Affiliations: [a] Department of Mathematics, Riphah International University Lahore, Pakistan
| [b] Faculty of Organizational Sciences, University of Belgrade, Belgrade, Serbia
| [c] College of Engineering, Yuan Ze University, Taiwan
| [d] Department of Computer Science and Mathematics, Lebanese American University, Byblos, Lebanon
| [e] Mathematics Department, College of Science, King Saud University, Riyadh, Saudi Arabia
Abstract: A T-spherical fuzzy set (TSFS) is an extended and logical algebraic representation to handle uncertainty, with the help of four functions describing four possible aspects of uncertain information. Aczel-Alsina triangular norm (TN) and conorm (TCN) are novel and proved to be more efficient than other existing TNs and TCNs. In our article, we establish the concept of a T-spherical fuzzy Aczel-Alsina graph (TSFAAG). We described the energy of TSFAAG along with the splitting and shadow energy of TSFAAG. Furthermore, we figured out the Randić energy of TSFAAG and obtained some useful results. Moreover, we give the notion of the Aczel-Alsina digraph (TSFAADG). To see the significance of the proposed TSFAADGs, we employed the energy and Randić energy of TSFAADGs for solving the problem of selecting the best investing company by using a decision-making algorithm. The sensitivity analysis of the variable parameters is also discussed and where the effect on ranking results is studied. To see the effectiveness of the proposed work, we did a comparative study and established some remarks.
