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Mathematical Problems in Engineering
Volume 2014, Article ID 507401, 8 pages
Research Article

The Dual Triple I Methods of FMT and IFMT

1College of Science, Xi’an University of Science and Technology, Xi’an 710054, China
2College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China

Received 11 April 2014; Revised 5 June 2014; Accepted 11 June 2014; Published 7 July 2014

Academic Editor: Ker-Wei Yu

Copyright © 2014 Liu Yan and Zheng Mucong. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The Triple I method for the model of intuitionistic fuzzy modus tollens (IFMT) satisfies the local reductivity instead of the reductivity. In order to improve the quality of the Triple I method for lack of reductivity, the paper is intended to present a new approximate reasoning method for IFMT problem. First, the concept of intuitionistic fuzzy difference operator is proposed and its properties on the lattice structure of intuitionistic fuzzy sets are studied. Then, the dual Triple I method for FMT based on residual fuzzy difference operator is presented and the dual Triple I method is generated for IFMT. Moreover, a decomposition method of IFMT is provided. Furthermore, the reductivity of methods is investigated. Finally, α-dual Triple I method of IFMT is proposed.