Malaysian Journal of Mathematical Sciences, December 2023, Vol. 17, No. 4
An Application on an Information System via Nano Ordered Topology
Shalil, S. H., El-Sheikh, S. A., and Kandil, S. A.
Corresponding Email: slamma_elarabi@yahoo.com
Received date: 2 August 2023
Accepted date: 9 October 2023
Abstract:
Rough set theory is commonly used to handle uncertainty in various applications. In order to broaden its application scope, the classical rough set model based on equivalence relations, it has been extended to include an additional partial order relation. This partial order relation represents an $m$-nano flou set, as defined in Section 5, between rough sets and is particularly useful in determining the levels of impact that key factors have on heart failure. The primary objective of the current research is to introduce a novel approximation method based on equivalence relations and partial order relations (ordered approximation spaces), which extends Pawlak's method and investigates related results. The paper establishes the equivalence between our approach and Pawlak's approach under the condition that we have an equivalence relation and a partial order relation that satisfies the criteria required for it to be considered an equality relation. The second objective is to extend the concept of nano topology to include nano ordered topology, which involves nano increasing or decreasing topological spaces. The research indicates that incorporating nano increasing or decreasing topological spaces results in enhanced data analysis accuracy when compared to solely utilizing nano topological spaces. This observation aligns with the discussions in the referenced work by Jayalakshmi. The findings of this research have the potential to significantly impact medical research related to heart failure. Improved methods for handling uncertainty and quantifying the influence of various factors can lead to more accurate and reliable predictions and diagnoses. Ultimately, this work aims to contribute to advancements in heart failure treatment and prevention. By bridging the gap between traditional rough set theory and the nuanced intricacies of heart failure analysis, our research strives to advance our comprehension of this critical medical condition and, in turn, support progress in heart failure treatment and prevention.
Keywords: increasing (decreasing, boundary) lower (upper) approximations; nano ordered topological spaces; $m$-nano flou set; decision making
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