# Improved Dominance Soft Set Based Decision Rules with Pruning for Leukemia Image Classification

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## Abstract

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## 1. Introduction

#### 1.1. Research Motivation

#### 1.2. Research Contribution

- A new algorithm is applied to segment the leukemia nucleus based on Particle Swarm Optimization (PSO), which is a popular search optimization algorithm.
- The Haralick texture-based GLCM is employed to extract features in four directions, and shape and color based features from the segmented image.
- Improved dominance soft set-based decision rules with pruning algorithm (IDSSDRP) is applied to classify the leukemia cancerous image. This is carried out in three phases:
- In the first phase, an improved dominance soft set-based reduction technique using AND operation in multi-soft set is applied to find the reduct set.
- In the second phase, the dominance soft set-based approach is applied to generate decision rules. Receiver operating characteristic (ROC) curve analysis is used to evaluate the efficiency of the proposed decision rules.
- In the third phase, the rule pruning method is employed to simplify the rules to minimize the processing time for predicting the diseases (tumor image).

- Different classification algorithms are evaluated using appropriate classification measures.

## 2. Related Work

## 3. Methods and Materials

#### 3.1. Input Image

#### 3.2. Preprocessing

#### 3.3. Segmentation

Algorithm 1 Pseudo Code for PSO algorithm |

$Input:\text{}\mathrm{Each}\text{}\mathrm{image}\text{}\mathrm{is}\text{}\mathrm{considered}\text{}\mathrm{as}\text{}\mathrm{a}\text{}\mathrm{particle}$ |

$Output:\mathrm{Segmented}\text{}\mathrm{image}$ |

$\mathrm{For}\text{}\mathrm{each}\text{}\mathrm{particle}$ |

$\mathrm{Initialize\; particle}$ |

End |

$\mathrm{Do}$ |

$\mathrm{For}\text{}\mathrm{each}\text{}\mathrm{particle}$ |

$\mathrm{Calculate}\text{}\mathrm{Data}\text{}\mathrm{fitness}\text{}\mathrm{value}$ |

$\mathrm{If}\text{}\mathrm{the}\text{}\mathrm{fitness}\_\mathrm{value}\text{}\mathrm{is}\text{}\mathrm{better}\text{}\mathrm{than}\text{}\mathrm{pBest}$ |

$\mathrm{Set}\text{}\mathrm{pBest}\text{}=\text{}\mathrm{currentfitnessvalue}$ |

$\mathrm{If}\text{}\mathrm{pBest}\text{}\mathrm{is}\text{}\mathrm{better}\text{}\mathrm{than}\text{}\mathrm{gBest}$ |

$\mathrm{Set}\text{}\mathrm{gBest}\text{}=\text{}\mathrm{pBest}$ |

$\mathrm{End}\text{}$ |

$\mathrm{For}\text{}\mathrm{each}\text{}\mathrm{particle}$ |

$\mathrm{Calculate}\text{}\mathrm{particle}\_\mathrm{Velocity}$ |

$\mathrm{Use}\text{}\mathrm{gBest}\text{}\mathrm{and}\text{}\mathrm{Velocity}\text{}\mathrm{to}\text{}\mathrm{update}\text{}\mathrm{the}\text{}\mathrm{particle}$ |

End |

$\mathrm{While}\mathrm{maximum}\text{}\mathrm{iterations}\text{}\mathrm{or}\text{}\mathrm{minimum}\text{}\mathrm{error}\text{}\mathrm{criteria}\text{}\mathrm{is}\text{}\mathrm{met}$ |

#### 3.4. Feature Extraction

#### 3.5. Dominance Based Soft Set Theory

#### 3.6. Dominance Soft Set Based Decision Rules

**Definition 1**:

**decision rules**

**Definition 2**:

**decision rules**

## 4. The Proposed Method: Improved Dominance Soft Set Based Decision Rules with Rule Pruning (IDSSDRP)

Algorithm 2 Improved dominance soft set-based attributes reduction using AND operation |

Phase 1: (Improved Dominance Soft Set based Attributes Reduction using AND operation) |

$\mathrm{IDSSA}\left(\mathrm{C},\mathrm{D}\right)$ |

$\mathrm{C},\text{}\mathrm{the}\text{}\mathrm{set}\text{}\mathrm{of}\text{}\mathrm{all}\text{}\mathrm{conditional}\text{}\mathrm{attributes}$ |

