Energy of Pythagorean Fuzzy Graphs with Applications

Muhammad Akram · Sumera Naz

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Fuzzy and Soft Set Theory Graph theory and applications Advanced Mathematical Theories

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.

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References

1986Intuitionistic fuzzy sets 2013Pythagorean Membership Grades in Multicriteria Decision Making 2013Pythagorean fuzzy subsets 2007Intuitionistic Fuzzy Aggregation Operators 2014Extension of TOPSIS to Multiple Criteria Decision Making with Pythagorean Fuzzy Sets 2013Pythagorean Membership Grades, Complex Numbers, and Decision Making 2015Some Results for Pythagorean Fuzzy Sets 2015Pythagorean fuzzy TODIM approach to multi-criteria decision making

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