Distance and Similarity Measures for Neutrosophic HyperSoft Set (NHSS) with Construction of NHSS-TOPSIS and Applications

Abstract

Neutrosophic HyperSoft Set (NHSS) is a new approach towards computational intelligence and decision making under uncertainty. In this paper, we first consider distances for NHSS, and then propose similarity measures for NHSS. We also consider aggregated operation for aggregating NHSS decision matrix. TOPSIS (Technique for the order preference by similarity to ideal solution) is a strong approach for multi-criteria decision making (MCDM) which has been studied under various extensions of fuzzy sets. These approaches have drawbacks in depicting fuzzy decision-making information for handling MCDM situations under NHSS environment. To efficiently and accurately express fuzzy attribute values provided by decision-makers (DMs), we construct the TOPSIS based on the proposed distances and similarity measures of NHSS, called NHSS-TOPSIS. The proposed NHSS-TOPSIS provides the weights of DMs by utilizing similarity measures dependent on Hamming distance. We then aggregate the opinions of decision-makers using the proposed aggregated operation. Utilizing the relative closeness coefficient, we select the most ideal alternative in the proposed NHSS-TOPSIS procedures. To exhibit the relevance and adequacy of the proposed NHSS-TOPSIS, we apply it in a medical diagnosis and an optimal selection for the sustainable green security system. The proposed method reveals that the hypersoft set with the neutrosophic set theory can be very helpful to construct a connection between alternatives and attributes. It demonstrates that the proposed method is effective and useful in real applications.