$\mathrm{D},\text{}\mathrm{the}\text{}\mathrm{decision}\text{}\mathrm{attribute}$ |

$\mathrm{A},\text{}\mathrm{Attributes}\text{}\mathrm{in}\text{}\mathrm{multivalued}\text{}\mathrm{information}\text{}\mathrm{system}$ |

$\left(1\right)\text{}\mathrm{S}\text{}\leftarrow \left\{\text{}\right\}$ |

$\left(2\right)\text{}\mathrm{do}$ |

$\left(3\right)\text{}$ Construct the Multi-valued information Table (F, S)$\text{}\mathrm{C}=\left(\mathrm{F},\text{}\mathrm{S}\right)\text{}\mathrm{where}$ S $\in \mathrm{A}$ |

U = $\left(\mathrm{F},{\mathrm{a}}_{1}\times {\mathrm{a}}_{2}\times {\mathrm{a}}_{3}\dots \dots \times {\mathrm{a}}_{\mathrm{i}}\right)\text{}\mathrm{i}=\mathrm{no}.\mathrm{of}\text{}\mathrm{attributes}\text{}\mathrm{in}\text{}\mathrm{C}$ |

$\left(4\right)\text{}\mathrm{T}\text{}\leftarrow \mathrm{S}$ |

$\left(5\right)\forall \text{}\mathrm{P}\subseteq \mathrm{C}$ |

$\left(6\right)\text{}\mathrm{Calculate}\text{}\mathrm{Dependency},{\mathsf{\gamma}}_{\mathrm{P}}\left(\mathrm{Cl}\right)\text{}\mathrm{using}\text{}\mathrm{Equation}\text{}\left(9\right)$ |

$\left(7\right)\text{}\mathrm{Find}\text{}\mathrm{Max}\left({\mathsf{\gamma}}_{\mathrm{P}}\left(\mathrm{C}\right)\right)$ |

$\left(8\right){\text{}\mathrm{if}\text{}\mathsf{\gamma}}_{\mathrm{S}\cup \left\{\mathrm{P}\right\}}\left(\mathrm{C}\right)\ge {\mathsf{\gamma}}_{\mathrm{C}}\left(\mathrm{C}\right)$ |

$\left(9\right)\text{}\mathrm{T}\leftarrow \text{}\mathrm{S}\cup \left\{\mathrm{P}\right\}$ |

$\left(10\right)\text{}\mathrm{S}\text{}\leftarrow \mathrm{T}$ |

$\left(11\right){\text{}\mathrm{until}\text{}\mathsf{\gamma}}_{\mathrm{P}}\left(\mathrm{Cl}\right)={\text{}\mathsf{\gamma}}_{\mathrm{C}}\left(\mathrm{Cl}\right)$ |

$\left(12\right)\text{}\mathrm{return}\text{}\mathrm{S}$ |

Algorithm 3 Decision Rules Generation |

Phase 2: (Decision Rules—DR Generation) |

$\mathrm{DR}\left(\mathrm{U},\mathrm{S}\right)$ |

$\mathrm{U},\text{}\mathrm{Universal}\text{}\mathrm{set}$ |

$\mathrm{S},\text{}\mathrm{Selected}\text{}\mathrm{attributes}$ |

$\left(1\right)\mathrm{Compute}\text{}\mathrm{lower}\text{}\mathrm{for}\text{}\mathrm{the}\text{}\mathrm{selected}\text{}\mathrm{attributes}\text{}\mathrm{S}\text{}\mathrm{for}\text{}\mathrm{both}\text{}\mathrm{the}\text{}\mathrm{classes}\text{}\mathrm{based}\text{}\mathrm{on}\text{}\mathrm{Equations}\text{}\left(3\right)\text{}\mathrm{and}\text{}\left(4\right).\text{}$ |

$\mathrm{f}\left(\mathrm{U},{\mathrm{S}}_{{\mathrm{Cl}}_{1}}\right)\to \text{}\mathrm{P}\text{}\_\left({\mathrm{Cl}}_{1}^{\ge}\right)$ |

$\mathrm{f}\left(\mathrm{U},{\mathrm{S}}_{{\mathrm{Cl}}_{2}}\right)\to \text{}\mathrm{P}\text{}\_\left({\mathrm{Cl}}_{2}^{\le}\right)$ |

