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We first introduce some operations on the fuzzy number intuitionistic fuzzy sets. Then, we further develop the fuzzy number intuitionistic fuzzy Hamacher weighted geometric (FNIFHWG) operator, fuzzy number intuitionistic fuzzy Hamacher ordered weighted geometric (FNIFHOWG) operator and fuzzy number intuitionistic fuzzy Hamacher hybrid geometric (FNIFHHG) operator. Then, we apply the fuzzy number intuitionistic fuzzy Hamacher hybrid geometric (FNIFHHG) operator to deal with multiple attribute decision making with the fuzzy number intuitionistic fuzzy information. Finally, to testify the effectiveness of the proposed method, we present an example to evaluate the security of information system authentication scheme with the fuzzy number intuitionistic fuzzy information.<\/jats:p>","DOI":"10.3233\/ifs-141504","type":"journal-article","created":{"date-parts":[[2015,7,1]],"date-time":"2015-07-01T11:36:27Z","timestamp":1435750587000},"page":"2225-2232","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":9,"title":["Study on the security of information system authentication scheme based on the fuzzy number intuitionistic fuzzy information"],"prefix":"10.1177","volume":"28","author":[{"given":"Ying","family":"Wang","sequence":"first","affiliation":[{"name":"College of Computer Science and Technology, Taiyuan University of Technology, Shanxi,Taiyuan, 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