Multi-Objective Welded Beam Design Optimization By Four Valued Refined Neutrosophic Optimization Technique: A Comparative Study

Abstract

Structural design optimization in precise or imprecise environment plays an important role in civil engineering as well as in mathematics. Conventionally in most of the situation structural designs are treated as single objective optimization problem with cost as objective function. Practically there exists some real life problems where multiple and conflicting objects frequently exist.So a methodology known as Multi-objective Four Valued Refined Neutrosophic Optimization (MOFVRNO) technique has been introduced in this paper.This optimization technique is generalization of fuzzy set (FS)theory,Intuitionistic Fuzzy Set (IFO)Theory and above all Single Valued  Neutrosophic Set Optimization (SVNSO)theory.In this problem cost and deflection of the beam have been considered as objective functions. Also in this welded beam design problem maximum shear stress in the weld group, maximum bending stress in the beam, buckling load of the beam have been considered as constraints. The design variables are length ,depth ,height,width in this optimization problem.Now from the mathematical point of view indeterminacy is again refined as uncertain(U),Contradiction(Truth∧Falsity,T) in Four valued Refined Neutrosophic Optimization technique.The results obtained by different methods like nonlinear optimization technique,Fuzzy optimization technique ,Intuitionistic Fuzzy Optimization technique ,Single Valued Neutrosophic Optimization technique andFour Valued Refined Neutrosophic Optimization technique have been discussed in the perspective of welded beam design problem in this paper. It helps to make comparison among them to find most cost effective method.