$\left(2\right){\mathrm{D}}_{\ge}{\mathrm{decision}\text{}\mathrm{rules}\text{}\mathrm{derived}\text{}\mathrm{from}\text{}\mathrm{the}\text{}\mathrm{P}}_{\mathrm{soft}}{\text{}\mathrm{lower}\text{}\mathrm{approximation}\text{}\mathrm{of}\text{}\mathrm{the}\text{}\mathrm{upward}\text{}\mathrm{unions}\text{}\mathrm{of}\text{}\mathrm{classes}\text{}\mathrm{Cl}}_{1}^{\ge}$ |

$\left(3\right){\mathrm{D}}_{\le}{\mathrm{decision}\text{}\mathrm{rules}\text{}\mathrm{derived}\text{}\mathrm{from}\text{}\mathrm{P}}_{\mathrm{soft}}{\text{}\mathrm{lower}\text{}\mathrm{approximation}\text{}\mathrm{of}\text{}\mathrm{the}\text{}\mathrm{downward}\text{}\mathrm{unions}\text{}\mathrm{of}\text{}\mathrm{classes}\text{}\mathrm{Cl}}_{2}^{\le}$ |

Algorithm 4 Decision Rule Pruning |

Phase 3: (Rule Pruning—RP) |

$\mathrm{RP}\left(\mathrm{Derived}-\mathrm{Rules}\right)$ |

$\mathrm{R},\text{}\mathrm{Set}\text{}\mathrm{of}\text{}\mathrm{derived}\text{}\mathrm{rules}$ |

${\mathrm{P}}_{\mathrm{r}},\text{}\mathrm{Pruned}\text{}\mathrm{rules}$ |

$\left(1\right){\text{}\mathrm{P}}_{\mathrm{r}}\to \left\{\text{}\right\}$ |

$\left(2\right)\text{}\mathrm{m}=\text{}\mathrm{no}.\text{}\mathrm{of}\text{}\mathrm{rules}\text{}\mathrm{in}\text{}\mathrm{R}$ |

$\left(3\right)\text{}\mathrm{For}\text{}\mathrm{i}=1\text{}\mathrm{to}\text{}\mathrm{m}-1$ |

${\text{}\mathrm{R}}_{\mathrm{u}}={\text{}\mathrm{R}}_{\mathrm{i}}$ |

$\mathrm{n}=\left|{\mathrm{R}}_{\mathrm{u}}\right|$ |

$\left(4\right)\text{}\mathrm{for}\text{}\mathrm{j}=1\text{}\mathrm{to}\text{}\mathrm{n}-1$ |

${\mathrm{Eliminate}\text{}\mathrm{the}\text{}\mathrm{j}}^{\mathrm{th}}{\text{}\mathrm{conditional}\text{}\mathrm{feature}\text{}\mathrm{C}}_{\mathrm{j}}{\mathrm{in}\text{}\mathrm{rule}\text{}\mathrm{R}}_{\mathrm{u}}$ |

${\mathrm{if}\text{}\mathrm{R}}_{\mathrm{i}}{\text{}\mathrm{inconsistent}\text{}\mathrm{with}\text{}\mathrm{any}\text{}\mathrm{rule}\text{}\mathrm{R}}_{\mathrm{m}}\text{}\mathrm{then}$ |

${\mathrm{Return}\text{}\mathrm{the}\text{}\mathrm{dropped}\text{}\mathrm{feature}\text{}\mathrm{C}}_{\mathrm{j}}$ |

$\mathrm{end}\text{}\mathrm{if}$ |

$\mathrm{end}\text{}\mathrm{for}$ |

$\left(5\right){\text{}\mathrm{if}\text{}\mathrm{R}}_{\mathrm{u}}\in {\mathrm{P}}_{\mathrm{r}}\text{}\mathrm{then}$ |

${\mathrm{Eliminate}\text{}\mathrm{rule}\text{}\mathrm{R}}_{\mathrm{u}}$ |

$\mathrm{else}$ |

${\text{}\mathrm{P}}_{\mathrm{r}}\text{}\to {\mathrm{R}}_{\mathrm{u}}\cup {\mathrm{P}}_{\mathrm{r}}$ |

