# Performance Evaluation of Construction Companies Using Integrated Entropy–Fuzzy VIKOR Model

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Research Development

#### 2.2. Proposed Entropy–Fuzzy VIKOR Model

_{ij}” of the index value of alternative m under criterion n.

_{j}” of criterion n.

_{j}” of criterion n.

_{ij}is the lowest ratio from the period of study for alternative i with respect to criterion j.

_{ij}is the average ratio from the period of study for alternative i with respect to criterion j.

_{ij}is the highest ratio from the period of study for alternative i with respect to criterion j.

_{ij}, b

_{ij}and c

_{ij}. DAR and DER should be minimized by assigning the smallest value for a

_{ij}, b

_{ij}and c

_{ij}.

_{ij}) for $i=1,\dots ,m$, $j=1,\dots ,n$. ${f}_{ij}$ refers to the score for alternative i with criterion j. The normalized fuzzy decision matrix is formed, and the equation to determine the new score of the alternative i with criterion j is shown below:

_{i}), regret (R

_{i}) and VIKOR indices (Q

_{i}) values, $i=1,\dots ,m$. v refers to the strategy of maximum group utility weight, while 1-v refers to the individual regret weight. When v = 0.5, the strategy could be compromised.

#### 2.3. VIKOR Model

_{ij}) for $i=1,\dots ,m$, $j=1,\dots ,n$. ${f}_{ij}$ refers to the score for alternative i with criterion j. The normalized decision matrix is formed, and the equation to determine the new score of the alternative i with criterion j is shown below:

_{i}), regret (R

_{i}) and VIKOR indices (Q

_{i}) values, $i=1,\dots ,m$. v refers to the strategy of maximum group utility weight, while 1-v refers to the individual regret weight. When v = 0.5, the strategy could be compromised.

## 3. Empirical Results

_{i}) and regret (R

_{i}) were determined by exploiting Equations (6) and (7), respectively.

_{i}were determined by using Equation (8). Based on the obtained entropy–fuzzy VIKOR scores (Q

_{i}), the alternative with the smallest Q

_{i}value was specified to be the best construction company.

_{i}) and the ranking of the companies were identified based on the proposed model. The Q

_{i}ranged from 0.090 to 0.998 according to the optimal solution of the proposed model that integrates the entropy weight and fuzzy VIKOR model. According to the proposed entropy–fuzzy VIKOR model, the decision alternative with the lowest Q value was determined as the best alternative or best construction company. Table 7 shows the results and findings generated by the proposed entropy–fuzzy VIKOR model. The ranking depicts that the best construction company in terms of financial performance was ECONBHD, followed by GADANG, KIMLUN, DKLS, KERJAYA, PTARAS, MITRA, MELATI, PRTASCO, GBGAQRS, BREM, HSL, GAMUDA, IJM, CRESBLD, EKOVEST, GKENT, HOHUP, WCT and lastly MUHIBAH. In this study, ECONBHD achieved the lowest value of Q, and thus ECONBHD outperformed the other construction companies in terms of financial performance. The results of this study show that the proposed model is applicable to solve the MCDM problems as illustrated by previous studies, such as the selection of sustainable third-party reverse logistics providers [10] and multi-criteria inventory classification problems [64] using the VIKOR model. The ranking of the companies was important in the financial performance evaluation because it helped the companies to identify their ranking among the competitors in the same field for benchmarking purposes [6].

_{i}) and optimal ranking of construction companies between the VIKOR model and entropy–fuzzy VIKOR model was performed and presented in Table 8.

## 4. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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Level | |
---|---|

Objective | Evaluation of the Financial Performance of Construction Companies |

Decision Criteria | Return on equity (ROE) |

(Financial Ratios) | Return on asset (ROA) |

Earnings per share (EPS) | |

Debt to equity ratio (DER) | |

Debt to assets ratio (DAR) | |

Current ratio (CR) | |

Decision Alternatives | BREM |

(Construction | CRESBLD |

Companies) | DKLS |

ECONBHD | |

EKOVEST | |

GADANG | |

GAMUDA | |

GBGAQRS | |

GKENT | |

HOHUP | |

HSL | |

IJM | |

KERJAYA | |

KIMLUN | |

MELATI | |

MITRA | |

MUHIBAH | |

PRTASCO | |

PTARAS | |

WCT |

Companies | CR | DAR | DER | EPS | ROA | ROE |
---|---|---|---|---|---|---|

BREM | (2.467, 4.694, 7.132) | (0.077, 0.132, 0.240) | (0.083, 0.157, 0.316) | (0.026, 0.063, 0.130) | (1.745, 5.043, 11.186) | (2.296, 5.664, 12.117) |

