Abstract
In contrast to a fuzzy and intuitionistic fuzzy (IF) set, a picture fuzzy (PF) set may be taken as an effective tool to tackle decision-making problems. Fuzzy and intuitionistic fuzzy set theory can be extended to PF-set theory. As per our knowledge, there is no PF-knowledge measure has been proposed by any researcher so far. A novel picture fuzzy knowledge measure is proposed in the present manuscript. Its mathematical properties are investigated along with its validation. Its performance is evaluated using four distinct examples. Besides this, the newly presented PF-knowledge measure is used to derive a new PF-Accuracy measure. The derived PF-accuracy measure is checked for its validation and its properties are explained. The applications of the derived PF-accuracy measure are given in pattern recognition. Furthermore, a VIKOR-TOPSIS approach based on the proposed PF-knowledge and accuracy measure is designed. Finally, the suggested approach is utilized to identify an appropriate adsorbent for extracting hexavalent chromium from wastewater.
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