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In this paper, we introduce and study a new class of sets called hexa regular closed (Rh -closed for short), hexa regular open (Rh -open for short), hexa regular semi-closed (RS)h -closed for short), hexa regular semi- open ((RS)h -open for short), hexa regular weakly closed sets ((RW)h -closed for short), hexa regular weakly open sets ((RW)h - open for short) in hexa topological space. Some interesting propositions based on this set are introduced and established with suitable examples and their properties are also discussed.

The textile and fashion industry are a huge industry with the multiple sectors which use multifold resources to meet the needs of the customers. The fast fashion has ended up with more environment threats. The sustainable fashion is the solution to minimize the ecological impacts and reduce the resources and wastes. It focuses on how the product can stay during its entire life cycle with less impact to the environment. It is big challenge to be sustainable textile and fashion sector because of non-vertical business model

The uncontrollable cells in the lungs are the main cause of lung cancer that reduces the ability to breathe. In this study, fusion of Computed Tomography (CT) lung image and Positron Emission Tomography (PET) lung image using their structural similarity is presented. The fused image has more information compared to individual CT and PET lung images which helps radiologists to make decision quickly. Initially, the CT and PET images are divided into blocks of predefined size in an overlapping manner. The structural similarity between each block of CT and PET are computed for fusion. Image fusion is performed using a combination of structural similarity and MAX rule. If the structural similarity between CT and PET block is greater than a particular threshold, the MAX rule is applied; otherwise the pixel intensities in CT image are used. A simple thresholding approach is employed to detect the lung nodule from the fused image. The qualitative analyses show that the fusion approach provides more information with accurate detection of lung nodules.

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