A Synthesis of an Infinitely Multi-valued Approximate Reasoning Engine by Means of Genetic Algorithm

Abstract

In the past papers, the author proposed a synthesis method of the approximate reasoning engine by means of a newly defined functions : the infinitely multi-valued threshold functions. The essential point of the method is to represent the hipersurface which a rule table expresses by the formula of the infinitely multi-valued threshold function. It is shown in the papers that the proposed method is effective to the process control. This paper discusses an unsolved problem in the synthesis method. The problme is to represent the rule table having the complicated properties such as non-unateness/non-linearlity etc.by one formula. As shown in the previous paper[10], a targetting hipersurface may be approximately realized by obtaining the finitely multi-valued logic function which the lattice points(correspondding to integer element I/Os)express and by giving analogue inputs to the function's formula. Thus, the question results in the realization problem of any finitely multi-valued logic function by threshold gates. For the problem, however, no computer-oriented simple methods were known. This paper proposes a multistage synthesis method of the thrershold gates by using Genetic Algorithm and Threshold Theory. The point of the method is as follows. First, we consider genotypes built of integer elements. We set initial integer values in the genotypes so that "the maximum weight" of a finitely multi-valued threshold function may be generated. Next, we apply the genetic argorithm to the genotypes. The complicated rule tables shown in the previous papers have been realized by a network of the threshold gates assuming analogue inputs. Together with the experiments of the realization, the capability of the method is discussed through another examples.