(MFA), for detecting and classifying image abnormalities for large and very small datasets. A fuzzy system is

an AI system used to handle imprecise data. There are more than three types of fuzziness in any image data set:

1) due to a projection of a 3D object on a 2D surface, 2) due to the digitalization of the scan, and 3) conversion

of the digital image to grayscale, and more. Thus, this was referred to in the previous study as a multilayer

fuzzy approach (MCM) that employs multiple diverse standard images to compare with the abnormal image.

For each abnormal image, the average similarity was calculated across multiple normal images, addressing

issues encountered with MFA, and enhancing versatility. In this study, an AI-based method of image analysis

automation that utilizes fuzzy systems was applied to a cancer data set for the first time. MCM proved to be

highly efficient in detecting the abnormality in all types of images and sample sizes and surpassed the gold

standard, the convolutional neural network (CNN), in detecting the abnormality in images from a very small

data set. Moreover, MCM detects and classifies abnormality without any training, validation, or testing steps

for large and small data sets. Hence, MCM may be used to address one of the research gaps in medicine, which

detects, quantifies, and classifies images related to rare diseases with small data sets. This has the potential to

assist a physician with early detection, diagnosis, monitoring, and treatment planning of several diseases,

1 Introduction

Medical images like computed tomography (CT)

scans are used by physicians and researchers to

understand and diagnose disease, and guide

treatments. There are many effective currently

available automated image analysis tools to

determine the abnormalities in the objects within an

image, such as a tumor. However, the minimum

number of images to run these tools is hundreds or

available using the AI concept of deep learning,

such as convolutional neural networks (CNNs).

However, most of these methods need a bulk

number of images that are already classified. Even

the methods that require fewer images still need

thousands of images. Consequently, these methods

are not as helpful for analyzing medical images

from rare diseases and diseases with limited

available data. Hence, to address this gap, we

previously developed an Artificial Intelligence (AI)

sources. The first source of fuzziness is present in

images, MFA proves beneficial in medical image

analysis, particularly with CT scans or images of

rare diseases, saving physicians’ time.

1.1 Rational for the MCM Study

In the MFA study, only one standard image was

used and compared with the abnormal image to find

the abnormality. The main issue with this was

biased results in detecting the abnormality in the

images. For instance, in classifying CT scans for

lung cancer, a high-contrast initial image can lead to

misjudgments if later replaced with a lower-contrast

image. The SSI depends on the standard image, and

the CT scans used in this study is the ‘.dcm’ format,

which is the Digital imaging and communications in

medicine (DICOM) format (Figure 1). The data sets

considered had two random samples of different

sizes, [5]. In the current study, the selection of data

size was contingent on the nature of the analysis.

The first analysis performed was to compare MFA

and MCM, and for this, a data set of 367 images

with confirmed lung cancer was analyzed. The

severity ranged from stage 1 to stage 4. In addition,

were negligible and were not analyzed further.

The mathematical formula [2] used in the current

study MCM to find the SSI is as follows:

SSI (N, A) = [(2µN µA + c1)⋅(2 σNA + c2)] / [( µ2N

+ µ2A + c1)⋅( σ2N + σ2A + c2)],

where N is the normal image, A is the abnormal

image being compared, SSI(N, A) stands for the SSI

current study, among many available similarity

measure metrics between two images, is that the SSI

is a metric for measuring the similarity between two

images, with a focus on quantifying the similarity in

structure, luminance, and contrast between the

reference image and the abnormal image.

3.3 Multilayer Fuzzy Dataset and the Fuzzy

follows: {ID of the object or patient, abnormality in

percentages}.

As introduced in our previous study MFA [1], as

well as in the introductory part of the current study,

fuzziness arises in an image in numerous ways. One

mode is when a three-dimensional object is

projected on a two-dimensional exterior. The second

mode is through conversion of an image into pixels

3.7 Method used in the Current Study MCM

The method used in MCM is similar to the method

to compare them with the image with abnormalities.

Additionally, all the SSI scores, obtained when

multiple standard images were compared with one

abnormal image, were averaged. When subtracted

from 100, this averaged SSI score in percentage

form provides quantitative information on the

abnormality in the image. This process was

continued for all the remaining images with

abnormalities allocated for this analysis. According

to the fuzzy set theory, the method used in MCM

described is a fuzzy many-to-many relation (Figure

parts. The first part is developing a method to find

abnormalities in images using the concept of fuzzy

many to many relations, and the second part is to

classify images based on abnormalities.

Fig. 4. The method of comparing images in the

MCM method using the concept of the fuzzy many-

to-many relation.

the spread of the abnormality in the images was

observed.

Step 6: If the folder contained images with varying

degrees of spread of abnormality, the thresholds

were adjusted accordingly. For instance, if Stage 2

images were classified within the Stage 1 folder, the

classification threshold for Stage 1 was modified.

This process was completed for each folder,

adjusting the thresholds within the software.

Step 7: After the thresholds were adjusted, the code

SSIs were stored, and the identity number of each

After acquiring the fuzzy set, logic, and intelligence

rules were used to classify the SSI score as per the

abnormality, and finally the images were classified.

If the thresholds of classification were not

classifying some images or if they were classifying

many images incorrectly, the thresholds were

modified as mentioned above, and manual software

testing was used.

2. Precision: precision, alternatively recognized as

Positive Predictive Value, was measured for the

accuracy of positive predictions, and was defined as

the ratio of true positives to the total number of

positive predictions.

Precision = (True positives) / (True positives + False

positives)

3. Recall: recall assesses how proficiently the model

5. Specificity evaluates how well the model

recognizes cases in which the characteristic being

assessed does not occur. It can also be defined using

the formula given below:

of the number of true negative values and number of

false positive values

true negative values

7. False negative rate:

False negative rate = number of false negative

values / sum of number of false negatives and

number of true positive values

The fuzzy classification and the fuzzy thresholds of

classification for MFA_c are as follows:

If SSI >= 0.89, then the spread of the cancer is at

Stage 1,

If SSI >= 0.83 and SSI <= 0.89, the spread of cancer

is at Stage 2,

If SSI >= 0.605 and SSI <= 0.83, the spread of

cancer is at Stage 3,

made using light or low contrast standard images.

The predictions were done by using the prediction

data mentioned in the previous sections which can

be seen in Table 3.