Fuzzy parameterized extensions of hypersoft set embedded with possibility-degree settings: an overview

The Hypersoft set marks a significant advancement in modeling vagueness and uncertainty. Concurrently, fuzzy parameterization and possibility-degree setting have been pivotal. The Hypersoft set addresses the complexity of a multi-argument domain through approximate mapping; fuzzy parameterization tackles the uncertain characteristics of parameters and their associated sub-parametric tuples; while the possibility-degree setting offers a dependable framework for evaluating the acceptance level of decision-makers’ views. This research aims to introduce several hybrid set structures by integrating the above-mentioned three ideas with fuzzy set extensions. The novelty of each structure is self-explanatory and justified. To grasp each structure’s true meaning, numerical examples have been used to explain the concept.