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This paper aims to introduce a new multiple attribute decision-making model named possibility Fermatean fuzzy soft set (PFFSS), which is a combination of the generalized fuzzy soft sets and Fermatean fuzzy sets. Some operations and properties of the new model, including complement, restricted union, and extended intersection are discussed. Further, an application of PFFSSs is modeled for multiple attribute decision-making and solved with the help of our newly launched algorithm, that is, the selection of the best eco-system model based on a computer simulation report. Finally, a comparative analysis between the initiated PFFSS model and some existing approaches is provided to show its reliability over them.

In this article, we will define the new notions (e.g., semi-θ-neighbor-hood system of point, semi-θ-closure (interior) of a set and semi-θ-closed (open) set) based on fuzzy logic (i.e., fuzzifying topology). Then, we will explain the interesting properties of above five notions in detail. Several basic results (for instance, Definition 2.3, Theorem 2.5 (iii), (v) and (vi), Theorem 2.10, Theorem 2.14 and Theorem 4.6) in classical topology are generalized to the fuzzy case based on Łukasiewicz logic. In addition to, we will show that every fuzzifying semi-θ-closed set is fuzzifying semi-closed set (by Theorem 2.5 (vi)). Further, we will study the notion of fuzzifying semi-θ-derived set and fuzzifying semi-θ-boundary set, and discuss several of their fundamental basic relations and properties. Also, we will present a new type of fuzzifying strongly semi-θ-continuous mapping between two fuzzifying topological spaces. Finally, several characterizations of fuzzifying strongly semi-θ-continuous mapping, fuzzifying strongly semi-θ-irresolute mapping, and fuzzifying weakly semi-θ-irresolute mapping along with different conditions for their existence are obtained.