### Abstract

A notion of the generalized pseudo-convolution of functions based on pseudo-operations is introduced. It is proved that such general pseudo-convolution is commutative, associative operation that, in some cases, has a unit element. We present that the generalized pseudo-convolution occurs as a basic notion in many different theories as probabilistic metric spaces, information theory, fuzzy numbers, optimization, system theory.

Original language | English |
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Pages (from-to) | 393-415 |

Number of pages | 23 |

Journal | Fuzzy Sets and Systems |

Volume | 102 |

Issue number | 3 |

DOIs | |

Publication status | Published - Mar 16 1999 |

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### Keywords

- Decomposable measure
- Fuzzy numbers
- G-integral
- Measure theory
- Optimization
- Pseudo-addition
- Pseudo-convolution
- Pseudo-integral
- Pseudo-multiplication

### ASJC Scopus subject areas

- Logic
- Artificial Intelligence