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Direct Sum of n Pythagorean Fuzzy Graphs with Application to Group Decision-Making
Muhammad Akram, Amna Habib and Bijan Davvaz

A Pythagorean fuzzy set is an influential approach for describing ambiguous concepts more precisely. The Pythagorean fuzzy set-based models bring more pliability in handling human analysis. The intention of present paper is to illustrate an operation, namely direct sum of Pythagorean fuzzy graphs. An attempt has been made to analyze certain crucial properties, including regularity, strongness, completeness and connectedness with examples. Furthermore, some necessary and sufficient conditions have been established for direct sum to retain prescribed properties. In particular, the direct sum of n Pythagorean fuzzy graphs is described. Finally, an application on group decision-making problem has been displayed in which a new approach is suggested for selection of the best entity by employing Pythagorean fuzzy digraphs.

Keywords: Regular pythagorean fuzzy graphs, strong pythagorean fuzzy graphs, connected pythagorean fuzzy graphs, n pythagorean fuzzy graphs, direct sum, group decision-making

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