Modelling and analysis of different optimization models under uncertainity

The construction of the different types of optimization problems under an imprecise environment can significantly tackle the situations involving vaguess in the parameters or in the variables. The intuitionistic fuzzy number associated with a point, is framed by two parameters, membership and non-membership degrees. The membership degree determines acceptance level of the point while the non-membership measures its non-belonginess (rejection level). However, a person, because of some hesitation, instead of giving a fixed real numbers to the acceptance and rejection levels, may assign them intervals. This new construction not only generalizes the idea of Intuitionistic to interval-valued intuitionistic fuzzy theory but also gives wider scope with more flexibility. In the present project, we shall formulate various optimization models under fuzzy, intuitionistic fuzzy or interval-valued fuzzy environment. Further, solution methodologies to handle such problems using pessimistic/optimistic/mixed approaches will be developed. To deal with the fuzzy constraint related to the objective function, different membership functions, linear, exponential or hyperbolic will be considered. The validation of the work will also be presented by showing numerical illustrations with practical relevance. Moreover, construction and analysis of robust optimization models based on duality principles and optimality conditions are also the part of the study.