CRESBLD | (0.615, 1.643, 4.115) | (0.235, 0.276, 0.360) | (0.307, 0.387, 0.563) | (0.037, 0.046, 0.050) | (2.358, 2.770, 3.098) | (3.150, 3.830, 4.123) |

DKLS | (37.573, 68.835, 114.062) | (0.003, 0.004, 0.004) | (0.003, 0.004, 0.004) | (0.094, 0.147, 0.185) | (3.732, 5.809, 7.722) | (3.745, 5.832, 7.750) |

ECONBHD | (10.872, 393.668, 1044.293) | (0.000, 0.001, 0.002) | (0.000, 0.001, 0.002) | (0.005, 0.020, 0.043) | (4.809, 12.112, 17.601) | (4.818, 12.126, 17.617) |

EKOVEST | (0.692, 1.123, 1.837) | (0.205, 0.406, 0.555) | (0.258, 0.783, 1.245) | (0.010, 0.065, 0.192) | (0.785, 5.702, 16.555) | (0.988, 11.907, 37.165) |

GADANG | (19.045, 175.893, 409.196) | (0.001, 0.006, 0.020) | (0.001, 0.006, 0.020) | (0.020, 0.043, 0.066) | (3.502, 6.671, 11.924) | (3.572, 6.699, 11.953) |

GAMUDA | (1.087, 1.629, 2.054) | (0.357, 0.385, 0.403) | (0.555, 0.626, 0.676) | (0.092, 0.248, 0.498) | (2.970, 7.266, 12.883) | (4.619, 11.857, 20.772) |

GBGAQRS | (1.007, 15.843, 67.467) | (0.009, 0.124, 0.237) | (0.009, 0.151, 0.310) | (0.007, 0.020, 0.038) | (1.068, 2.775, 5.957) | (1.287, 3.122, 6.881) |

GKENT | (1.275, 1.464, 1.871) | (0.420, 0.562, 0.618) | (0.723, 1.342, 1.621) | (0.082, 0.152, 0.226) | (4.780, 10.416, 14.886) | (12.438, 23.787, 34.063) |

HOHUP | (1.931, 2.429, 2.794) | (0.360, 0.431, 0.489) | (0.562, 0.775, 0.957) | (0.005, 0.059, 0.179) | (0.330, 4.892, 14.369) | (0.613, 7.907, 22.441) |

HSL | (2.234, 2.764, 3.394) | (0.188, 0.241, 0.308) | (0.231, 0.322, 0.445) | (0.064, 0.084, 0.125) | (4.386, 5.769, 9.699) | (5.744, 7.532, 12.169) |

IJM | (1.399, 2.273, 3.011) | (0.305, 0.324, 0.341) | (0.438, 0.480, 0.517) | (0.054, 0.082, 0.111) | (2.144, 3.039, 4.015) | (3.084, 4.518, 6.040) |

KERJAYA | (8.762, 65.731, 171.582) | (0.005, 0.013, 0.042) | (0.005, 0.014, 0.044) | (0.030, 0.058, 0.101) | (3.640, 7.323, 11.589) | (3.659, 7.414, 11.688) |

KIMLUN | (40.845, 78.293, 102.539) | (0.002, 0.003, 0.006) | (0.002, 0.003, 0.006) | (0.045, 0.057, 0.072) | (5.755, 6.958, 8.172) | (5.792, 6.977, 8.184) |

MELATI | (0.508, 14.647, 37.898) | (0.011, 0.046, 0.163) | (0.011, 0.053, 0.194) | (0.013, 0.070, 0.247) | (0.781, 4.426, 15.612) | (0.801, 4.588, 15.782) |

MITRA | (0.116, 42.494, 128.804) | (0.002, 0.072, 0.143) | (0.002, 0.082, 0.166) | (0.009, 0.033, 0.052) | (1.451, 5.059, 8.293) | (1.615, 5.358, 8.312) |

