Rough set theory is an advanced uncertainty tool that is capable of processing sophisticated real-world data satisfactorily. Rough approximation operators are used to determine the confirmed and possible data that can be obtained by using subsets. Numerous rough approximation models, inspired by neighborhood systems, have been proposed in earlier studies for satisfying axioms of Pawlak approximation spaces (P-approximation spaces) and improving the accuracy measures. This work provides a formulation a novel type of generalized approximation spaces (G-approximation spaces) based on new neighborhood systems inspired by $ \mathbb{I}_j $-neighborhoods and ideal structures. The originated G-approximation spaces are offered to fulfill the axiomatic requirements of P-approximation spaces and give more information based on the data subsets under study. That is, they are real simulations of the P-approximation spaces and provide more accurate decisions than the previous models. Several examples are provided to compare the suggested G-approximation spaces with existing ones. To illustrate the application potentiality and efficiency of the provided approach, a numerical example for Chikungunya disease is presented. Ultimately, we conclude our study with a summary and direction for further research.
Citation: Tareq M. Al-shami, M. Hosny. Generalized approximation spaces generation from $ \mathbb{I}_j $-neighborhoods and ideals with application to Chikungunya disease[J]. AIMS Mathematics, 2024, 9(4): 10050-10077. doi: 10.3934/math.2024492
Rough set theory is an advanced uncertainty tool that is capable of processing sophisticated real-world data satisfactorily. Rough approximation operators are used to determine the confirmed and possible data that can be obtained by using subsets. Numerous rough approximation models, inspired by neighborhood systems, have been proposed in earlier studies for satisfying axioms of Pawlak approximation spaces (P-approximation spaces) and improving the accuracy measures. This work provides a formulation a novel type of generalized approximation spaces (G-approximation spaces) based on new neighborhood systems inspired by $ \mathbb{I}_j $-neighborhoods and ideal structures. The originated G-approximation spaces are offered to fulfill the axiomatic requirements of P-approximation spaces and give more information based on the data subsets under study. That is, they are real simulations of the P-approximation spaces and provide more accurate decisions than the previous models. Several examples are provided to compare the suggested G-approximation spaces with existing ones. To illustrate the application potentiality and efficiency of the provided approach, a numerical example for Chikungunya disease is presented. Ultimately, we conclude our study with a summary and direction for further research.
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Tareq M. Al-shami, M. Hosny. Generalized approximation spaces generation from $ \mathbb{I}_j $-neighborhoods and ideals with application to Chikungunya disease[J]. AIMS Mathematics, 2024, 9(4): 10050-10077. doi: 10.3934/math.2024492
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