Mathematical Morphology View of Topological Rough Sets and Its Applications

This article focuses on the relationship between mathematical morphology operations and rough sets,mainly based on the context of image retrieval and the basic image correspondence problem.Mathematical morphological procedures and set approximations in rough set theory have some clear parallels.Numerous initiatives have been made to connect rough sets with mathematical morphology.Numerous significant publications have been written in this field.Others attempt to show a direct connection between mathematical morphology and rough sets through relations,a pair of dual operations,and neighborhood systems.Rough sets are used to suggest a strategy to approximatemathematicalmorphology within the general paradigm of soft computing.A single framework is defined using a different technique that incorporates the key ideas of both rough sets and mathematical morphology.This paper examines rough set theory from the viewpoint of mathematical morphology to derive rough forms of themorphological structures of dilation,erosion,opening,and closing.These newly defined structures are applied to develop algorithm for the differential analysis of chest X-ray images from a COVID-19 patient with acute pneumonia and a health subject.The algorithm and rough morphological operations show promise for the delineation of lung occlusion in COVID-19 patients from chest X-rays.The foundations of mathematical morphology are covered in this article.After that,rough set theory ideas are taken into account,and their connections are examined.Finally,a suggested image retrieval application of the concepts from these two fields is provided.

Attribute Reduction for Information Systems via Strength of Rules and Similarity Matrix

An information system is a type of knowledge representation,and attribute reduction is crucial in big data,machine learning,data mining,and intelligent systems.There are several ways for solving attribute reduction problems,but they all require a common categorization.The selection of features in most scientific studies is a challenge for the researcher.When working with huge datasets,selecting all available attributes is not an option because it frequently complicates the study and decreases performance.On the other side,neglecting some attributes might jeopardize data accuracy.In this case,rough set theory provides a useful approach for identifying superfluous attributes that may be ignored without sacrificing any significant information;nonetheless,investigating all available combinations of attributes will result in some problems.Furthermore,because attribute reduction is primarily a mathematical issue,technical progress in reduction is dependent on the advancement of mathematical models.Because the focus of this study is on the mathematical side of attribute reduction,we propose some methods to make a reduction for information systems according to classical rough set theory,the strength of rules and similarity matrix,we applied our proposed methods to several examples and calculate the reduction for each case.These methods expand the options of attribute reductions for researchers.