A nonlinear-programming methodology for multi-attribute decision-making problem with interval-valued intuitionistic fuzzy soft sets information

Interval-valued intuitionistic fuzzy (IVIF) soft set is one of the useful extensions of the fuzzy soft set which efficiently deals with the uncertain data for the decision-making processes. In this paper, an attempt has been made to present a nonlinear-programming (NP) model based on the technique for order preference by similarity to ideal solution (TOPSIS), to solve multi-attribute decision-making problems. In this approach, both ratings of alternatives on attributes and weights of attributes are represented by IVIF sets. Based on the available information, NP models are constructed on the basis of the concepts of the relative-closeness coefficient and the weighted distance. Some NP models are further deduced to calculate relative-closeness of sets of alternatives which can be used to generate the ranking order of the alternatives. A real example is taken to demonstrate the applicability and validity of the proposed methodology.