MUHIBAH | (0.951, 1.076, 1.200) | (0.667, 0.745, 0.811) | (2.003, 3.079, 4.302) | (0.033, 0.153, 0.440) | (0.803, 4.072, 12.201) | (3.108, 14.210, 36.642) |

PRTASCO | (5.442, 6.604, 8.688) | (0.046, 0.064, 0.078) | (0.048, 0.068, 0.084) | (0.000, 0.048, 0.076) | (0.014, 7.628, 11.783) | (0.015, 8.189, 12.673) |

PTARAS | (7.606, 10.674, 11.892) | (0.094, 0.098, 0.103) | (0.103, 0.109, 0.115) | (0.028, 0.181, 0.405) | (2.021, 10.805, 23.721) | (2.230, 12.002, 26.368) |

WCT | (2.125, 7.311, 25.602) | (0.274, 0.385, 0.459) | (0.377, 0.645, 0.847) | (0.001, 0.015, 0.067) | (0.025, 0.297, 1.322) | (0.034, 0.534, 2.397) |

Financial Ratios | Best (${f}_{j}*$) | Worst (${f}_{j}{}^{-}$) |
---|---|---|

CR | (40.845, 393.668, 1044.293) | (0.116, 1.076, 1.200) |

DAR | (0.000, 0.001, 0.002) | (0.667, 0.745, 0.811) |

DER | (0.000, 0.001, 0.002) | (2.003, 3.079, 4.302) |

EPS | (0.094, 0.248, 0.498) | (0.000, 0.015, 0.038) |

ROA | (5.755, 12.112, 23.721) | (0.014, 0.297, 1.322) |

ROE | (12.438, 23.787, 37.165) | (0.015, 0.534, 2.397) |

**Table 4.**The normalized fuzzy decision matrix for the companies with respect to all financial ratios.

Companies | CR | DAR | DER | EPS | ROA | ROE |
---|---|---|---|---|---|---|

BREM | (0.366, 0.385, 0.386) | (0.019, 0.029, 0.048) | (0.011, 0.014, 0.020) | (0.058, 0.063, 0.064) | (0.028, 0.024, 0.023) | (0.046, 0.044, 0.040) |

CRESBLD | (0.384, 0.388, 0.387) | (0.058, 0.061, 0.073) | (0.042, 0.034, 0.035) | (0.048, 0.069, 0.077) | (0.024, 0.032, 0.037) | (0.042, 0.048, 0.053) |

DKLS | (0.031, 0.321, 0.346) | (0.001, 0.001, 0.000) | (0.000, 0.000, 0.000) | (0.000, 0.034, 0.054) | (0.014, 0.022, 0.029) | (0.039, 0.043, 0.048) |

ECONBHD | (0.286, 0.000, 0.000) | (0.000, 0.000, 0.000) | (0.000, 0.000, 0.000) | (0.075, 0.078, 0.079) | (0.007, 0.000, 0.011) | (0.034, 0.028, 0.032) |

EKOVEST | (0.383, 0.388, 0.388) | (0.051, 0.089, 0.112) | (0.035, 0.069, 0.078) | (0.071, 0.062, 0.053) | (0.035, 0.022, 0.013) | (0.052, 0.029, 0.000) |

GADANG | (0.208, 0.215, 0.236) | (0.000, 0.001, 0.004) | (0.000, 0.000, 0.001) | (0.063, 0.070, 0.075) | (0.016, 0.019, 0.021) | (0.040, 0.041, 0.041) |

GAMUDA | (0.379, 0.388, 0.388) | (0.088, 0.085, 0.082) | (0.075, 0.055, 0.043) | (0.002, 0.000, 0.000) | (0.020, 0.017, 0.020) | (0.035, 0.029, 0.026) |

GBGAQRS | (0.380, 0.374, 0.364) | (0.002, 0.027, 0.048) | (0.001, 0.013, 0.019) | (0.073, 0.078, 0.079) | (0.033, 0.032, 0.032) | (0.050, 0.050, 0.049) |

GKENT | (0.377, 0.388, 0.388) | (0.103, 0.124, 0.125) | (0.098, 0.118, 0.102) | (0.011, 0.033, 0.047) | (0.007, 0.006, 0.016) | (0.000, 0.000, 0.005) |

HOHUP | (0.371, 0.387, 0.388) | (0.089, 0.095, 0.099) | (0.076, 0.068, 0.060) | (0.075, 0.064, 0.055) | (0.038, 0.025, 0.017) | (0.053, 0.038, 0.024) |

