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Open AccessArticle

Measures of Probabilistic Neutrosophic Hesitant Fuzzy Sets and the Application in Reducing Unnecessary Evaluation Processes

by Songtao Shao 1,2,†,‡ and Xiaohong Zhang 1,3,*,‡
1
Department of Mathematics, School of Arts and Sciences, Shaanxi University of Science & Technology, Xi’an 710021, China
2
College of Information Engineering, Shanghai Maritime University, Shanghai 201306, China
3
Department of Mathematics, College of Arts and Sciences, Shanghai Maritime University, Shanghai 201306, China
*
Author to whom correspondence should be addressed.
Current address: Xi’an Weiyang University Park, Xi’an 710016, China.
These authors contributed equally to this work.
Mathematics 2019, 7(7), 649; https://doi.org/10.3390/math7070649
Received: 20 June 2019 / Revised: 15 July 2019 / Accepted: 16 July 2019 / Published: 19 July 2019
(This article belongs to the Special Issue New Challenges in Neutrosophic Theory and Applications)
Distance measure and similarity measure have been applied to various multi-criteria decision-making environments, like talent selections, fault diagnoses and so on. Some improved distance and similarity measures have been proposed by some researchers. However, hesitancy is reflected in all aspects of life, thus the hesitant information needs to be considered in measures. Then, it can effectively avoid the loss of fuzzy information. However, regarding fuzzy information, it only reflects the subjective factor. Obviously, this is a shortcoming that will result in an inaccurate decision conclusion. Thus, based on the definition of a probabilistic neutrosophic hesitant fuzzy set (PNHFS), as an extended theory of fuzzy set, the basic definition of distance, similarity and entropy measures of PNHFS are established. Next, the interconnection among the distance, similarity and entropy measures are studied. Simultaneously, a novel measure model is established based on the PNHFSs. In addition, the new measure model is compared by some existed measures. Finally, we display their applicability concerning the investment problems, which can be utilized to avoid redundant evaluation processes. View Full-Text
Keywords: probabilistic neutrosophic hesitant fuzzy set; distance measure; similarity measure; entropy measure; multi-criteria decision-making (MCDM) probabilistic neutrosophic hesitant fuzzy set; distance measure; similarity measure; entropy measure; multi-criteria decision-making (MCDM)
MDPI and ACS Style

Shao, S.; Zhang, X. Measures of Probabilistic Neutrosophic Hesitant Fuzzy Sets and the Application in Reducing Unnecessary Evaluation Processes. Mathematics 2019, 7, 649.

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