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In this paper, intuitionistic fuzzy spiking neural P (IFSNP) systems as a variant are proposed by integrating intuitionistic fuzzy logic into original spiking neural P systems. Compared with a common fuzzy set, intuitionistic fuzzy set can more finely describe the uncertainty due to its membership and non-membership degrees. Therefore, IFSNP systems are very suitable to deal with fault diagnosis of power systems, specially with incomplete and uncertain alarm messages. The fault modeling method and fuzzy reasoning algorithm based on IFSNP systems are discussed. Two examples are used to demonstrate the availability and effectiveness of IFSNP systems for fault diagnosis of power systems. Case studies involve single fault, complex fault, and multiple faults with protection device failures and incorrect tripping signals.