$\mathrm{end}\text{}\mathrm{if}$ |

$\mathrm{End}\text{}\mathrm{for}$ |

$\left(6\right){\text{}\mathrm{Return}\text{}\mathrm{P}}_{\mathrm{r}}$ |

#### 4.1. Case Study

#### 4.1.1. Phase-1 (Attribute Reduction)

#### 4.1.2. Phase-2 (Decision Rules Generation)

- Rule 1: $\mathrm{if}\text{}\mathrm{f}\left(\mathrm{c},{\mathrm{a}}_{1}\right)\ge \mathrm{MBA}\text{}\mathrm{and}\text{}\mathrm{f}\left(\mathrm{c},{\mathrm{a}}_{2}\right)\ge \mathrm{High}\text{}\mathrm{then}\text{}\mathrm{c}\in {\mathrm{Cl}}_{1}^{\ge}$
- Rule 2: $\mathrm{if}\text{}\mathrm{f}\left(\mathrm{c},{\mathrm{a}}_{1}\right)\ge \mathrm{MBA}\text{}\mathrm{and}\text{}\mathrm{f}\left(\mathrm{c},{\mathrm{a}}_{2}\right)\ge \mathrm{Medium}\text{}\mathrm{then}\text{}\mathrm{c}\in {\mathrm{Cl}}_{1}^{\ge}$
- Rule 3: $\mathrm{if}\text{}\mathrm{f}\left(\mathrm{c},{\mathrm{a}}_{1}\right)\ge \mathrm{MCA}\text{}\mathrm{and}\text{}\mathrm{f}\left(\mathrm{c},{\mathrm{a}}_{2}\right)\ge \mathrm{High}\text{}\mathrm{then}\text{}\mathrm{c}\in {\mathrm{Cl}}_{1}^{\ge}$

- Rule 4: $\mathrm{if}\text{}\mathrm{f}\left(\mathrm{c},{\mathrm{a}}_{1}\right)\le \mathrm{MBA}\text{}\mathrm{and}\text{}\mathrm{f}\left(\mathrm{c},{\mathrm{a}}_{2}\right)\le \mathrm{Low}\text{}\mathrm{then}\text{}\mathrm{c}\in {\mathrm{Cl}}_{2}^{\le}$
- Rule 5: $\mathrm{if}\text{}\mathrm{f}\left(\mathrm{c},{\mathrm{a}}_{1}\right)\le \mathrm{M}.\mathrm{Sc}\text{}\mathrm{and}\text{}\mathrm{f}\left(\mathrm{c},{\mathrm{a}}_{2}\right)\le \mathrm{Low}\text{}\mathrm{then}\text{}\mathrm{c}\in {\mathrm{Cl}}_{2}^{\le}$
- Rule 6: $\mathrm{if}\text{}\mathrm{f}\left(\mathrm{c},{\mathrm{a}}_{1}\right)\le \mathrm{MCA}\text{}\mathrm{and}\text{}\mathrm{f}\left(\mathrm{c},{\mathrm{a}}_{2}\right)\le \mathrm{Medium}\text{}\mathrm{then}\text{}\mathrm{c}\in {\mathrm{Cl}}_{2}^{\le}$

#### 4.1.3. Phase-3 (Decision Rule Pruning)

- Rule 1: $\mathrm{if}\text{}\mathrm{f}\left(\mathrm{c},{\mathrm{a}}_{1}\right)\ge \mathrm{MBA}\text{}\mathrm{then}\text{}\mathrm{c}\in {\mathrm{Cl}}_{1}^{\ge}$
- Rule 2: $\mathrm{if}\text{}\mathrm{f}\left(\mathrm{c},{\mathrm{a}}_{2}\right)\ge \mathrm{High}\text{}\mathrm{then}\text{}\mathrm{c}\in {\mathrm{Cl}}_{1}^{\ge}$
- Rule 3: $\mathrm{if}\text{}\mathrm{f}\left(\mathrm{c},{\mathrm{a}}_{2}\right)\le \mathrm{Low}\text{}\mathrm{then}\text{}\mathrm{c}\in {\mathrm{Cl}}_{2}^{\le}$

## 5. Results and Discussions

#### 5.1. Performance Analysis of Attribute Reduction Algorithm

#### 5.2. Evaluation of Proposed IDSSDRP Algorithm

_{soft}lower approximation of the upward and downward unions of class 1 and class 2 for the GLCM_0 dataset as shown in Appendix A. The pruned rules after applying the proposed rule pruning algorithm for the GLCM_0 dataset are shown in Appendix B. The number of rules generated for class 1 is three and that of class 2 is one.

