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Picture Fuzzy Sets (PFSs) originated by Cuong and Kreinovich are more capable to capture uncertain, inconsistent and vague information in multi-criteria decision making. In this paper, we propose a new picture fuzzy divergence measure based on Jensen-Tsallis function between PFSs. Further, the concept has been extended from fuzzy sets to novel picture fuzzy divergence measure. Besides the validation of the proposed measure, some of its key properties with specific cases are additionally talked about. The performance of the proposed measure is compared with other existing measures in the literature. Some illustrative examples are provided in the context of novel rapacious COVID-19 and pattern recognition which demonstrate the adequacy and practicality of the proposed approach in solving real-life problems.

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In this paper, based on the concept of Renyi-Tsallis entropy, we propose an inaccuracy measure for a pair of probability distribution and discuss its relationship with mean codeword length. Furthermore, we propose a new fuzzy entropy measure in the setting of fuzzy set theory and its several properties are examined. Comparison with several existing entropies shows that the proposed fuzzy information measure has a greater ability in discriminating different FSs (fuzzy sets). Furthermore, we introduce a new fuzzy mean codeword length and give their relationship with fuzzy information measure. The upper bounds of these entropies in terms of mean codeword lengths have been provided and some basic properties of the proposed codeword length have been studied. In addition, we introduce a new similarity measure for fuzzy sets and give its applications in pattern recognition and cluster analysis. To implement the application of proposed similarity measure in real life problem, we have taken real data from the repository of machine learning. These practical examples are given to support the findings and also show the availability of similarity measure between fuzzy sets.

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