Journal
COMPLEXITY
Volume 21, Issue 5, Pages 277-290Publisher
WILEY-HINDAWI
DOI: 10.1002/cplx.21654
Keywords
multicriteria decision making; normal interval-valued intuitionistic fuzzy numbers; normal interval-valued intuitionistic fuzzy aggregation operator
Funding
- National Natural Science Foundation of China [71471172, 71271124]
- Humanities and Social Sciences Research Project of Ministry of Education of China [13YJC630104]
- Shandong Provincial Social Science Planning Project [13BGLJ10]
- National Soft Science Project [2014GXQ4D192]
- Graduate education innovation projects in Shandong Province [SDYY12065]
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On the basis of the normal intuitionistic fuzzy numbers (NIFNs), we proposed the normal interval-valued intuitionistic fuzzy numbers (NIVIFNs) in which the values of the membership and nonmembership were extended to interval numbers. First, the definition, the properties, the score function and accuracy function of the NIVIFNs are briefly introduced, and the operational laws are defined. Second, some aggregation operators based on the NIVIFNs are proposed, such as normal interval-valued intuitionistic fuzzy weighted arithmetic averaging operator, normal interval-valued intuitionistic fuzzy ordered weighted arithmetic averaging operator, normal interval-valued intuitionistic fuzzy hybrid weighted arithmetic averaging operator, normal interval-valued intuitionistic fuzzy weighted geometric averaging operator, normal interval-valued intuitionistic fuzzy ordered weighted geometric averaging operator, normal interval-valued intuitionistic fuzzy hybrid weighted geometric averaging operator, and normal interval-valued intuitionistic fuzzy generalized weighted averaging operator, normal interval-valued intuitionistic fuzzy generalized ordered weighted averaging operator, normal interval-valued intuitionistic fuzzy generalized hybrid weighted averaging operator, and some properties of these operators, such as idempotency, monotonicity, boundedness, commutativity, are studied. Further, an approach to the decision making problems with the NIVIFNs is established. Finally, an illustrative example is given to verify the developed approach and to demonstrate its practicality and effectiveness. (C) 2015 Wiley Periodicals, Inc.
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