#### 5.3. Graphical Performance Assessment for IDSSDRP

## 6. Conclusions and Future Scope

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## Appendix A

## Appendix B

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**Figure 3.**Segmentation results using PSO. as (

**a**) Im114_1, Im070_1 and Im073_1; (

**b**) Im192_0, Im259_0 and Im248_0; (

**c**) Im001_1, Im002_1 and Im018_1; (

**d**) Im056_1, Im057_1 and Im060_1.

**Figure 10.**ROC curve analysis. as (

**a**) IDSSDRP method - GLCM_0; (

**b**) IDSSDRP method - GLCM_45; (

**c**) IDSSDRP method - GLCM_90; (

**d**) IDSSDRP method - GLCM_135; (

**e**) IDSSDRP method - Shape and Colour.

Candidate | a1 (Degree) | a2 (Work_Experience) | a3 (German_Lang) | a4 (Personality) | d Decision_Class |
---|---|---|---|---|---|

1 | MBA | Medium | Known | Excellent | Accept |

2 | MBA | Low | Known | Normal | Reject |

3 | M.Sc | Low | Known | Good | Reject |

4 | MCA | High | Known | Normal | Accept |

5 | MCA | Medium | Known | Normal | Reject |

6 | MCA | High | Known | Excellent | Accept |

7 | MBA | High | Unknown | Good | Accept |

8 | M.Sc | Low | Unknown | Excellent | Reject |

a1 | a2 | a3 | a4 | d | ||||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

MBA | M.Sc | MCA | Medium | Low | High | Known | Unknown | Excellent | Normal | Good | Accept | Reject |

1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 |

1 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 |

0 | 1 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 0 | 1 | 0 | 1 |

0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 1 | 0 |

0 | 0 | 1 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 |

0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 1 | 0 | 0 | 1 | 0 |

1 | 0 | 0 | 0 | 0 | 1 | 0 | 1 | 0 | 0 | 1 | 1 | 0 |

0 | 1 | 0 | 0 | 1 | 0 | 0 | 1 | 1 | 0 | 0 | 0 | 1 |

Dataset | No. of Features Extracted | IDSSA |
---|---|---|

GLCM_0 | 22 | 10 |

GLCM_45 | 22 | 11 |

GLCM_90 | 22 | 11 |

GLCM_135 | 22 | 11 |

Shape and Colour | 22 | 12 |

Description | Results Obtained for Confusion Matrix | ||||||||||||||

Actual Output | - | Predicted Output | DT | J48 | JRip | LMT | RF | Proposed | |||||||

Healthy Image (HI) | Unhealthy Image (UI) | HI | UI | HI | UI | HI | UI | HI | UI | HI | UI | HI | UI | ||

Healthy Image | Correctly Predicted as Healthy Image (TP) | Incorrectly Predicted as Unhealthy Image (FN) | 119 | 56 | 122 | 53 | 114 | 61 | 122 | 53 | 106 | 68 | 162 | 13 | |

Unhealthy Image | Incorrectly Predicted as Healthy Image (FP) | Correctly Predicted as Unhealthy Image (TN) | 13 | 180 | 14 | 179 | 14 | 179 | 14 | 179 | 2 | 191 | 3 | 190 |

Metrics | Explanation | Equation |

Sensitivity (or Recall) (in %) | It is employed to measure the True positive rates | $\mathrm{TP}/\left(\mathrm{TP}\text{}+\text{}\mathrm{FN}\right)$ |

Specificity (in %) | Measure the true negative rates | $\mathrm{TN}/\left(\mathrm{TN}\text{}+\text{}\mathrm{FP}\right)$ |

Accuracy (in %) | Calculate the probability of the true value of the class attributes. | $\left(\mathrm{TP}+\mathrm{TN}\right)/\left(\mathrm{TP}+\mathrm{TN}+\mathrm{FP}+\mathrm{FN}\right)$ |

Precision (in %) | Degree of exactness | $\mathrm{TP}/\left(\mathrm{TP}\text{}+\text{}\mathrm{FP}\right)$ |

