Abstract
Pythagorean fuzzy sets (PFSs), an extension of intuitionistic fuzzy sets (IFSs), inherit the duality property of IFSs and have a more powerful ability than IFSs to model the obscurity in practical decision-making problems. In this research study, we compute the energy and Laplacian energy of Pythagorean fuzzy graphs (PFGs) and Pythagorean fuzzy digraphs (PFDGs). Moreover, we derive the lower and upper bounds for the energy and Laplacian energy of PFGs. Finally, we present numerical examples, including the design of a satellite communication system and the evaluation of the schemes of reservoir operation to illustrate the applications of our proposed concepts in decision making.
Highlights
Yager recently [1,2] introduced the concept of the Pythagorean fuzzy set (PFS) as a generalization of the intuitionistic fuzzy set (IFS) [3], to manage the complex impreciseness and uncertainty in practical decision-making problems
Naz et al [27] proposed the concept of Pythagorean fuzzy graphs (PFGs), a generalization of the notion of Akram and Davvaz intuitionistic fuzzy graph (IFG) [17], along with its applications in decision-making
A PFG can describe the uncertainty of all kinds of networks well
Summary
Yager recently [1,2] introduced the concept of the Pythagorean fuzzy set (PFS) as a generalization of the intuitionistic fuzzy set (IFS) [3], to manage the complex impreciseness and uncertainty in practical decision-making problems. Akram et al [20,21,22,23,24,25,26] put forward many new concepts concerning the extended structures of fuzzy graphs and provided their pertinent applications in decision-making. Naz et al [27] proposed the concept of Pythagorean fuzzy graphs (PFGs), a generalization of the notion of Akram and Davvaz IFGs [17], along with its applications in decision-making. In this research study, we introduce certain novel concepts, including the energy and Laplacian energy of PFGs, as well as the energy and Laplacian energy of Pythagorean fuzzy digraphs (PFDGs). For more definitions and terminologies, the readers are referred to [30,31,32,33,34,35,36,37,38,39,40,41]
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