The roughness and similarity measure for two different information in the same universal set is useful in explaining the strength and completeness of the information given. Then, for rough neutrosophic multisets environment, the lower and upper approximation was a concerned property to study in explaining the roughness of the information needed. Meanwhile, the vectorial models of information which are cosine measure and dice measure represent the result for the similarity measure of rough neutrosophic multisets. The finding of this set theory gives a new generalization about similarity measure for multiple information involving indeterminacy information in the same environment. Besides that, the rough neutrosophic multisets theory also applicable set-in decision making for medical diagnosis. The comparison result showed that the roughness approximation of information is essential to get the best result in a close similarity measure.

In this paper, we define a rough cosine similarity measure between two rough neutrosophic sets. The notions of rough neutrosophic sets (RNS) will be used as vector representations in 3D-vector space. The rating of all elements in RNS is expressed with the upper and lower approximation operator and the pair of neutrosophic sets which are characterized by truth-membership degree, indeterminacy-membership degree, and falsity-membership degree. A numerical example of the medical diagnosis is provided to show the effectiveness and flexibility of the proposed method.

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In this paper one generalizes the intuitionistic fuzzy set (IFS), paraconsistent set, and intuitionistic set to the neutrosophic set (NS). Many examples are presented. Distinctions between NS and IFS are underlined.

As a generalization of fuzzy sets and intuitionistic fuzzy sets, neutrosophic sets have been developed to represent uncertain, imprecise, incomplete, and inconsistent information existing in the real world. And interval neutrosophic sets (INSs) have been proposed exactly to address issues with a set of numbers in the real unit interval, not just a specific number.However, there are fewer reliable operations for INSs, as well as the INS aggregation operators and decisionmakingmethod. For this purpose, the operations for INSs are defined and a comparison approach is put forward based on the related research of interval valued intuitionistic fuzzy sets (IVIFSs) in this paper. On the basis of the operations and comparison approach, two interval neutrosophic number aggregation operators are developed. Then, amethod formulticriteria decisionmaking problems is explored applying the aggregation operators. In addition, an example is provided to illustrate the application of the proposed method.