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Mathematical Problems in Engineering
Volume 2015, Article ID 965040, 9 pages
Research Article

A Novel MADM Approach Based on Fuzzy Cross Entropy with Interval-Valued Intuitionistic Fuzzy Sets

School of Management, Shanghai University, Shanghai 200444, China

Received 16 October 2014; Revised 24 December 2014; Accepted 25 December 2014

Academic Editor: Guangming Xie

Copyright © 2015 Xin Tong and Liying Yu. 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 paper presents a novel multiple attribute decision-making (MADM) approach for the problem with completely unknown attribute weights in the framework of interval-valued intuitionistic fuzzy sets (IVIFS). First, the fuzzy cross entropy and discrimination degree of IVIFS are defied. Subsequently, based on the discrimination degree of IVIFS, a nonlinear programming model to minimize the total deviation of discrimination degrees between alternatives and the positive ideal solution PIS as well as the negative ideal solution (NIS) is constructed to obtain the attribute weights and, then, the weighted discrimination degree. Finally, all the alternatives are ranked according to the relative closeness coefficients using the extended TOPSIS method, and the most desirable alternative is chosen. The proposed approach extends the research method of MADM based on the IVIF cross entropy. Finally, we illustrate the feasibility and validity of the proposed method by two examples.