Intuitionistic fuzzy scale-invariant entropy with correlation coefficients-based VIKOR approach for multi-criteria decision-making

In this paper, a parametric generalization of Shannon entropy, i.e., Logarithmic \(\beta\)-Norm entropy measure has been discussed. We have also derived the desired entropy characteristics of new generalized entropy measure including its positivity, expandability, extensivity and additivity and in addition, provided the much desired scale invariance property. This striking property is satisfied neither by Shannon entropy nor by its existing generalization like Renyi’s and Tsallis entropies, etc. Then we define the scale-invariant entropy measure in intuitionistic fuzzy set and discuss its several mathematical properties and validity. Thereafter, we suggested a new multi-criteria decision-making (MCDM) method using weighted correlation coefficient-based VIKOR approach for finding the ranking and measuring the uncertainity in place of distance measure. The proposed decision-making technique is well described through the numerical example based on supplier selection with the help of two approaches. In first approach we considered the case of partially known criteria weights, whereas unknown criteria weights are discussed in second approach. The comparative results show the flexibility and effectiveness of the proposed approach to solve problems in real life.