An Application of the Pythagorean Fuzzy Sets in the Fault Diagnosis

Abstract In this paper, a comprehensive review and critical analyses of methods based on the ordinary fuzzy set, Atanassov’s intuitionistic fuzzy set, and its extensions have been conducted to show their limitations and defects. Then, a novel similarity measure based on the generalized score function has been introduced that incorporates the significance (importance) of information, making it more intuitive to compare them. The proposed method is employed for the fault diagnosis of steam turbine generator unit under Pythagorean fuzzy environment. Ten fault types of rotating machines are established as failure patterns in nine different vibration frequency ranges, expressed in terms of Pythagorean fuzzy numbers. The superiority of the proposed method in dealing with uncertain and vague information is shown by comparing it with some existing measures in numerical examples.