Journal
INTERNATIONAL JOURNAL OF FUZZY SYSTEMS
Volume 20, Issue 3, Pages 958-969Publisher
SPRINGER HEIDELBERG
DOI: 10.1007/s40815-017-0441-8
Keywords
Picture 2-tuple linguistic set; Inappropriateness; Novel operational laws; Multi-criteria decision-making; Modified aggregation operator
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Funding
- National Natural Science Foundation of China [71571193]
- National Natural Science Foundation of China [71571193]
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This paper primarily focuses on multi-criteria decision-making (MCDM) based on picture 2-tuple linguistic information. Since the picture 2-tuple linguistic set is structured by a linguistic 2-tuple and a picture fuzzy set, we first point out the inappropriateness of existing operations relating to picture fuzzy numbers and picture 2-tuple linguistic numbers. For the purpose of improving these misleading computations, we further propose novel operational laws for picture 2-tuple linguistic numbers from a correct version. Counterexamples, which are in one-to-one correspondence with the listed counterintuitive cases, are furnished to illustrate the limitations of existing operations and prove the feasibility of our newly presented operations. Moreover, by applying the novel operations, we put forward some modified aggregation operators which are further employed to a handling method for the MCDM problem with a picture 2-tuple linguistic matrix. Finally, two comparative and illustrative examples are furnished to verify the applicability and advantages of the proposed method.
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