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Open AccessArticle

Cosine Distance Measure between Neutrosophic Hesitant Fuzzy Linguistic Sets and Its Application in Multiple Criteria Decision Making

by Donghai Liu 1,†, Xiaohong Chen 2,3,† and Dan Peng 1,*
1
Department of Mathematics, Hunan University of Science and Technology, Xiangtan 411201, China
2
Mobile E-business Collaborative Innovation Center of Hunan Province, Hunan University of Commerce, Changsha 410205, China
3
Business School, Central South University, Changsha 410083, China
*
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Symmetry 2018, 10(11), 602; https://doi.org/10.3390/sym10110602
Received: 6 October 2018 / Revised: 2 November 2018 / Accepted: 2 November 2018 / Published: 7 November 2018
(This article belongs to the Special Issue Multi-Criteria Decision Aid methods in fuzzy decision problems)
This paper proposes a neutrosophic hesitant fuzzy linguistic term set (NHFLTS) based on hesitant fuzzy linguistic term set (HFLTS) and neutrosophic set (NS), which can express the inconsistent and uncertainty information flexibly in multiple criteria decision making problems. The basic operational laws of NHFLTS based on linguistic scale function are also discussed. Then we propose the generalized neutrosophic hesitant fuzzy linguistic distance measure and discuss its properties. Furthermore, a new similarity measure of NHFLTS combines the generalized neutrosophic hesitant fuzzy linguistic distance measure and the cosine function is given. A corresponding cosine distance measure between NHFLTSs is proposed according to the relationship between the similarity measure and the distance measure, and we develop the technique for order preference by similarity to an ideal solution (TOPSIS) method to the obtained cosine distance measure. The main advantages of the proposed NHFLTS is defined on linguistic scale function, the decision makers can flexibly convert the linguistic information to semantic values, and the proposed cosine distance measure between NHFLTSs with TOPSIS method can deal with the related decision information not only from the point of view of algebra, but also from the point of view of geometry. Finally, the reasonableness and effectiveness of the proposed method is demonstrated by the illustrative example, which is also compared to the other existing methods. View Full-Text
Keywords: neutrosophic hesitant fuzzy linguistic set; cosine distance measure; similarity measure; linguistic scale function; TOPSIS neutrosophic hesitant fuzzy linguistic set; cosine distance measure; similarity measure; linguistic scale function; TOPSIS
MDPI and ACS Style

Liu, D.; Chen, X.; Peng, D. Cosine Distance Measure between Neutrosophic Hesitant Fuzzy Linguistic Sets and Its Application in Multiple Criteria Decision Making. Symmetry 2018, 10, 602.

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