Structural design optimization such as three bar truss design optimization by mathematical method is an important notion in civil engineering as well as in mathematics. Traditionally structural optimization is well known concept and in many situations it is treated as single objective form ,where the objective is known as cost function. The extension of this form can be defined as optimization where one or more constraints are simultaneously satisfied next to the minimization of cost function. This does not always hold good in real world problem where multiple and conflicting objects frequently exist. In this context, a methodology known as multi-objective structural optimization is introduced. Again Neutrosophic Theory is the existing mathematical theory that generalizes 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 discussed to optimize weight and deflection of the load joint that all satisfy all stress constraints in member of the structure.The design variables are cross section in members.From the set theoretic point of view indeterminacy is further refined as Uncertain(U) and contradiction in four valued refined neutrosophic set. Particularly based on truth, uncertain, contradiction and falsity membership functions this multi-objective FVRNSO algorithm has been discussed in this paper.This method and this application show that the method is very much cost effective as compare to prevailing non deterministic method.

Neutrosophic Set,Single Valued Neutrosophic Set,Four Valued Refined Neutrosophic Set, Multi-objective Four Valued Refined Neutrosophic Optimization, Multi-objective Three Bar Truss Design Optimization.