### Abstract

The generalized DEMATEL theory pointed out that the results of the traditional DEMATEL theory are always unbalanced and unfair, since their indirect relations are always far greater than their responding direct relations, respectively, it can be improved by using an external shrinkage coefficient of the indirect relation matrix of a DEMATEL. However, on other contrary, the indirect relations sometimes may be smaller than their corresponding direct relations respectively, it is still unbalanced, and it can be not improved by using the above-mentioned method. In this paper, Liu’s balanced coefficient was proposed, which can be used to detect any DEMATEL whether it is balanced; furthermore, we proved that if the internal shrinkage coefficient is smaller than 0.5, then its indirect relation is smaller than its direct relation. For overcoming this drawback, we propose a new method, called the balanced DEMATEL theory, by normalizing the indirect relation matrix as the direct relation matrix has been done. For any cases, according to Liu’s validity index, we can find that the performance of the new method is better than that of the generalized DEMATEL theory. Some important properties of this new theory were discussed, and a simple data was also provided in this paper to illustrate the advantages of the proposed theory.

Original language | English |
---|---|

Pages (from-to) | 315-321 |

Number of pages | 7 |

Journal | ICIC Express Letters, Part B: Applications |

Volume | 7 |

Issue number | 2 |

Publication status | Published - Feb 1 2016 |

### Keywords

- Liu’s balanced coefficient
- Liu’s validity Index
- Normalized indirect relation matrix

### ASJC Scopus subject areas

- Computer Science(all)

### Cite this

*ICIC Express Letters, Part B: Applications*,

*7*(2), 315-321.

**A balanced dematel theory with normalized indirect relation matrix.** / Liu, Hsiang Chuan; Ou, Yih Chang; Tsai, Hsien Chang; Shia, Ben Chang; Ju, Jing Ming.

Research output: Contribution to journal › Article

*ICIC Express Letters, Part B: Applications*, vol. 7, no. 2, pp. 315-321.

}

TY - JOUR

T1 - A balanced dematel theory with normalized indirect relation matrix

AU - Liu, Hsiang Chuan

AU - Ou, Yih Chang

AU - Tsai, Hsien Chang

AU - Shia, Ben Chang

AU - Ju, Jing Ming

PY - 2016/2/1

Y1 - 2016/2/1

N2 - The generalized DEMATEL theory pointed out that the results of the traditional DEMATEL theory are always unbalanced and unfair, since their indirect relations are always far greater than their responding direct relations, respectively, it can be improved by using an external shrinkage coefficient of the indirect relation matrix of a DEMATEL. However, on other contrary, the indirect relations sometimes may be smaller than their corresponding direct relations respectively, it is still unbalanced, and it can be not improved by using the above-mentioned method. In this paper, Liu’s balanced coefficient was proposed, which can be used to detect any DEMATEL whether it is balanced; furthermore, we proved that if the internal shrinkage coefficient is smaller than 0.5, then its indirect relation is smaller than its direct relation. For overcoming this drawback, we propose a new method, called the balanced DEMATEL theory, by normalizing the indirect relation matrix as the direct relation matrix has been done. For any cases, according to Liu’s validity index, we can find that the performance of the new method is better than that of the generalized DEMATEL theory. Some important properties of this new theory were discussed, and a simple data was also provided in this paper to illustrate the advantages of the proposed theory.

AB - The generalized DEMATEL theory pointed out that the results of the traditional DEMATEL theory are always unbalanced and unfair, since their indirect relations are always far greater than their responding direct relations, respectively, it can be improved by using an external shrinkage coefficient of the indirect relation matrix of a DEMATEL. However, on other contrary, the indirect relations sometimes may be smaller than their corresponding direct relations respectively, it is still unbalanced, and it can be not improved by using the above-mentioned method. In this paper, Liu’s balanced coefficient was proposed, which can be used to detect any DEMATEL whether it is balanced; furthermore, we proved that if the internal shrinkage coefficient is smaller than 0.5, then its indirect relation is smaller than its direct relation. For overcoming this drawback, we propose a new method, called the balanced DEMATEL theory, by normalizing the indirect relation matrix as the direct relation matrix has been done. For any cases, according to Liu’s validity index, we can find that the performance of the new method is better than that of the generalized DEMATEL theory. Some important properties of this new theory were discussed, and a simple data was also provided in this paper to illustrate the advantages of the proposed theory.

KW - Liu’s balanced coefficient

KW - Liu’s validity Index

KW - Normalized indirect relation matrix

UR - http://www.scopus.com/inward/record.url?scp=84959320847&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84959320847&partnerID=8YFLogxK

M3 - Article

VL - 7

SP - 315

EP - 321

JO - ICIC Express Letters, Part B: Applications

JF - ICIC Express Letters, Part B: Applications

SN - 2185-2766

IS - 2

ER -