Affiliations: Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur, Chengalpattu District, Tamil Nadu, India
Correspondence:
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Corresponding author. S. Mohanaselvi, Department of Mathematics, Faculty of Engineering and Technology, SRM Institute of Science and Technology, Kattankulathur 603 203, Chengalpattu District, Tamil Nadu, India. E-mail: [email protected].
Abstract: Consolidating cubical fuzzy numbers (CFNs) is essential in an uncertain decision-making process. This study focuses on creating innovative cubical fuzzy aggregation operators based on the newly proposed Einstein operational laws, utilizing the Bonferroni mean function to capture the interrelationships among the aggregated CFNs. The first contribution of this paper is introducing a novel cubical fuzzy Einstein Bonferroni mean averaging operator. Building upon this operator, we extend our research to develop cubical fuzzy Einstein Bonferroni mean weighted, ordered weighted, and hybrid averaging operators, taking into account the weights of the aggregated CFNs. To ensure their effectiveness, we thoroughly investigate the desirable properties of these proposed operators. Furthermore, we leverage the introduced operators to establish a new approach known as the cubical fuzzy linear assignment method, which proves valuable in resolving multiple criteria group decision-making problems. As a practical demonstration of the method’s utility, we apply it to address a real-life challenge: identifying the optimal location for constructing a wind power plant under a cubical fuzzy environment. To validate the effectiveness of our approach, we compare its results with those obtained using existing methods from the literature. Additionally, we conduct a statistical analysis to visualize the correlative conjunction between the ranking outcomes obtained by different operators
Keywords: Cubical fuzzy set, Einstein operational laws, Bonferroni mean, averaging
aggregation operators, linear assignment method, wind power plant location selection
