, FLAI 1993, Proceedings |

Publisher | Springer Verlag |

Pages | 16-26 |

Number of pages | 11 |

ISBN (Print) | 9783540569206 |

Publication status | Published - Jan 1 1993 |

Event | 8th Austrian Artificial Intelligence Conference on Fuzzy Logic, FLAI 1993 - Linz, Austria Duration: Jun 28 1993 → Jun 30 1993 |

### Publication series

Name | Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) |
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Volume | 695 LNAI |

ISSN (Print) | 0302-9743 |

ISSN (Electronic) | 1611-3349 |

### Other

Other | 8th Austrian Artificial Intelligence Conference on Fuzzy Logic, FLAI 1993 |
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Country | Austria |

City | Linz |

Period | 6/28/93 → 6/30/93 |

### Fingerprint

### ASJC Scopus subject areas

- Theoretical Computer Science
- Computer Science(all)

### Cite this

*Fuzzy Logic in Artificial Intelligence - 8th Austrian Artificial Intelligence Conference, FLAI 1993, Proceedings*(pp. 16-26). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 695 LNAI). Springer Verlag.

**Non-conventional conjunctions and implications in fuzzy logic.** / Fodor, J.; Keiesztfalvi, Tibor.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Fuzzy Logic in Artificial Intelligence - 8th Austrian Artificial Intelligence Conference, FLAI 1993, Proceedings.*Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 695 LNAI, Springer Verlag, pp. 16-26, 8th Austrian Artificial Intelligence Conference on Fuzzy Logic, FLAI 1993, Linz, Austria, 6/28/93.

}

TY - GEN

T1 - Non-conventional conjunctions and implications in fuzzy logic

AU - Fodor, J.

AU - Keiesztfalvi, Tibor

PY - 1993/1/1

Y1 - 1993/1/1

N2 - First, we make some remarks concerning the definition of connectives in fuzzy logic. We point out possible disadvantages of considering exclusively t-norms and t-conorms as proper models for the conjunction and disjunction. Coincidence of S- and It-implications is investigated by solving functional equations for conjunctions. Then, we suggest a constructive approach to axiomatics of the generalized modus ponens (GMP). Besides a special model, a particular class of conjunctions satisfying the axioms for GMP and based on the Hamacher family of t-norms is also characterized. On the other hand, the coincidence of R- and S-implications defined by the members of this class is verified.

AB - First, we make some remarks concerning the definition of connectives in fuzzy logic. We point out possible disadvantages of considering exclusively t-norms and t-conorms as proper models for the conjunction and disjunction. Coincidence of S- and It-implications is investigated by solving functional equations for conjunctions. Then, we suggest a constructive approach to axiomatics of the generalized modus ponens (GMP). Besides a special model, a particular class of conjunctions satisfying the axioms for GMP and based on the Hamacher family of t-norms is also characterized. On the other hand, the coincidence of R- and S-implications defined by the members of this class is verified.

UR - http://www.scopus.com/inward/record.url?scp=84911347523&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84911347523&partnerID=8YFLogxK

M3 - Conference contribution

SN - 9783540569206

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 16

EP - 26

BT - Fuzzy Logic in Artificial Intelligence - 8th Austrian Artificial Intelligence Conference, FLAI 1993, Proceedings

PB - Springer Verlag

ER -