Abstract
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.
Highlights
Neutrosophic set (NS) [1,2] as a more general theory form of fuzzy sets (FS) [3] provides a simple method to describe uncertain information under the MCDM environment
The different types of fuzziness related to the uncertainty neutrosophic space are investigated
According to the drawbacks of distance and similarity measures, a new method is established to describe the measures of probabilistic neutrosophic hesitant fuzzy set (PNHFS)
Summary
Neutrosophic set (NS) [1,2] as a more general theory form of fuzzy sets (FS) [3] provides a simple method to describe uncertain information under the MCDM environment. Afterwards, in order to better combine with practical problems, Wang et al proposed the single-valued neutrosophic set (SVNS) [4,5,6]. In development, according to the complexity of the information in the MCDM problems, SVNS and INS have been applied to deal with some different types of problems [10,11,12,13,14,15,16]. When some decision makers (DMs) make a decision, some DMs may at the hesitancy among truth membership, indeterminacy membership and falsity membership. Different forms of NS have been proposed, like single-valued neutrosophic hesitant FS (SVNHFS) [17,18,19], multi-valued NS (MVNS) [20,21,22,23], Mathematics 2019, 7, 649; doi:10.3390/math7070649 www.mdpi.com/journal/mathematics
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