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Mathematical Problems in Engineering
Volume 2013, Article ID 160610, 11 pages
http://dx.doi.org/10.1155/2013/160610
Research Article

Some Induced Correlated Aggregating Operators with Interval Grey Uncertain Linguistic Information and Their Application to Multiple Attribute Group Decision Making

School of Economic and Management, Southwest Jiaotong University, Chengdu, Sichuan 610031, China

Received 3 November 2012; Accepted 30 December 2012

Academic Editor: Youqing Wang

Copyright © 2013 Zu-Jun Ma et al. 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.

Abstract

We propose the interval grey uncertain linguistic correlated ordered arithmetic averaging (IGULCOA) operator and the induced interval grey uncertain linguistic correlated ordered arithmetic averaging (I-IGULCOA) operator based on the correlation properties of the Choquet integral and the interval grey uncertain linguistic variables to investigate the multiple attribute group decision making (MAGDM) problems, in which both the attribute weights and the expert weights are correlative. Firstly, the relative concepts of interval grey uncertain linguistic variables are defined and the operation rules between the two interval grey uncertain linguistic variables are established. Then, two new aggregation operators: the interval grey uncertain linguistic correlated ordered arithmetic averaging (IGULCOA) operator and the induced interval grey uncertain linguistic correlated ordered arithmetic averaging (I-IGULCOA) operator are developed and some desirable properties of the I-IGULCOA operator are studied, such as commutativity, idempotency, monotonicity, and boundness. Furthermore, the IGULCOA and I-IGULCOA operators based approach is developed to solve the MAGDM problems, in which both the attribute weights and the expert weights are correlative and the attribute values take the form of the interval grey uncertain linguistic variables. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness.