Double Hierarchy Linguistic Soft and Soft Covering Based Sets and Their Application

Recent developments in mathematics have resulted in the creation of the soft set theory as a method for dealing with uncertainty. The classical soft sets, however, are not well suitable for dealing with double hierarchy linguistic term parameters. This study's objective is to expand traditional soft sets to include double hierarchy linguistic soft sets and double hierarchy linguistic soft covering based sets, whereby the DHLTSs, soft sets, and soft covering-based sets merge. Next, we describe upper and lower approximation, positive, negative, and border regions for double hierarchy linguistic soft sets and double hierarchy linguistic soft covering based sets. Ultimately, the double hierarchy linguistic soft set is applied to a decision-making issue with the help of fuzzy soft sets, and the value is demonstrated with a numerical example. In this example, we chose the best suitable Renewable Energy Source (RES) alternative for installation at Abdul Wali Khan University Mardan (AWKUM), using the recently established MCDM approach VIKOR method.