Distance and Similarity Measures Using Max-Min Operators of Neutrosophic Hypersoft Sets With Application in Site Selection for Solid Waste Management Systems

The idea of a neutrosophic hypersoft set (NHSS) was coined by Smarandache in 2018 as a generalization of the soft set. This structure is a hybrid of a neutrosophic set with a hypersoft set. It can be a valuable structure for dealing with multi-attributes, multi-objective problems with disjoint attributive values. Similarity measures (SM) play a vital role in measuring the similarity index that how much the things are similar. Different types of similarity measures were developed in literature with different fuzzy, intuitionistic, and neutrosophic theories. It is intended to merge the neutrosophic theory with the hypersoft set theory and propose different similarity measures with the help of new proposed distances with max-min operators. Also, we proved different theorems and properties of distance and similarity measures. Then as solid waste management is a global issue, and there are some Solid Waste Management Systems (SWMS) for environment protection, so an example will be given for the site selection for SWMS to check the validity of proposed techniques. To verify the validity and superiority of the suggested work, it is contrasted to several existing methodologies, which show that decision-making issues with more bifurcation attributes provide more accurate and precise outcomes and can only be solved using this technique. In the future, the presented methodologies could be used in case studies with several qualities that are further bifurcated and multiple decision-makers. This proposed work can also be extended to many existing hypersoft set hybrids, such as Fuzzy hypersoft sets (FHSs), Intuitionistic hypersoft sets (IHSs), bipolar hypersoft sets (Bi-HSs), m-polar HSs, and Pythagorean hypersoft sets (PHSs).