Abstract
In recent papers, a new threshold function is defined on a continuous logic. The function is denominated the fuzzy threshold function and it provides a way of expressing reasoning rules in fuzzy reasoning into a mathematical function. It has been shown in the previous works that the method is fast and stable, but there remains a problem of devising an effective scheme for expressing non-linear fuzzy rules into mathematical formulas. In this paper, firstly, a fuzzy multi-threshold threshold function is newly defined, and its theoretical aspects are considered. Next, a general mehtod is proposed in order to represent a reasoning rule table which involves non-linearlity with a mathematical formula employing the fuzzy multi-threshold threshold function. The formulas obtained by the proposed method are not necessarily minimum but the method is available for any reasoning rule table. Together with this method, other means are discussed on their feasibility.
