Continuity of approximate reasoning using fuzzy number under Łukasiewicz t-norm

In this study, we analyzed the fuzzy approximate reasoning using t-norm calculation. We apply theoretical results to fuzzy optimal control. The input of the IF-THEN rules is conducted using fuzzy numbers instead of crisp numbers. We concluded that there is continuity in approximate reasoning, as well as compactness in the set of membership functions for fuzzy inference. In addition, the existence of a minimum value of the function that evaluates non-linear control is presented.

I. Introduction

Interest in fuzzy inference has been stimulated by the improving processing capabilities of computer hardware. Fuzzy inference is the process of formulating human subjective cognition and is based on IF-THEN rules. We expected that fuzzy inference would re-create the subjective judgments of professionals. In this context, IF-THEN rules can be said to contain the knowledge and skill of professionals. The IF-THEN rules, however, tend to take a rudimentary form by means of simplification.