Abstract
A neutrosophic number (a + bI) is a significant mathematical tool to deal with indeterminate and incomplete information which exists generally in real-world problems, where a and bI denote the determinate component and indeterminate component, respectively. We define score functions and accuracy functions for ranking neutrosophic numbers. We then define a cosine function to determine the unknown weight of the criteria. We define the neutrosophic number harmonic mean operators and prove their basic properties. Then, we develop two novel multi-criteria group decision-making (MCGDM) strategies using the proposed aggregation operators. We solve a numerical example to demonstrate the feasibility, applicability, and effectiveness of the two proposed strategies. Sensitivity analysis with the variation of “I” on neutrosophic numbers is performed to demonstrate how the preference ranking order of alternatives is sensitive to the change of “I”. The efficiency of the developed strategies is ascertained by comparing the results obtained from the proposed strategies with the results obtained from the existing strategies in the literature.
Highlights
Multi-criteria decision-making (MCDM), and multi-criteria group decision-making (MCGDM)are significant branches of decision theories which have been commonly applied in many scientific fields
We develop two new MCGDM strategies based on a neutrosophic numbers (NN) harmonic mean operator (NNHMO) and a NN weighted harmonic mean operator (NNWHMO) to solve MCGDM problems
We have proposed NNHMO and NNWHMO
Summary
Multi-criteria decision-making (MCDM), and multi-criteria group decision-making (MCGDM). The application of NNs is more appropriate to deal with the indeterminate and incomplete information in real-world decision-making situations. Park et al [49] proposed multi-attribute group decision-making (MAGDM) strategy based on HM operators under uncertain linguistic environments. Ye [51] proposed a multi-attribute decision-making (MADM) strategy based on harmonic averaging projection for a simplified neutrosophic sets (SNS) environment. Zheng et al [54] proposed a MAGDM strategy based on a NN generalized hybrid weighted averaging operator. Motivated from the works of Ye [52], Liu and Liu [53], Zheng et al [54], and Pramanik et al [55], we consider the proposed strategies to handle MCGDM problems in a NN environment.
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