Interpolative reasoning in sparse rule base has been an important research topic in the field of artificial intelligence. To solve effectively the problem of reasoning in multivariable sparse rule base whose resulting consequences are restricted in a finite set, this paper developed a new interpolative reasoning approach and offered its algorithm. The approach deduced consequent results by converting domains of antecedent and consequent variables into ternary qualitative spaces and building ternary qualitative function among such spaces as model of system for calculation. By applying this approach to an example, the paper illustrated that the new approach is more accurate and simple than the existing interpolative reasoning methods for such problem.
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