A generalised hybrid similarity measure of rough Neutrosophic set with roughness approximation / Hafiza Jamaludin, Nik Nur Auni Rahman Nik Shaidin and Nur Hidayah Abdul Faatah.

The findings of the similarity measure between two or more expert-provided information are categorized as either a strong or a weak relationship. As a result, getting the results for the similarity measure as the best conclusion for the information relationship is important. Based on the justification from previous studies, the generalised hybrid similarity measure of hamming and cosine similarity measure was chosen as the similarity measure method in this study. In addition, a rough neutrosophic set was chosen as the uncertainty set theory information, which includes the upper and lower approximation and a boundary set was chosen as the set theory application. The objectives of the study are to propose a hybrid similarity measure of rough neutrosophic set with roughness approximation, to formulate a properties of a hybrid similarity measure of rough neutrosophic set satisfied the distance measure properties and to apply the propose hybrid similarity measure of a rough neutrosophic set in the smartphone selection decision making process. The roughness approximation is used in the definition of the generalised hybrid similarity measure between hamming and cosine similarity measure. Following that, the derivation algorithm for smartphone selection is presented. The roughness approximation for a rough neutrosophic set is used to compare the similarity results. The proving result is complete. Then, the derivation of generalised hybrid similarity measure of rough neutrosophic set is well defined. As a validation process, the similarity properties for selection of smartphone is used such as features, a reasonable price, customer care, and risk factor. Finally, if either value of the similarity measure is close to one, a strong relationship between the information given or vice versa is defined.