On intuitionistic fuzzy order-α divergence and entropy measures with MABAC method for multiple attribute group decision-making

• Published in: Journal of intelligent & fuzzy systems 2021-01, Vol.40 (1), p.1191-1217
• Main Author: Verma, Rajkumar
• Format: Article
• Language: English
• Subjects: Decision making; Entropy; Fuzzy logic; Fuzzy sets; Personnel selection; Robustness (mathematics)
• ISSN: 1064-1246; 1875-8967
• DOI: 10.3233/JIFS-201540

The development of information measures associated with fuzzy and intuitionistic fuzzy sets is an important research area from the past few decades. Divergence and entropy are two significant information measures in the intuitionistic fuzzy set (IFS) theory, which have gained wider attention from researchers due to their extensive applications in different areas. In the literature, the existing information measures for IFSs have some drawbacks, which make them irrelevant to use in application areas. In order to obtain more robust and flexible information measures for IFSs, the present work develops and studies some parametric information measures under the intuitionistic fuzzy environment. First, the paper reviews the existing intuitionistic fuzzy divergence measures in detail with their shortcomings and then proposes four new order-α divergence measures between two IFSs. It is worth mentioning that the developed divergence measures satisfy several elegant mathematical properties. Second, we define four new entropy measures called order-α intuitionistic fuzzy entropy measures in order to quantify the fuzziness associated with an IFS. We prove basic and advanced properties of the order-α intuitionistic fuzzy entropy measures for justifying their validity. The paper shows that the introduced measures include various existing fuzzy and intuitionistic fuzzy information measures as their special cases. Further, utilizing the conventional multi-attributive border approximation area comparison (MABAC) model, we develop an intuitionistic fuzzy MABAC method to solve real-life multiple attribute group decision-making problems. Finally, the proposed method is demonstrated by using a practical application of personnel selection.