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Mathematical Problems in Engineering
Volume 2015 (2015), Article ID 451987, 21 pages
Research Article

Interval Entropy of Fuzzy Sets and the Application to Fuzzy Multiple Attribute Decision Making

1School of Control Science and Engineering, Dalian University of Technology, Dalian 116024, China
2School of Science, Shenyang Ligong University, Shenyang 110159, China
3School of Science, Dalian University of Technology, Panjin Campus, Panjin 124221, China

Received 20 May 2015; Revised 27 August 2015; Accepted 2 September 2015

Academic Editor: Rita Gamberini

Copyright © 2015 Yiying Shi and Xuehai Yuan. 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.


A series of new concepts including interval entropy, interval similarity measure, interval distance measure, and interval inclusion measure of fuzzy sets are introduced. Meanwhile, some theorems and corollaries are proposed to show how these definitions can be deduced from each other. And then, based on interval entropy, a fuzzy multiple attribute decision making (FMADM) model is set up. In this model, interval entropy is used as the weight, by which the evaluation values of all alternatives can be obtained. Then all alternatives with respect to each criterion can be ranked as the order of the evaluation values. At last, a practical example is given to illustrate an application of the developed model and a comparative analysis is made.