{"title":"Some equations to identify the threshold value in the DEMATEL method","authors":"Seyed Hossain Ebrahimi","doi":"10.37190/ord230201","DOIUrl":null,"url":null,"abstract":"DEMATEL technique is a graphical representation method to deal with complex systems. The final analyzed cause and effect categorization would be fundamentally dependent on the threshold value setting. This research is intended to present some mathematical models for calculating the threshold value in the DEMATEL method. The min(max) operator has been intentionally used for considering three equations to identify the threshold value. Additionally, the proposed mathematical equations are gradually developed to gain more useful data to yield a threshold value as well. Particularly, the expert’s initial scoring for building the primary matrix would also be applied in one equation. Results show eliciting an expert’s opinions regarding the value of a threshold value determination leads to setting relatively high thresholds. But, there would be an equation which takes advantage of more data derived from the total influence matrix T. Moreover, a span of different threshold values is gained by making use of the Hamacher t-conorms operator which especially would cause better complexity management of the final total matrix T based on expert’s opinions. As a contribution to this research, threshold value determination is developed mathematically by making use of the direct data gained by the total matrix T. Besides combining data derived from total matrix T, the initial influence direct matrix given by experts, a simpler aggregating procedure and no need for statistical information compared to special Lenth’s method hints at this research’s novelty as well.","PeriodicalId":43244,"journal":{"name":"Operations Research and Decisions","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Operations Research and Decisions","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.37190/ord230201","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"OPERATIONS RESEARCH & MANAGEMENT SCIENCE","Score":null,"Total":0}
引用次数: 0
Abstract
DEMATEL technique is a graphical representation method to deal with complex systems. The final analyzed cause and effect categorization would be fundamentally dependent on the threshold value setting. This research is intended to present some mathematical models for calculating the threshold value in the DEMATEL method. The min(max) operator has been intentionally used for considering three equations to identify the threshold value. Additionally, the proposed mathematical equations are gradually developed to gain more useful data to yield a threshold value as well. Particularly, the expert’s initial scoring for building the primary matrix would also be applied in one equation. Results show eliciting an expert’s opinions regarding the value of a threshold value determination leads to setting relatively high thresholds. But, there would be an equation which takes advantage of more data derived from the total influence matrix T. Moreover, a span of different threshold values is gained by making use of the Hamacher t-conorms operator which especially would cause better complexity management of the final total matrix T based on expert’s opinions. As a contribution to this research, threshold value determination is developed mathematically by making use of the direct data gained by the total matrix T. Besides combining data derived from total matrix T, the initial influence direct matrix given by experts, a simpler aggregating procedure and no need for statistical information compared to special Lenth’s method hints at this research’s novelty as well.
DEMATEL技术是一种处理复杂系统的图形表示方法。最终分析的因果分类将从根本上取决于阈值的设置。本研究旨在提出计算DEMATEL方法中阈值的一些数学模型。最小(最大)运算符被有意用于考虑三个方程来确定阈值。此外,所提出的数学方程逐渐发展,以获得更多有用的数据,以产生一个阈值。特别地,专家为建立主矩阵的初始得分也将应用于一个方程。结果表明,征求专家对阈值确定值的意见会导致设置相对较高的阈值。但是,会有一个方程利用了从总影响矩阵T中导出的更多数据,并且利用Hamacher T - connorm算子获得了不同阈值的跨度,特别是可以根据专家的意见更好地管理最终的总矩阵T的复杂性。作为本研究的贡献之一,利用总矩阵T获得的直接数据,从数学上确定阈值。此外,结合总矩阵T获得的数据,专家给出的初始影响直接矩阵,与特殊的Lenth方法相比,聚合过程更简单,不需要统计信息,也表明了本研究的新颖性。