Robust neutrosophic modelling and optimisation approach for solving multi-objective multi-product production planning problem

Neutrosophic set theory is a generalised version of fuzzy and intuitionistic fuzzy set theory, where membership degrees of acceptance, rejection, and indeterminacy are both measured. In this article, we formulate a multi-product production planning problem with multi-objectives with parameters as neutrosophic environments. The uncertain parameters are depicted as trapezoidal neutrosophic numbers, and the crisp version is developed by a new accuracy function. In the solution procedure, we have investigated interactive neutrosophic optimisation techniques with neutrosophic parameters. Furthermore, various sorts of membership functions, such as linear, exponential, and hyperbolic, are depicted so that the marginal evaluation of each objective is determined. The proposed method represents an opportunity for select decision-makers with desired membership functions. To show the relations among the multi-objective multi-product production planning problem, its equivalent crisp formulation obtained by applying three different membership functions is established. Finally, the stepwise solution procedures are discussed, and the solution is compared with different membership functions.