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In fuzzy mathematics fuzzy system reliability can be analysed by fuzzy sets. We can use various types of fuzzy sets for that analyzing the fuzzy system reliability but here we specially used intuitionistic fuzzy set theory. At first, TrIFNs and their arithmetic operations are introduced. Expressions for computing the fuzzy reliability of a series system, parallel system, series-parallel and parallel-series system following TrIFNs have been described. Here an imprecise failure to start of a truck is taken. To compute the imprecise failure of the above said system, failure of each component of the systems is represented by Trapezoidal Intuitionistic Fuzzy Number. This process can be utilise to measure the failure is various aspects like portfolio in stock market etc. The numerical expression also calculated and presented in this paper for the failure to start of a truck using TrIFN.

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