A new generalization of Renyi’s entropy of order β with coding theory in fuzzy environment

Abstract

The main problem in coding theorem is to transfer the message on noiseless medium and length of code should be selected in such a way that average code length is minimized. Therefore, a new approach of generalization of Renyi’s entropy of parameter β has been discussed in this paper. We have also considered a number of its characteristics in comparison with Shannon and other existing entropies. Thereafter, we discussed the monotonous behavior of MCWL (Mean Code Word Length) using the noiseless coding theorem with the different values of β. We also proved that entropy function is lower bound of average code word length i.e. average code word length is upper bound of entropy value. Additionally, we proposed a new information measure for fuzzy set and proved its validation. To demonstrate the better results attained by proposed measure, numerical examples are also provided. Further, comparison has been given with other entropies which shows the reliability and supremacy of proposed measure.