Citation: Dounis, A.; Avramopoulos, A.-N.; Kallergi, M. Advanced Fuzzy Sets and Genetic Algorithm Optimizer for Mammographic Image Enhancement. Electronics 2023, 12, 3269. https://doi.org/10.3390/ electronics12153269 Academic Editor: Maria Evelina Fantacci Received: 5 July 2023 Revised: 26 July 2023 Accepted: 28 July 2023 Published: 29 July 2023 Copyright: © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). electronics Article Advanced Fuzzy Sets and Genetic Algorithm Optimizer for Mammographic Image Enhancement Anastasios Dounis * , Andreas-Nestor Avramopoulos and Maria Kallergi Department of Biomedical Engineering, Egaleo Park Campus, University of West Attica, 12243 Athens, Greece; bme18388061@uniwa.gr (A.-N.A.); kallergi@uniwa.gr (M.K.) * Correspondence: aidounis@uniwa.gr Abstract: A well-researched field is the development of Computer Aided Diagnosis (CADx) Systems for the benign-malignant classification of abnormalities detected by mammography. Due to the nature of the breast parenchyma, there are significant uncertainties about the shape and geometry of the abnormalities that may lead to an inaccurate diagnosis. These same uncertainties give mammograms a fuzzy character that is essential to the application of fuzzy processing. Fuzzy set theory considers uncertainty in the form of a membership function, and therefore fuzzy sets can process imperfect data if this imperfection originates from vagueness and ambiguity rather than randomness. Fuzzy contrast enhancement can improve edge detection and, by extension, the quality of related classification features. In this paper, classical (Linguistic hedges and fuzzy enhancement functions), advanced fuzzy sets (Intuitionistic fuzzy set (IFS), Pythagorean fuzzy set (PFS), and Fermatean fuzzy sets (FFS)), and a Genetic Algorithm optimizer are proposed to enhance the contrast of mammographic features. The advanced fuzzy sets provide better information on the uncertainty of the membership function. As a result, the intuitionistic method had the best overall performance, but most of the techniques could be used efficiently, depending on the problem that needed to be solved. Linguistic methods could provide a more manageable way of spreading the histogram, revealing more extreme values than the conventional methods. A fusion technique of the enhanced mammography images with Ordered Weighted Average operators (OWA) achieves a good-quality final image. Keywords: advanced fuzzy sets; linguistic hedges; intuitionist fuzzy set; pythagorean fuzzy set; fermatean fuzzy set; genetic algorithm; contrast enhancement; mammography images; OWA operators; image fusion; multi-fuzzy set 1. Introduction Breast cancer has preoccupied scientists for many years because of the worrisome statistics that arise. Globally, 1 in every 6 women, or 16%, who have breast cancer died in 2020 [1] (p. 15). In the United States, for the years 2017–2019, women have a lifetime probability of 12.9%, or 1 in every 8 women to develop invasive breast cancer [2] (p. 23). This creates the urge to develop and improve systems that can help physicians accurately and consistently identify features linked to invasive breast cancer at an initial stage. The importance of Decision Support Systems (DSS) in the health field has become crucial. Computer Aided Diagnosis (CADx) is part of the DSS and supports physicians in the accurate classification of mammographic findings, with promising results to date. Medical images are inherently noisy and blurry due to the physical properties of the imaging devices. Edges and outlines of mammographic features have additional blurring due to the nature of the parenchyma [3–7]. Accurate diagnosis requires that physicians have a good knowledge of the diverse appearance of pathology on the images. Noise and blur distort the appearance of pathology and lead to misclassification. Contrast enhancement techniques could improve contrast, restore pathological features, and, hence, assist in accurate diagnostic decisions [4,5,7,8]. Electronics 2023, 12, 3269. https://doi.org/10.3390/electronics12153269 https://www.mdpi.com/journal/electronics