‎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.