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The complementary dual of entropy is termed “knowledge measure” in recent studies concerning fuzzy and intuitionistic fuzzy sets. A picture fuzzy set is an extended and generalized form of fuzzy and intuitionistic fuzzy sets. The broader perspective of the picture fuzzy set inculcated the possibility of the formulation of a picture fuzzy knowledge measure and its potential implications. In this paper, we set up an axiomatic framework for obtaining a complementary dual of the picture fuzzy entropy. Subsequently, we derive two new knowledge measures that strictly follow the axiomatic requirements. Some empirical investigations establish the advantages of our proposed knowledge measure over the existing measures. We also present a novel multiple attribute decision-making (MADM) algorithm, wherein the proposed knowledge measure computes attribute weights and exhibits encouraging performance. The comparative analysis shows the potential implications and advantages of the proposed measures.

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