Journal
APPLIED SOFT COMPUTING
Volume 11, Issue 4, Pages 3402-3418Publisher
ELSEVIER SCIENCE BV
DOI: 10.1016/j.asoc.2011.01.011
Keywords
Fuzzy multiattribute decision making; Interval-valued intuitionistic fuzzy set; Mathematical programming; Uncertainty; Preference; Closeness coefficient
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Funding
- Natural Science Foundation of China [70871117, 70902041]
- Ministry of Education of China [08JC630072]
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The aim of this paper is to develop a closeness coefficient based nonlinear programming method for solving multiattribute decision making problems in which ratings of alternatives on attributes are expressed using interval-valued intuitionistic fuzzy (IVIF) sets and preference information on attributes is incomplete. In this methodology, nonlinear programming models are constructed on the concept of the closeness coefficient, which is defined as a ratio of the square of the weighted Euclidean distance between an alternative and the IVIF negative ideal solution (IVIFNIS) to the sum of the squares of the weighted Euclidean distances between the alternative and the IVIF positive ideal solution (IVIFPIS) as well as the IVIFNIS. Simpler nonlinear programming models are deduced to calculate closeness intuitionistic fuzzy sets of alternatives to the IVIFPIS, which are used to estimate the optimal degrees of membership and hereby generate ranking order of the alternatives. The derived auxiliary nonlinear programming models are shown to be flexible with different information structures and decision environments. The proposed method is validated and compared with other methods. A real example is examined to demonstrate applicability of the proposed method in this paper. (C) 2011 Elsevier B.V. All rights reserved.
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