# Toward Automatic Cardiomyocyte Clustering and Counting through Hesitant Fuzzy Sets
## 1 Introduction  
According to the World Health Organization (WHO), more than 12 million people die of heart disease each year [1]. Heart disease has become the number one killer of global population and the incidence is getting increasingly younger. Because the cardiac organ function is directly related to the cardiovascular function, studying the characteristics of cardiomyocytes is one of the fundamental approaches to studying heart diseases and cardiovascular diseases. In studying cardiomyocytes during medical cell research, one crucial step is to isolate and observe cardiomyocytes because the cardiomyocytes isolated from adult animals carry many characteristics representing disease-relevant models that are not available in cells from other developmental stages. Moreover, because the functional properties of adult cardiomyocytes are irreplaceable in other developmental stages, adult cardiomyocytes have become an important tool for studying cardiac structure, metabolism, function, pathophysiology, and its mechanisms [2; 3]. With the advances of the genetic studies on cardiac functions using cellular electrophysiology and molecular biology approaches, adult cardiomyocytes have been widely used [4]. At present, most adult rat cardiomyocytes not only resemble human cellsin structure and function, but also exclude fibroblasts [5] interference in the vitro culture. The normal cardiomyocytes that have just been isolated are in the shape of rods. Thus, we can distinguish the status of the cardiomyocytes according to the morphological characteristics of the cardiomyocytes. Nevertheless, the immediate rod rate after cardiomyocytes separation was low (only 10% to 15%). It is also difficult to configure cultures that extend the physiological activity of cardiomyocytes. In order to enable the technician to discover the success rate and the quality of the culture liquid in a timely manner, an automated computer system is highly desired to timely count the isolated cardiomyocytes and observe the morphological changes of the subsequent culture process, e.g., through cell clustering. Clustering is the process of dividing a series of objects, schemes, or events into several classes that are not predefined (i.e., unsupervised). The characteristics of objects in each class are more akin to each other than those from distinct classes. Cluster analysis usually takes mathematical methods to classify objective items according to certain criteria, relying on the similarity of samples as the principle of division; therefore, choosing an appropriate similarity becomes a key factor to a successful clustering [6]. Currently, most studies on cell clustering in biology [7; 8] focus on how to prevent cell clustering growth in the process of culture. However, for the studies on cell classification [9; 10; 11], most of them are known target categories, and the target to be classified has obvious characteristics of which category it belongs to. In the classification of cardiomyocyte shape, manual approaches are criticized for the fact that different people may hold discrepant judgments on which cardiomyocytes should be classified into which group. However, common clustering algorithms (such as k-means algorithm [12], graph theory clustering algorithm [13], and density clustering algorithm [14]) cannot work for solving the problem of cardiomyocyte clustering because their thoughts are, respectively, according to determining which category it belongs to based on the distance between the object to be clustered and the center point, or according to determining classification based on graph theory and network detection ideas, or divide the type by comparing the number of objects in the circle of the unclassified object with the radius r of the circle and the critical minimum number. Some target recognition and detection algorithms based on clustering [15; 16; 17; 18] are applicable to specific algorithms in image processing according to different application scenarios, which will be introduced in detail.