Some Picture Fuzzy Information Inequalities with Applications in Market Behaviours and Pattern Recognition
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Abstract
Quantifying uncertainty in robust datasets is essential in decision analysis. Merging such data with the concepts of information theory opens various aspects of uncertainty. The additional degree of uncertainty can be addressed by picture fuzzy divergences. This study precisely handles such datasets by introducing a novel picture fuzzy divergence measure (PFDM) using generalized f-divergence. The validity of the measure has been proved, and some properties are discussed. Furthermore, some information inequalities are established for classical dissimilarity measures. These inequalities offer critical mathematical boundaries for analyzing and comparing various fuzzy information measures. Additionally, the application of the measure is discussed for market behaviour trends and pattern recognition problems. The obtained results aims to minimize the divergence and maximize the result accuracy and the measures successfully quantify the variations within fuzzy sets.
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