‎Intuitionistic Hesitant Fuzzy Algorithm for Multi-Objective Structural Model Using Various Membership Functions

In real life‎, ‎structural problems can be described in linear and nonlinear forms‎. ‎This nonlinear structural problem is very challenging to solve when its all parameters are imprecise in nature‎. ‎Intuitionistic fuzzy sets were proposed to manage circumstances in which experts have some membership and non-membership value to judge an option‎. ‎Hesitant fuzzy sets were used to manage scenarios in which experts pause between many possible membership values while evaluating an alternative‎. ‎A new growing area of a generalized fuzzy set theory called intuitionistic hesitant fuzzy set (IHFS) provides useful tools for dealing with uncertainty in structural design problem that is observed in the actual world‎. ‎In this article‎, ‎we have developed a procedure to solve non-linear structural problem in an intuitionistic hesitant fuzzy (IHF) environment‎. ‎The concept of an intuitionistic hesitant fuzzy set is introduced to provide a computational basis to manage the situations in which experts assess an alternative in possible membership values and non-membership values‎. ‎This important feature is not available in the intuitionistic fuzzy optimization technique‎. ‎Here we have discussed the solution procedure of intuitionistic hesitant fuzzy optimization technique dedicatedly for linear‎, ‎exponential‎, ‎and hyperbolic types of membership and non-membership functions‎. ‎Some theoretical development based on these functions has been discussed‎. ‎A numerical illustration is given to justify the effectiveness and efficiency of the proposed method in comparison with fuzzy multi-objective nonlinear programming method and intuitionistic fuzzy multi-objective nonlinear programming method‎. ‎Finally‎, ‎based on the proposed work‎, ‎conclusions and future research directions are addressed‎.