HSL | (0.368, 0.387, 0.387) | (0.046, 0.053, 0.062) | (0.031, 0.028, 0.028) | (0.025, 0.056, 0.064) | (0.010, 0.022, 0.025) | (0.030, 0.039, 0.040) |

IJM | (0.376, 0.387, 0.388) | (0.075, 0.071, 0.069) | (0.059, 0.042, 0.032) | (0.034, 0.057, 0.067) | (0.025, 0.031, 0.036) | (0.042, 0.047, 0.050) |

KERJAYA | (0.306, 0.324, 0.325) | (0.001, 0.003, 0.008) | (0.001, 0.001, 0.003) | (0.054, 0.064, 0.069) | (0.015, 0.016, 0.022) | (0.040, 0.040, 0.041) |

KIMLUN | (0.000, 0.312, 0.351) | (0.000, 0.000, 0.001) | (0.000, 0.000, 0.000) | (0.041, 0.065, 0.074) | (0.000, 0.018, 0.028) | (0.030, 0.041, 0.047) |

MELATI | (0.385, 0.375, 0.375) | (0.003, 0.010, 0.033) | (0.001, 0.005, 0.012) | (0.069, 0.060, 0.043) | (0.035, 0.026, 0.015) | (0.053, 0.046, 0.035) |

MITRA | (0.388, 0.347, 0.341) | (0.000, 0.016, 0.029) | (0.000, 0.007, 0.010) | (0.072, 0.073, 0.077) | (0.030, 0.024, 0.028) | (0.049, 0.045, 0.047) |

MUHIBAH | (0.380, 0.388, 0.388) | (0.164, 0.164, 0.164) | (0.271, 0.271, 0.271) | (0.052, 0.032, 0.010) | (0.035, 0.028, 0.021) | (0.042, 0.023, 0.001) |

PRTASCO | (0.338, 0.383, 0.386) | (0.011, 0.014, 0.015) | (0.006, 0.006, 0.005) | (0.079, 0.068, 0.073) | (0.040, 0.015, 0.022) | (0.056, 0.038, 0.040) |

PTARAS | (0.317, 0.379, 0.384) | (0.023, 0.021, 0.021) | (0.014, 0.009, 0.007) | (0.056, 0.023, 0.016) | (0.026, 0.004, 0.000) | (0.046, 0.028, 0.017) |

WCT | (0.369, 0.382, 0.379) | (0.067, 0.085, 0.093) | (0.051, 0.057, 0.053) | (0.079, 0.079, 0.074) | (0.040, 0.040, 0.040) | (0.056, 0.056, 0.056) |

