Some picture fuzzy mean operators and their applications in decision-making

Picture fuzzy set is the generalization of fuzzy set and intuitionistic fuzzy set. It is useful for handling uncertainty by considering the positive membership, neutral membership and negative membership degrees independently for each element of a universal set. The main objective of this article is to develop some picture fuzzy mean operators, including Picture Fuzzy Harmonic Mean (PFHM), Picture Fuzzy Weighted Harmonic Mean (PFWHM), Picture Fuzzy Arithmetic Mean (PFAM), Picture Fuzzy Weighted Arithmetic Mean (PFWAM), Picture Fuzzy Geometric Mean (PFGM) and Picture Fuzzy Weighted Geometric Mean (PFWGM), to aggregate the picture fuzzy sets. Moreover, we discuss some relevant properties of these operators. Furthermore, we apply these mean operators to make decisions with practical examples. Finally, to show the efficiency and the validity of the proposed operators, we compare our results with the results of existing methods and concluded from the comparison that our proposed methods are more effective and reliable.                                                                                                                                                            

Keywords:

Picture Fuzzy Set , Harmonic mean operator , Arithmetic mean operator , Geometric mean operator