Soft Computing

, Volume 21, Issue 9, pp 2251–2262 | Cite as

A unified framework for the key weights in MAGDM under uncertainty

Methodologies and Application


A novel technique is suggested in this paper for determining the two kinds of key weights, namely the weights of decision makers and the weights of attributes, for multi-attribute group decision making (MAGDM) with Atanassov’s intuitionistic fuzzy sets (A-IFSs). Several clustering technologies are used here such as fuzzy entropy, similarity measure, and fuzzy transformation. This makes our technique easily adaptable to a changing decision making environment and helps to bring about more intuitively appealing results. More generally, an effort is made to find some common ground between our previous and present work, based upon which a unified framework is established for deriving these two kinds of key weights in MAGDM under uncertainty, with the aiming of providing a durable solution to some challenges this type of issue confronts. Experimentation shows an excellent performance of the developed framework that is flexible enough to accommodate more complex decision making environments where the attribute values can be expressed in terms of crisp values, intervals, A-IFSs, or hybrid data.


Atanassov’s intuitionistic fuzzy sets (A-IFSs) Multi-attribute group decision making (MAGDM) Weights Uncertainty 



This work was partially supported by the Key Project of National Natural Science Foundation of China under Grant No. 71431002, and the Ph.D. Research Startup Foundation of Liaoning University. The authors would like to thank the editors and the anonymous reviewers for their constructive comments and suggestions, which have greatly improved the presentation of this research.

Compliance with ethical standards

Conflict of interest

Both the authors, their immediate family, and any research foundation with which they are affiliated did not receive any financial payments or other benefits from any commercial entity related to the subject of this article.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.School of InformationLiaoning UniversityShenyangChina
  2. 2.Institute of System EngineeringDalian University of TechnologyDalianChina

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