In most of the practical applications the concept of vague environment [1] gives a simple way for fuzzy approximate reasoning. If the fuzzy partitions (used as primary sets of the fuzzy rulebase) can be described by vague environments [1], the primary fuzzy sets of the antecedent and the consequent parts of the fuzzy rules can be characterised by points in their vague environments. So the fuzzy rules themselves can be characterised by points in their vague environment too. It means, that the question of approximate fuzzy reasoning can be reduced to the problem of interpolation of the rule points in the vague environment of the fuzzy rulebase relation [2,3]. In this paper an approximate fuzzy reasoning method based on rational interpolation in the vague environment of the fuzzy rulebase will be introduced, and as an example of a practical application of the method, a path tracking control strategy for differential steered AGVs (Automated Guided Vehicle) [4] implemented on such a fuzzy logic controller will be introduced.