Fuzzy arithmetic on systolic arrays

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.