In the realm of the pathological test, pathologists diagnose diseases viewing specimen on pathological slides based on the size, shape, texture, colour, and darkness of cells. There is no doubt that the detection process is critical and highly depends on experience. In most of the cases, it has been found that the visibility of the microscopic images is not very clear due to improper brightness and contrast. In this paper, the authors propose a new grey level image enhancement technique called fuzzy entropic bi-histogram fuzzy contrast stretching (FEBHFCS) method which is developed depending on the concept of fuzzy logic and appropriate histogram thresholding. The FEBHFCS method is associated with three controlling parameters which crucially influence the FEBHFCS’s image enhancement efficiency, and manual selection of these parameters does not provide full automation to the FEBHFCS. Therefore, this study formulates the image enhancement as a maximization problem which has been solved by employing bat algorithm with the combination of fractal dimension and quality index based on local variance as the objective function. The proposed FEBHFCS provides superior results to some well-known existing histogram equalization variants and has been applied for colour images through one proposed improved hue–saturation–value (HSV) colour model which has the capability to preserve the hue and tackle the out-of-gamut problem. Experimental results show that the proposed improved HSV colour model produces better outcomes than some existing classical and improved colour models by considering the quality of the enhanced colour images and computational time.