Intuitionistic fuzzy three-way ranking-based TOPSIS approach with a novel entropy measure and its application to medical treatment selection

Intuitionistic fuzzy set (IFS) is one of the tools to address the uncertainties in the data by using the two membership degrees. On the other hand, entropy is a useful index for characterizing the uncertainty of fuzzy information. This paper aims to propose an entropy to measure the uncertainty of IFSs from a new perspective and apply it to multi-criteria decision-making (MCDM). To accomplish this, firstly, a new score function (SF) for intuitionistic fuzzy numbers is proposed based on a probabilistic perspective to mitigate the deficiencies of existing SFs. The merits of the proposed SF are also highlighted. Then we construct an entropy index by using the proposed SF. The various axioms and properties are described in detail. Two numerical examples are shown, in detail, to illustrate the performance of the proposed entropy by comparing it with other existing ones. Finally, by combining the proposed entropy with Three-Way Ranking-based method (TWR) and Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), a decision-making framework called IFTWR-TOPSIS, is presented to address the MCDM problem in medical treatment selection. Through sensitivity and comparative analyses, the IFTWR-TOPSIS method is feasible and effective. More importantly, it follows that our proposed method is superior to some classical MCDM methods and has broad application prospects.