Companies | S_{i} | R_{i} |
---|---|---|

BREM | (0.528, 0.558, 0.581) | (0.366, 0.385, 0.386) |

CRESBLD | (0.597, 0.631, 0.663) | (0.384, 0.388, 0.387) |

DKLS | (0.086, 0.421, 0.477) | (0.039, 0.321, 0.346) |

ECONBHD | (0.402, 0.106, 0.121) | (0.286, 0.078, 0.079) |

EKOVEST | (0.626, 0.659, 0.645) | (0.383, 0.388, 0.388) |

GADANG | (0.327, 0.346, 0.378) | (0.208, 0.215, 0.236) |

GAMUDA | (0.599, 0.573, 0.558) | (0.379, 0.388, 0.388) |

GBGAQRS | (0.540, 0.574, 0.591) | (0.380, 0.374, 0.364) |

GKENT | (0.596, 0.668, 0.683) | (0.377, 0.388, 0.388) |

HOHUP | (0.703, 0.677, 0.643) | (0.371, 0.387, 0.388) |

HSL | (0.511, 0.585, 0.608) | (0.368, 0.387, 0.387) |

IJM | (0.612, 0.635, 0.641) | (0.376, 0.387, 0.388) |

KERJAYA | (0.416, 0.449, 0.467) | (0.306, 0.324, 0.325) |

KIMLUN | (0.072, 0.436, 0.500) | (0.041, 0.312, 0.351) |

MELATI | (0.545, 0.523, 0.512) | (0.385, 0.375, 0.375) |

MITRA | (0.540, 0.512, 0.531) | (0.388, 0.347, 0.341) |

MUHIBAH | (0.945, 0.907, 0.856) | (0.380, 0.388, 0.388) |

PRTASCO | (0.531, 0.524, 0.540) | (0.338, 0.383, 0.386) |

PTARAS | (0.482, 0.465, 0.446) | (0.317, 0.379, 0.384) |

WCT | (0.663, 0.700, 0.696) | (0.369, 0.382, 0.379) |

${S}^{*}$ | (0.07189, 0.10573, 0.12119) |

${S}^{-}$ | (0.94510, 0.90708, 0.85570) |

${R}^{*}$ | (0.03930, 0.07757, 0.07856) |

${R}^{-}$ | (0.38831, 0.38831, 0.38831) |

Companies | Entropy-Fuzzy VIKOR Scores (Q_{i}) | Optimal Ranking |
---|---|---|

BREM | 0.774 | 11 |

CRESBLD | 0.828 | 15 |

DKLS | 0.506 | 4 |

ECONBHD | 0.090 | 1 |

EKOVEST | 0.841 | 16 |

GADANG | 0.384 | 2 |

GAMUDA | 0.791 | 13 |

GBGAQRS | 0.768 | 10 |

GKENT | 0.845 | 17 |

HOHUP | 0.851 | 18 |

HSL | 0.789 | 12 |

IJM | 0.826 | 14 |

KERJAYA | 0.609 | 5 |

KIMLUN | 0.505 | 3 |

MELATI | 0.744 | 8 |

MITRA | 0.704 | 7 |

MUHIBAH | 0.998 | 20 |

PRTASCO | 0.747 | 9 |

PTARAS | 0.697 | 6 |

WCT | 0.855 | 19 |

**Table 8.**The comparison of the scores (Q

_{i}) and optimal ranking of construction companies between the VIKOR model and entropy–fuzzy VIKOR model.

Entropy-Fuzzy VIKOR Model | VIKOR Model | |||
---|---|---|---|---|

Companies | Scores (Q_{i}) | Optimal Ranking | Scores (Q_{i}) | Optimal Ranking |

BREM | 0.774 | 11 | 0.770 | 12 |

CRESBLD | 0.828 | 15 | 0.888 | 18 |

DKLS | 0.506 | 4 | 0.194 | 1 |

ECONBHD | 0.090 | 1 | 0.437 | 5 |

EKOVEST | 0.841 | 16 | 0.833 | 15 |

GADANG | 0.384 | 2 | 0.345 | 4 |

GAMUDA | 0.791 | 13 | 0.676 | 8 |

GBGAQRS | 0.768 | 10 | 0.808 | 14 |

GKENT | 0.845 | 17 | 0.693 | 10 |

HOHUP | 0.851 | 18 | 0.870 | 17 |

HSL | 0.789 | 12 | 0.780 | 13 |

IJM | 0.826 | 14 | 0.866 | 16 |

KERJAYA | 0.609 | 5 | 0.248 | 3 |

KIMLUN | 0.505 | 3 | 0.202 | 2 |

MELATI | 0.744 | 8 | 0.684 | 9 |

MITRA | 0.704 | 7 | 0.573 | 7 |

MUHIBAH | 0.998 | 20 | 0.968 | 19 |

PRTASCO | 0.747 | 9 | 0.697 | 11 |

PTARAS | 0.697 | 6 | 0.521 | 6 |

WCT | 0.855 | 19 | 1.000 | 20 |

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**MDPI and ACS Style**

Lam, W.S.; Lam, W.H.; Jaaman, S.H.; Liew, K.F. Performance Evaluation of Construction Companies Using Integrated Entropy–Fuzzy VIKOR Model. *Entropy* **2021**, *23*, 320.
https://doi.org/10.3390/e23030320

**AMA Style**

Lam WS, Lam WH, Jaaman SH, Liew KF. Performance Evaluation of Construction Companies Using Integrated Entropy–Fuzzy VIKOR Model. *Entropy*. 2021; 23(3):320.
https://doi.org/10.3390/e23030320

**Chicago/Turabian Style**

Lam, Weng Siew, Weng Hoe Lam, Saiful Hafizah Jaaman, and Kah Fai Liew. 2021. "Performance Evaluation of Construction Companies Using Integrated Entropy–Fuzzy VIKOR Model" *Entropy* 23, no. 3: 320.
https://doi.org/10.3390/e23030320