Modified Non-Linear Programming Methodology for Multi-Attribute Decision-Making Problem with Interval-Valued Intuitionistic Fuzzy Soft Sets Information

Abstract

The presented work is an extensive study of the existing non-linear programming (NLP) methods in an uncertain environment of an interval-valued intuitionistic fuzzy soft set (IVIFSS) for solving multi-attribute decision-making (MADM) problems. IVIFSS is an intriguing extension of a fuzzy set (FS) involving both interval-valued intuitionistic fuzzy set (IVIFS) (which considers interval-value of both membership and non-membership elements of an intuitionistic fuzzy set (IFS)) and soft set (SS) (which gives importance to each parameter in an alternative). A comprehensive study projects that the existing NLP method in accordance with the technique for order preference by similarity to ideal solution (TOPSIS) for solving interval-valued intuitionistic fuzzy soft multi-attribute decision-making (IVIFSMADM) problems (decision-making (DM) problems in which assessment of rating of each alternative, over each character is rendered by an IVIFSS) is posing some limitations due to some mathematical incorrect assumptions and hence incorporating ambiguous results in real-life applications. Henceforth, an attempt has been made to properly understand the root cause of the posed shortcoming and suggested a new NLP method for solving IVIFSMADM problems, and also to validate this proposed NLP method a real-life problem is solved successfully.