Reliability optimization problems with multiple constraints under fuzziness

In reliability optimization problems diverse situation occurs due to which it is not always possible to get relevant precision in system reliability. the imprecision in data can often be represented by triangular fuzzy numbers. in this manuscript, we have considered different fuzzy environment for reliability optimization problem of redundancy. we formulate a redundancy allocation problem for a hypothetical series-parallel system inwhich the parameters of the systemare fuzzy. two different cases are then formulated as non-linear programming problem and the fuzzy nature is defuzzified into crisp problems using three different defuzzification methods viz. ranking function, graded mean integration value and α-cut. the result of the methods is compared at the end of the manuscript using a numerical example.