Journal of Applied Mathematics
Volume 2013 (2013), Article ID 981762, 10 pages
Research Article

The Interval-Valued Intuitionistic Fuzzy Optimized Weighted Bonferroni Means and Their Application

School of Economics and Management, Southeast University, Nanjing 211189, China

Received 3 May 2013; Accepted 18 June 2013

Academic Editor: Guangchen Wang

Copyright © 2013 Ya-ming Shi and Jian-min He. 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.


We investigate and propose two new Bonferroni means, that is, the optimized weighted BM (OWBM) and the generalized optimized weighted BM (GOWBM), whose characteristics are to reflect the preference and interrelationship of the aggregated arguments and can satisfy the basic properties of the aggregation techniques simultaneously. Further, we propose the interval-valued intuitionistic fuzzy optimized weighted Bonferroni mean (IIFOWBM) and the generalized interval-valued intuitionistic fuzzy optimized weighted Bonferroni mean (GIIFOWBM) and detailed study of their desirable properties such as idempotency, monotonicity, transformation, and boundary. Finally, based on IIFOWBM and GIIFOWBM, we give an approach to group decision making under the interval-valued intuitionistic fuzzy environment and utilize a practical case involving the assessment of a set of agroecological regions in Hubei Province, China, to illustrate the developed methods.