F1 score | The harmonic mean of precision and recall | $2\times \left(\mathrm{Precision}\text{}\times \text{}\mathrm{Recall}\right)/\left(\mathrm{Precision}\text{}+\text{}\mathrm{Recall}\right)$ |

Error Rate (=1 − accuracy) | An approximation of misclassification probability. | $\mathrm{FP}+\mathrm{FN}/\mathrm{TP}+\mathrm{TN}+\mathrm{FP}+\mathrm{FN}$ |

Matthews Correlation Coefficient (MCC) | The association between the actual and predicted class | $\frac{\left(\mathrm{TP}\text{}\times \text{}\mathrm{TN}\right)-\left(\mathrm{FP}\text{}\times \text{}\mathrm{FN}\right)}{\sqrt{\left(\mathrm{TP}\text{}+\mathrm{FP}\right)\times \left(\mathrm{TP}\text{}+\text{}\mathrm{FN}\right)\times \left(\mathrm{TN}\text{}+\text{}\mathrm{FP}\right)\times \left(\mathrm{TN}\text{}+\text{}\mathrm{FN}\right)}}$ |

Lift | The proportion among the outcomes obtained with and without the Model | $\left(\mathrm{TP}/\left(\mathrm{TP}+\mathrm{FP}\right)\right)/\left(\left(\mathrm{TP}+\mathrm{FN}\right)/\left(\mathrm{TP}+\mathrm{TN}+\mathrm{FP}+\mathrm{FN}\right)\right)$ |

G-mean | The product of the prediction accuracies for both classes | $\sqrt{\mathrm{precison}\text{}\times \mathrm{recall}}$ |

Youden’s index | The arithmetic mean among sensitivity and specificity | $\mathrm{sensitivity}\text{}+\text{}\mathrm{specificity}\text{}-\text{}1$ |

Balanced Classification Rate (BCR) | The mean of sensitivity and specificity. | $\text{\xbd}\left(\mathrm{sensitivity}\text{}+\text{}\mathrm{specificity}\right)$ |

Balanced Error Rate (BER)or | The mean of the errors in each class. It also named as Half Total Error Rate (HTER) | $1\text{}-\text{}\mathrm{BCR}$ |

Prediction Metrics | Decision Tree | J48 | JRip | LMT | Random Forest | Proposed |
---|---|---|---|---|---|---|

Accuracy | 79.81 | 79.81 | 78.37 | 78.85 | 78.37 | 98.08 |

Sensitivity | 94.52 | 94.52 | 97.26 | 93.84 | 93.84 | 98.63 |

Specificity | 45.16 | 45.16 | 33.87 | 43.55 | 41.94 | 96.77 |

Precision | 80.23 | 80.23 | 77.60 | 79.65 | 79.19 | 98.63 |

Error Rate | 0.20 | 0.20 | 0.22 | 0.21 | 0.22 | 0.02 |

MCC | 0.48 | 0.48 | 0.44 | 0.45 | 0.44 | 0.95 |

F1 measure | 86.79 | 86.79 | 86.32 | 86.16 | 85.89 | 98.63 |

G-mean | 87.08 | 87.08 | 86.87 | 86.45 | 86.20 | 98.63 |

Lift value | 1.14 | 1.14 | 1.11 | 1.13 | 1.13 | 1.41 |

Youden’s index | 0.40 | 0.40 | 0.31 | 0.37 | 0.36 | 0.95 |

BCR | 69.84 | 69.84 | 65.57 | 68.69 | 67.89 | 97.70 |

BER | 0.30 | 0.30 | 0.34 | 0.31 | 0.32 | 0.02 |

Prediction Metrics | Decision Tree | J48 | JRip | LMT | Random Forest | Proposed |
---|---|---|---|---|---|---|

