Breast cancer is one of the major causes of death among women. Small clusters of micro calcifications appearing as collection of white spots on mammograms show an early warning of breast cancer. Image segmentation is an important element of Digital Image processing that subdivides the image into discrete regions/objects, each identified by the property of homogeneity of pixels. X-ray mammography is used as diagnostic tool for diagnosis of breast cancer. Edge detection of micro calcification clusters in mammogram images is the main issue of early detection of breast cancer. Fractals are of rough or fragmented geometric shape that can be subdivided in parts, each of which is a reduced similar of the whole. Fractal dimension and Hurst exponent are used to locate the micro calcifications in the mammogram. The concept of fractal is associated with geometrical objects satisfying criteria such as self-similarity and fractal dimensionality. Present method of edge detection is superior compared to conventional Sobel method, in which detection of edges of the regions or objects in an image takes place by the Fudge factor. The paper presents the application of fractals for early detection of breast cancer.
Setup time is the amount of time required for a machine to adjust its settings or the preparation of a device at each stage to process and deliver a completed job. A novel approach for the n-job 2-machine generalized intuitionistic fuzzy flow shop scheduling problem, subject to the setup time, was proposed. When the machines are kept in different places, the transporting and return times of transport play a significant role in the production. Generalized triangular intuitionistic fuzzy numbers were considered to represent the processing, setup, transportation, and return times. This study aims to minimize the intuitionistic fuzzy total production time with less vagueness.
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