### 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) |
---|---|

Pages (from-to) | 1283-1301 |

Number of pages | 19 |

Journal | Parallel Computing |

Volume | 19 |

Issue number | 11 |

DOIs | |

State | Published - Jan 1 1993 |

### Fingerprint

### Keywords

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

### ASJC Scopus subject areas

- Theoretical Computer Science
- Software
- 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

**Fuzzy arithmetic on systolic arrays.** / Dhrif, Hassen; Sarkar, Dilip.

Research output: Contribution to journal › Article

*Parallel Computing*, vol. 19, no. 11, pp. 1283-1301. https://doi.org/10.1016/0167-8191(93)90032-G

}

TY - JOUR

T1 - Fuzzy arithmetic on systolic arrays

AU - Dhrif, Hassen

AU - Sarkar, Dilip

PY - 1993/1/1

Y1 - 1993/1/1

N2 - 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(n2) 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(n2) 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.

AB - 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(n2) 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(n2) 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.

KW - fuzzy arithmetic

KW - linear array of processors

KW - mesh-of-trees of processors

KW - speed-up analysis

KW - Systolic arrays

UR - http://www.scopus.com/inward/record.url?scp=0027694926&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0027694926&partnerID=8YFLogxK

U2 - 10.1016/0167-8191(93)90032-G

DO - 10.1016/0167-8191(93)90032-G

M3 - Article

AN - SCOPUS:0027694926

VL - 19

SP - 1283

EP - 1301

JO - Parallel Computing

JF - Parallel Computing

SN - 0167-8191

IS - 11

ER -