Accuracy | 77.88 | 78.85 | 79.33 | 79.81 | 78.85 | 97.12 |

Sensitivity | 92.47 | 97.26 | 92.47 | 92.47 | 93.15 | 97.26 |

Specificity | 43.55 | 35.48 | 48.39 | 50.00 | 45.16 | 96.77 |

Precision | 79.41 | 78.02 | 80.84 | 81.33 | 80.00 | 98.61 |

Error Rate | 0.22 | 0.21 | 0.21 | 0.20 | 0.21 | 0.03 |

MCC | 0.43 | 0.45 | 0.47 | 0.48 | 0.45 | 0.93 |

F1 measure | 85.44 | 86.59 | 86.26 | 86.54 | 86.08 | 97.93 |

G-mean | 85.69 | 87.11 | 86.46 | 86.72 | 86.33 | 97.93 |

Lift value | 1.13 | 1.11 | 1.15 | 1.16 | 1.14 | 1.40 |

Youden’s index | 0.36 | 0.33 | 0.41 | 0.42 | 0.38 | 0.94 |

BCR | 68.01 | 66.37 | 70.43 | 71.23 | 69.16 | 97.02 |

BER | 0.32 | 0.34 | 0.30 | 0.29 | 0.31 | 0.03 |

Prediction Metrics | Decision Tree | J48 | JRip | LMT | Random Forest | Proposed |
---|---|---|---|---|---|---|

Accuracy | 81.25 | 81.25 | 81.25 | 82.21 | 82.21 | 99.04 |

Sensitivity | 96.58 | 96.58 | 96.58 | 97.26 | 97.26 | 99.32 |

Specificity | 45.16 | 45.16 | 45.16 | 46.77 | 46.77 | 98.39 |

Precision | 80.57 | 80.57 | 80.57 | 81.14 | 81.14 | 99.32 |

Error Rate | 0.19 | 0.19 | 0.19 | 0.18 | 0.18 | 0.01 |

MCC | 0.52 | 0.52 | 0.52 | 0.55 | 0.55 | 0.98 |

F1 measure | 87.85 | 87.85 | 87.85 | 88.47 | 88.47 | 99.32 |

G-mean | 88.21 | 88.21 | 88.21 | 88.84 | 88.84 | 99.32 |

Lift value | 1.15 | 1.15 | 1.15 | 1.16 | 1.16 | 1.41 |

Youden’s index | 0.42 | 0.42 | 0.42 | 0.44 | 0.44 | 0.98 |

BCR | 70.87 | 70.87 | 70.87 | 72.02 | 72.02 | 98.85 |

BER | 0.29 | 0.29 | 0.29 | 0.28 | 0.28 | 0.01 |

Prediction Metrics | Decision Tree | J48 | JRip | LMT | Random Forest | Proposed |
---|---|---|---|---|---|---|

Accuracy | 79.81 | 79.81 | 79.81 | 78.85 | 76.92 | 97.60 |

Sensitivity | 94.52 | 94.52 | 92.47 | 91.10 | 89.04 | 98.63 |

Specificity | 45.16 | 45.16 | 50.00 | 50.00 | 48.39 | 95.16 |

Precision | 80.23 | 80.23 | 81.33 | 81.10 | 80.25 | 97.96 |

Error Rate | 0.20 | 0.20 | 0.20 | 0.21 | 0.23 | 0.02 |

MCC | 0.48 | 0.48 | 0.48 | 0.46 | 0.41 | 0.94 |

F1 measure | 86.79 | 86.79 | 86.54 | 85.81 | 84.42 | 98.29 |

G-mean | 87.08 | 87.08 | 86.72 | 85.95 | 84.53 | 98.29 |

Lift value | 1.14 | 1.14 | 1.16 | 1.16 | 1.14 | 1.40 |

Youden’s index | 0.40 | 0.40 | 0.42 | 0.41 | 0.37 | 0.94 |

BCR | 69.84 | 69.84 | 71.23 | 70.55 | 68.71 | 96.90 |

BER | 0.30 | 0.30 | 0.29 | 0.29 | 0.31 | 0.03 |

Prediction Metrics | Decision Tree | J48 | JRip | LMT | Random Forest | Proposed |
---|---|---|---|---|---|---|

