Affiliations: [a] Institute of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan, Punjab, Pakistan
| [b] Department of Mathematics, Deanship of Applied Sciences, Umm Al-Qura University, Mecca, Saudi Arabia
Correspondence:
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Corresponding author. Shahzaib Ashraf, Institute of Mathematics, Khwaja Fareed University of Engineering & Information Technology, Rahim Yar Khan 64200, Punjab, Pakistan. E-mail: drshahzaibashraf@gmail.com.
Abstract: One of the hottest areas for applying the solutions currently available is the internet of things-based smart housing society architecture and its uncertainty analysis. When intelligent parking, waste management, public transportation, public safety, and other automatic methods for housing society’s growth were implemented, it became even more crucial. An intelligent, smart system is necessary to manage these problems and provide smooth services. Additionally, it will be helpful in reducing issues with time waste and societal safety. However, the issue comes up when describing accurate, approximate, or questionable parking, transit, safety, and waste management areas. This paper discusses several mathematical solutions for the smart housing society that use fuzzy rough sets, probabilistic hesitant fuzzy sets, and their extensions with neutrosophic sets. For further growth, a few studies on the graphic display of the evolution of the smart housing society are also considered. The rough set theory can be useful when dealing with imprecise, incomplete, or indeterminate data sets. The core contribution of this work is the construction of a novel generalized notion of a single-valued neutrosophic probabilistic hesitant fuzzy rough set (SV-NPHFRS), which is a hybrid structure of the single-valued neutrosophic set, the probabilistic hesitant fuzzy set, and the rough set. In contrast to the present literature, the underlying idea of SV-NPHFRS is that it is a powerful mathematical tool for managing uncertainty and imperfect information. This method is particularly beneficial when there are a number of competing criteria to consider. The aggregation technique plays an important role in decision-making concerns, especially when more competing criteria are present. In the study’s comparison phase, the suggested decision support system is compared to relevant existing approaches. The results suggest that, in terms of choice flexibility, the suggested technique has the potential to outperform the drawbacks of the current decision-making tools. The proposed study is expected to be useful for a number of researchers conducting future work on housing societies, waste management, public safety diagnostics, and hybridization.
