### Abstract

This paper presents parallel algorithms for fuzzy arithmetic operations on systolic arrays. A large part of the arithmetic on fuzzy numbers is referred to as fuzzy convolutions, which take O(n^{2}) time steps when implemented sequentially. In this paper, we present two parallel algorithms. The first algorithm runs on a linear array machine in O(n) time, using O(n) processors, and thus, achieving optimal time and cost. The second algorithm runs on a mesh-of-trees type of computer architecture in L(log n) time steps, using O(n^{2}) processors. The latter, although not optimal achieved high speedup. Both can be adapted to handle larger linear fuzzy numbers of fuzzy numbers with higher dimension.

Original language | English (US) |
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Pages (from-to) | 1283-1301 |

Number of pages | 19 |

Journal | Parallel Computing |

Volume | 19 |

Issue number | 11 |

DOIs | |

State | Published - Nov 1993 |

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### Keywords

- Systolic arrays
- fuzzy arithmetic
- linear array of processors
- mesh-of-trees of processors
- speed-up analysis

### ASJC Scopus subject areas

- Software
- Theoretical Computer Science
- Hardware and Architecture
- Computer Networks and Communications
- Computer Graphics and Computer-Aided Design
- Artificial Intelligence

### Cite this

*Parallel Computing*,

*19*(11), 1283-1301. https://doi.org/10.1016/0167-8191(93)90032-G