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### INTERPOLATION BASED ON SEMANTIC DISTANCE WEIGHTING IN HEDGE ALGEBRA AND ITS APPLICATION

Nguyen Tien Duy

#### Abstract

When solving the approximation problems proposed by a Linguistic Rule Base System (LRBS), the choice of reasoning method has a great influence on the result. The chosen reasoning method should ensure the correctness of the variable relationship between the outputs versus the inputs. According to the Hedge Algebra’s approach, we can convert the LRBS to a real “hyper surface” in semantic space, called the Quantified Semantic Rule Base System (QRBS), and use an interpolative method for reasoning. In this paper, we propose the use of the interpolation to ensure the correctness mentioned above. It is interpolation based on the semantic distance weighting of the input semantic values ​​versus the semantic value of the elements appearing in the rule. In the input semantic value vector, for each component we define its distance weight to the semantic value of the corresponding language class that appears in the rule. This distance-weighted value is used to join the output value. With this proposal, we have designed and simulated the controller that control rules are given by LRBS for the resistance furnace. The results show that the controller works well under the control requirements.

#### Keywords

Hedge algebras; Approximate reasoning; Bi-linear interpolation; Linguistic Rule Base System; Fuzzy control

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