TOPSIS based on nonlinear-programming methodology for solving decision-making problems under cubic intuitionistic fuzzy set environment

Abstract

The objective of this work is to discuss a novel nonlinear-programming (NLP) models based on the “Technique for Order Preference with respect to the Similarity to the Ideal Solution (TOPSIS)” method to solve the decision-making problems under the cubic intuitionistic fuzzy sets (CIFSs) environment. In the existing studies, the information related to an element is collected either as an interval-valued intuitionistic fuzzy sets (IVIFSs) or intuitionistic fuzzy sets (IFSs) information. An alternative to this, CIFS is one of the extensions of these sets where the information is gathered by considering both the IVIFS and IFS simultaneously. Thus, motivated by this, we modeled the NLP models by considering the interval weights as well as the concept of the relative closeness coefficient and weighted distance measures. Some of the salient features of the models are also examined. Furthermore, we present a novel multicriteria decision-making (MCDM) method and illustrate with a real-life example related to signal processing in sound navigation and ranging. A comparative analysis is also conducted to verify effectiveness and rationality of the method.