Novel entropy and distance measures for interval-valued intuitionistic fuzzy sets with application in multi-criteria group decision-making

Entropy and distance are the most important information-theoretic measures. These measures have found useful applications in different areas. In the present communication, we study the entropy and distance measures under an interval-valued intuitionistic fuzzy (IVIF) environment using an exponential function. First, it presents the novel exponential entropy and distance measures for interval-valued intuitionistic fuzzy sets (IVIFSs) with proof of their authenticity. A method is offered to solve multi-criteria group decision-making (MCGDM) problems in the IVIF environment based on the weighted exponential entropy measure. The performance of the proposed IVIF MCGDM method is shown by taking two case studies. Second, the success and strength of the proposed IVIF distance measures are demonstrated by comparing them with the existing ones. Further, the paper advances an approach to solve multi-attribute decision-making problems under the IVIF environment. Finally, it considers a real-world example to illustrate the applicability and authenticity of the proposed approach. In doing so, the proposed approach is compared with existing methods to exhibit its advantages. Thus, the proposed IVIF information measures and multi-criteria group decision-making method are more suitable to solve real-life decision-making problems.