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2 2023

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Some equations to identify the threshold value in the DEMATEL method

Ebrahimi Seyed Hossain

Operations Research and Decisions

2023

Vol. 33, No. 2

1--22

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.

A Modified Hybrid Objective Model to Calculate the Weights of Cause and Effect Criteria in a System: DEMATEL and DEVELOPED SWARA (D-DS) Based Model

Ebrahimi Seyed Hossain

Foundations of Computing and Decision Sciences

2023

Vol. 48, No. 2

101--152

Criteria weighting is a widely used and also an important feature of multi criteria decision making problems specially in engineering, computer science and management investigations. In particular in many studies related to complex systems there would be usually two main groups of cause and effect criteria. In this research it is intended to make an hybrid objective model comprising DEMATEL and SWARA techniques to assign classified weights to the subgroup of cause and effect criteria. As a main goal, the proposed hybrid model in this presented paper can afford to assign greater values for criteria who belong to cause group. In this regard we apply the objective information which derived from the parameters of (R, equal to sum of direct and indirect influence of a criteria), (R/C, named as net influence power of a criteria) and (R-C, named as net effect of a criteria) related to the final total influence matrix T in DEMATEL methodology. The main contribution in this work lies in utilizing the SWARA methodology and making us of its revision where the relatively Comparative Importance Sj, applied in SWARA technique is reconfigured by some aggregation operators including max, Einstein and Hamacher operators for obtaining more uniformed weights of cause and effect criteria relatively to SWARA basic methodology. Finally results shows that the (R/C) and (R-C)would transfer more clear and refined data and numeric information achieving better and highly reliable weights of criteria categorized into two groups of cause and effect group.