Abstract
In inconsistent and indeterminate settings, as a usual tool, the neutrosophic cubic set (NCS) containing single-valued neutrosophic numbers and interval neutrosophic numbers can be applied in decision-making to present its partial indeterminate and partial determinate information. However, a few researchers have studied neutrosophic cubic decision-making problems, where the similarity measure of NCSs is one of the useful measure methods. For this work, we propose the Dice, cotangent, and Jaccard measures between NCSs, and indicate their properties. Then, under an NCS environment, the similarity measures-based decision-making method of multiple attributes is developed. In the decision-making process, all the alternatives are ranked by the similarity measure of each alternative and the ideal solution to obtain the best one. Finally, two practical examples are applied to indicate the feasibility and effectiveness of the developed method.
Highlights
The classic fuzzy set [1] is expressed by its membership degree in the unit interval [0,1].But in many complicated cases of the real world, the data often are vague and uncertain, and are difficult to express as classic fuzzy sets
The neutrosophic set (NS) concept was presented by Smarandache [2], which is an extension of the fuzzy set and intuitionistic fuzzy sets
The nonstandard interval is difficult to apply in real situations, so a simplified neutrosophic set (SNS), including single-valued and interval neutrosophic sets, was presented by Ye [3], which is depicted by the truth, indeterminacy, and falsity degrees in the interval [0,1], to conveniently apply it in science and engineering fields, such as decision-making [4,5,6,7,8], medical diagnoses [9,10], image processing [11,12], and clustering analyses [13]
Summary
The classic fuzzy set [1] is expressed by its membership degree in the unit interval [0,1]. Lu and Ye [30] used cosine measures for NCSs for the first time to handle decision-making problems in an NCS setting. Few researchers have studied neutrosophic cubic MADM problems, where the similarity measure of NCSs is one of the useful measure methods. Since NCS is combined with an interval neutrosophic set (INS) and a single-valued neutrosophic set (SVNS), we can extend them to NCSs. Motivated by the similarity measures of INSs and SVNSs in the literature [35,37], we propose the Dice, cotangent, and Jaccard measures between NCSs to enrich the existing similarity measures of NCSs. a MADM method is developed based on the proposed similarity measures in an NCS setting.
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