Abstract
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).
Highlights
While addressing different real-life problems, we need to choose the best option from a list of many
DISTANCE MEASURES WITH THEORY AND APPLICATIONS Based on the axiomatic concept of distance and similarity between SVNHSs, we offer numerous new formulas for SVNHS distance and similarity measures
S1, S3 and S4 are straightforward so we only prove the conditions S2 and S4 in the interest of brevity we only present the proof of Sk (P, Q) for k = 1, and the proofs for k = 2, 3, 4 . . . 6 can be generated in a similar way
Summary
While addressing different real-life problems, we need to choose the best option from a list of many. Maji et al [8], [9] redefined the aggregation operators of SS, and developed a decision-making algorithm using choice values of objects He applied the proposed algorithm in the house selection problem. Saeed et al [57], [58] proposed complex multi-fuzzy hypersoft sets to solve MCDM problems using entropy and similarity measures. Cotangent similarity measures of single value neutrosophic soft set and its application in fault diagnosis in the steam turbine are given by Ye et al [33], Khan et al [70], and Ahsan et al [71] CMFHS mapping and applied in HIV diagnosis with treatment. This study has chosen four distinct factors to analyze which type of site will be more suitable for which type of solid waste management system These factors include AQI, distance from the population, economic values, and slope of the land. We gave a real-life case study, and the conclusion portion is in Section VI, and future investigations are covered
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