Dental scaling has high importance in oral health due to its effect on preventing the teeth root destruction. Moreover, it can influence other health aspects such as reducing the risk factor of infective endocarditis. There are various devices applicable to dental scaling. It is essential to select the most appropriate type of instrument to achieve more efficient scaling. Multi-Attribute Decision Making (MADM) is a mathematical approach widely applied in for selecting the best alternative based on essential criteria. In the present research, several criteria including cost, ease of use and sterilization, durability and effectiveness considered as criteria for device selection. The experts in the related field were asked to score the criteria and corresponded alternative. According to the results, obtained by applying the TOPSIS method, Piezon Master is the most option which is mainly due to its durability and effectiveness. The second rank belongs to Cavitron due to its ease of use and sterilization in addition to affordable cost.

Multi-criteria decision-making (MCDM) methods and techniques have been applied to many real-world problems in different fields of engineering science and technology. The evaluation based on distance from average solution (EDAS) method is a new and efficient MCDM method. The aim of this study is to propose a modification to address two exceptional cases in which the EDAS method fails to solve an MCDM problem.

The paper presents attribute based characterization of nanomaterials method for computer storage and retrieval as knowledgebase. The knowledgebase permits indepth understanding and comparison between nanomaterials available with the scientists and product developers to satisfy their research and development (R & D) needs. Techniques for order preference by similarity to ideal solution (TOPSIS) is proposed to evaluate nanomaterials in the presence of multiple attributes. The method normalizes attributes to nullify the effect of different units and their values in the range of 0 to 1. The relative importance of different attributes for different applications is considered. The weight vector is derived using Eigen value formulation. The positive and negative benchmark solutions are derived. Euclidean distance of alternatives from these best and worst solution leads to the development of proximity /goodness/suitability index for ranking. Final decision is taken by decision makers by SWOT analysis and short and long term strategies of the organisation. The methodology is illustrated with the help of an example and step-by-step procedure. Results, discussion and conclusion highlights the importance and practical application.

Quantitative and qualitative fuzzy measures have been proposed to hesitant fuzzy sets (HFSs) from different points. However, few of the existing HFSs fuzzy measures refer to the grey relational analysis (GRA) theory. Actually, the GRA theory is very useful in the fuzzy measure domain, which has been developed for such the intuitionistic fuzzy sets. Therefore, in this paper, we apply the GRA theory to the HFSs and interval-valued hesitant fuzzy sets (IVHFS) domain. We propose the HFSs grey relational degree, HFSs slope grey relational degree, HFSs synthetic grey relational degree and IVHFSs grey relational degree, which describe the closeness, the variation tendency and both the closeness and variation tendency of HFSs and closeness of IVHFSs, respectively, greatly enriching the fuzzy measures of HFSs. Furthermore, with the help of the TOPSIS method, we develop the grey relational based MADM methodology to solve the HFSs and IVHFSs MADM problems. Finally, combined with two practical MADM examples about energy policy selection with HFSs information and emergency management evaluation with IVHFSs information, we obtain the most desirable decision results, and compared with the previous methods, the validity, effectiveness and accuracy of the proposed grey relational degree for HFSs and IVHFSs are demonstrated in detail.