Novel and high-speed algorithm for solving the inverse problem of fuzzy correspondence

The inverse problem of fuzzy correspondence was first formulated by T. Tashiro, T. Terano and Y. Tsukamoto (1978). They proposed a algorithm to solve the problem. However, that algorithm takes tremendous computation time to solve the large-scale inverse problem even in high performance computer environments. Consequently, it is difficult to apply the algorithm to real-time expert systems as an inference engine. First, this paper proposes a very fast algorithm for solving the inverse problem of fuzzy correspondence. Next, it shows that computational complexity of Tsukamoto´s algorithm is O(mⁿ⁺¹ n). On the other hand, the authors´ algorithm requires O(mn) time, where m is the number of causes and n is the number of symptoms. The validity of the algorithm is also proven. Furthermore, to prove its practicability, results of numerical experiments are given. The results showed that the proposed algorithm has about a four hundred thousand-fold speed-up on average for solving the inverse problem as compared with the previous algorithm