Accuracy | 81.25 | 81.73 | 79.81 | 81.73 | 80.29 | 95.67 |

Sensitivity | 96.58 | 95.89 | 92.47 | 95.21 | 92.47 | 97.26 |

Specificity | 45.16 | 48.39 | 50.00 | 50.00 | 51.61 | 91.94 |

Precision | 80.57 | 81.40 | 81.33 | 81.76 | 81.82 | 96.60 |

Error Rate | 0.19 | 0.18 | 0.20 | 0.18 | 0.20 | 0.04 |

MCC | 0.52 | 0.54 | 0.48 | 0.54 | 0.50 | 0.90 |

F1 measure | 87.85 | 88.05 | 86.54 | 87.97 | 86.82 | 96.93 |

G-mean | 88.21 | 88.35 | 86.72 | 88.23 | 86.98 | 96.93 |

Lift value | 1.15 | 1.16 | 1.16 | 1.16 | 1.17 | 1.38 |

Youden’s index | 0.42 | 0.44 | 0.42 | 0.45 | 0.44 | 0.89 |

BCR | 70.87 | 72.14 | 71.23 | 72.60 | 72.04 | 94.60 |

BER | 0.29 | 0.28 | 0.29 | 0.27 | 0.28 | 0.05 |

Classification Algorithms | Accuracy | Sensitivity | Specificity |
---|---|---|---|

Existing Approach | |||

NB | 80.95 | 69.49 | 88.4 |

KNN | 78.57 | 79.59 | 78.43 |

MLP | 78.57 | 85.9 | 75.53 |

RBFN | 79.05 | 64.12 | 81.05 |

SVM | 91.43 | 75.13 | 98.7 |

GLCM_0 Dataset | |||

Decision Tree | 79.81 | 94.52 | 45.16 |

J48 | 79.81 | 94.52 | 45.16 |

JRip | 78.37 | 97.26 | 33.87 |

LMT | 78.85 | 93.84 | 43.55 |

Random Forest | 78.37 | 93.84 | 41.94 |

Proposed IDSSDRP | 98.08 | 98.63 | 96.77 |

GLCM_45 Dataset | |||

Decision Tree | 77.88 | 92.47 | 43.55 |

J48 | 78.85 | 97.26 | 35.48 |

JRip | 79.33 | 92.47 | 48.39 |

LMT | 79.81 | 92.47 | 50 |

Random Forest | 78.85 | 93.15 | 45.16 |

Proposed IDSSDRP | 97.12 | 97.26 | 96.77 |

GLCM_90 Dataset | |||

Decision Tree | 81.25 | 96.58 | 45.16 |

J48 | 81.25 | 96.58 | 45.16 |

JRip | 81.25 | 96.58 | 45.16 |

LMT | 82.21 | 97.26 | 46.77 |

Random Forest | 82.21 | 97.26 | 46.77 |

Proposed IDSSDRP | 99.04 | 99.32 | 98.39 |

GLCM_135 Dataset | |||

Decision Tree | 79.81 | 94.52 | 45.16 |

J48 | 79.81 | 94.52 | 45.16 |

JRip | 79.81 | 92.47 | 50 |

LMT | 78.85 | 91.1 | 50 |

Random Forest | 76.92 | 89.04 | 48.39 |

Proposed IDSSDRP | 97.6 | 98.63 | 95.16 |

Shape and Colour | |||

Decision Tree | 81.25 | 96.58 | 45.16 |

J48 | 81.73 | 95.89 | 48.39 |

JRip | 79.81 | 92.47 | 50 |

LMT | 81.73 | 95.21 | 50 |

Random Forest | 80.29 | 92.47 | 51.61 |

Proposed IDSSDRP | 95.67 | 97.26 | 91.94 |

© 2020 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Jothi, G.; Inbarani, H.H.; Azar, A.T.; Koubaa, A.; Kamal, N.A.; Fouad, K.M.
Improved Dominance Soft Set Based Decision Rules with Pruning for Leukemia Image Classification. *Electronics* **2020**, *9*, 794.
https://doi.org/10.3390/electronics9050794

**AMA Style**

Jothi G, Inbarani HH, Azar AT, Koubaa A, Kamal NA, Fouad KM.
Improved Dominance Soft Set Based Decision Rules with Pruning for Leukemia Image Classification. *Electronics*. 2020; 9(5):794.
https://doi.org/10.3390/electronics9050794

**Chicago/Turabian Style**

Jothi, Ganesan, Hannah H. Inbarani, Ahmad Taher Azar, Anis Koubaa, Nashwa Ahmad Kamal, and Khaled M. Fouad.
2020. "Improved Dominance Soft Set Based Decision Rules with Pruning for Leukemia Image Classification" *Electronics* 9, no. 5: 794.
https://doi.org/10.3390/electronics9050794