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Interval neutrosophic sets (INSs) provide us with a more flexible and effective way to express incomplete, indeterminate, and inconsistent information. The purpose of this paper is to introduce the new multicriteria decision-making (MCDM) method based on the improved projection model under the interval neutrosophic environment. In this paper, we investigated the basic concepts and operational rules of interval neutrosophic numbers (INNs), then proposed the projection of two INNs and improved the entropy formula of the INNs. Furthermore, this paper took account into the decision maker’s attitude towards the indeterminacy and risk and proposed two different methods to determine the ideal solutions. Based on this, we presented an improved MCDM method based on the projection model under the interval neutrosophic environment. Finally, the practicability and reliability of the proposed method were explained by the example of software quality-in-use evaluation.

Single-valued neutrosophic set (SVNS) is an extension of fuzzy set, which combines the truth, indeterminacy, and falsity information. The measurement of distance of single-valued neutrosophic set will bring new ideas to pattern recognition. This paper introduces the distance definitions and properties of SVNS, and proposes the improved distance definition of single-valued neutrosophic set based on decision maker attitude towards indeterminacy information and applied them to pattern recognition. By assigning a value to decision-maker’s attitude towards indeterminacy information, this attitude comes from the historical experience and risk preference etc. The distance calculated in this way can often get a matching result closer to the reality. The results show that the improved distance formula of SVNSs is more effective and more practical for pattern recognition.