Using Bézier curves in approximate reasoning

The possibilities of using Bézier curves as a concrete tool in the development of the inference engine of a decision support system allowing approximate reasoning are explored. We propose using Bézier curves for representing membership functions or implementing some kind of fuzzy implication. The effects on the axioms characterizing fuzzy implications are investigated. Bézier curves are easily computable, flexible and have nice smooth properties. They are extensively used in the CAD/CAM domain. They could play an important role in some processes of imprecise knowledge representation and manipulation. Such techniques are promising in the implementation of several stages of developing the inference engine of a fuzzy decision support system. Moreover, these methods capture some of the flexibility and subtlety characteristic of human reasoning.