This paper investigates multi-objective Neutrosophic Optimization (NSO) approach to optimize the cost of welding and deflection at the tip of a welded steel beam, while the maximum shear stress in the weld group, maximum bending stress in the beam, and buckling load of the beam have been considered as constraints. The problem of designing an optimal welded beam consists of dimensioning a welded steel beam and the welding length so as to minimize its cost, subject to the constraints as stated

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... ve. The purpose of the present study firstly to investigate the effect of truth, indeterminacy and falsity membership function in neutrosophic optimization in perspective of welded beam design and secondly is to analyse the results obtained by different optimization methods like fuzzy, intuitionistic fuzzy so that the welding cost of the welded steel beam become most cost effective with minimum deflection. Specifically based on truth, indeterminacy and falsity membership function, a multi objective NSO algorithm has been developed to optimize the welding cost, subjected to a set of constraints. It has been shown that NSO is an efficient method in finding out the optimum value in comparison to other iterative methods for nonlinear welded beam design in imprecise environment till investigated. Numerical example is also given to demonstrate the efficiency of the proposed NSO approach.