Abstract
It needs to calculate the distance between the vague sets based on the approximate reasoning on the clustering rules of vague set. In this study, two new distance formulae for vague sets are presented, which are proved to satisfy the known axioms. With a suitable distance formula, a more reasonable clustering of Vague set rule can be obtained. Therefore, the searching scope of vague reasoning is decreased, and the reasoning complexity is reduced in the approximate reasoning of Vague set rules.
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