Abstract
Vague set, as well as intuitionistic fuzzy set, is a further generalization of fuzzy set. Instead of using point-based membership in fuzzy set, interval-based membership is used in vague set. As a result, vague set has more powerful ability to process fuzzy information than fuzzy set in some degree. By exploring the uncertainty of vague set, the disadvantages of existing methods for measuring fuzziness of vague set are analyzed. In order to overcome these disadvantages in existing measuring methods and better characterize uncertainty of vague set, the concept of fuzziness interval of vague set is defined and a new measuring method, average fuzziness is proposed based on integral calculus method. Accordingly, the proposed method is compared with the existing methods in property, which shows the accuracy of measuring fuzziness of vague set is better than the other methods. Whereas the advantages of the average fuzziness of a vague set, the method of transforming vague set into fuzzy set is proposed and discussed.