Moderator intuitionistic fuzzy sets with applications in multi-criteria decision-making

The concept of intuitionistic fuzzy sets (IFSs) supports an observer to integrate the hesitancy index in membership function. The hesitancy index originates from his basic awareness, past information, situation, lack of the standard terminologies and a lot of other parameters, so membership degree involved uncertainty under IFSs. Therefore, the uncertainty index included with an observer in choosing membership grade under IFSs requires additional improvement. Keeping it in mind, the notion of moderator intuitionistic fuzzy set (MIFS) introduced by Joshi and Kharayat (Adv Intell Syst Comput, 2016) by adding a parameter in IFS environment to make the uncertain behaviour more accurate. Some properties and operators were also defined over MIFSs and applied in a real-life problem of medical diagnosis. In this paper, firstly two operational laws are defined over MIFNs to apply the concept of MIFSs to multi-criteria decision-making problems. Then, a moderator intuitionistic fuzzy weighted averaging (MIFWA) operator and a moderator intuitionistic fuzzy weighted geometric (MIFWA) operator are proposed to combine MIFNs to take decisions. Finally, a numerical example is considered to illustrate the proposed approach effectively.