The Neutrosophic Set(NS) theory is the existing mathematical theory that generalize the notion of Fuzzy Set(FS) theory. It also analyses the connectivity between impreciseness and neutralities. In this present study an advanced Neutrosophic optimization technique namely Four Valued Refined Neutrosophic Optimization(FVRNSO) method is introduced to optimize cost of welding of a welded steel beam. In this single objective Welded Beam(WB) design problem maximum shear stress in the weld group, maximum bending stress in the beam maximum deflection at the tip and buckling load of the beam have been considered as flexible constraints. The design variables in dimensioning the welded beam are height, length, depth and width. From the set theoretic point of view indeterminacy is further refined as Uncertain (U)and Contradiction(C = T∧ F) in Four Valued Refined Neutrosophic Set. Particularly based on truth, uncertain, contradiction and falsity membership function this single objective FVRNSO algorithm has been developed in this paper. This method and its application show that the method is very much cost-effective as compare to prevailing deterministic and non deterministic method.

Neutrosophic set, Single Valued Neutrosophicset, Four valued refined Neutrosophic set, Single objective four valued refined Neutrosophic optimization, Single objective welded beam design,