Journal
APPLIED MATHEMATICAL MODELLING
Volume 37, Issue 6, Pages 4112-4126Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2012.09.017
Keywords
Multi-attribute group decision making; Trapezoidal intuitionistic fuzzy number; Hausdorff metric; Power average operator
Funding
- National Natural Science Foundation of China [71061006, 61263018]
- Humanities Social Science Programming Project of Ministry of Education of China [09YGC630107]
- Natural Science Foundation of Jiangxi Province of China [20114BAB201012]
- Science and Technology Project of Jiangxi province educational department of China [GJJ12265]
- Excellent Young Academic Talent Support Program of Jiangxi University of Finance and Economics
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Trapezoidal intuitionistic fuzzy numbers (TrIFNs) is a special intuitionistic fuzzy set on a real number set. TrIFNs are useful to deal with ill-known quantities in decision data and decision making problems themselves. The focus of this paper is on multi-attribute group decision making (MAGDM) problems in which the attribute values are expressed with TrIFNs, which are solved by developing a new decision method based on power average operators of TrIFNs. The new operation laws for TrIFNs are given. From a viewpoint of Hausdorff metric, the Hamming and Euclidean distances between TrIFNs are defined. Hereby the power average operator of real numbers is extended to four kinds of power average operators of TrIFNs, involving the power average operator of TrIFNs, the weighted power average operator of TrIFNs, the power ordered weighted average operator of TrIFNs, and the power hybrid average operator of TrIFNs. In the proposed group decision method, the individual overall evaluation values of alternatives are generated by using the power average operator of TrIFNs. Applying the hybrid average operator of TrIFNs, the individual overall evaluation values of alternatives are then integrated into the collective ones, which are used to rank the alternatives. The example analysis shows the practicality and effectiveness of the proposed method. (C) 2012 Elsevier Inc. All rights reserved.
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