RETRACTED ARTICLE: Recycling of waste materials based on decision support system using picture fuzzy Dombi Bonferroni means

A picture fuzzy set (PFS) is the extended version of an intuitionistic fuzzy set (IFS) and can deal with dubious and imprecision information. Dombi aggregation models are powerful mathematical tools utilized to aggregate human opinions and information in different fields, including social networking, data analysis, architecture, and neurosciences. Bonferroni means (BM) and geometric Bonferroni means (GBM) operators are allowed to define interrelationships among input arguments and play an extensive role in multi-attribute group decision-making (MAGDM) problems. In this article, we anticipated some robust aggregation operators (AOs) of PFSs based on Dombi aggregation models, namely “picture fuzzy Dombi Bonferroni mean” (PFDBM), “picture fuzzy Dombi weighted Bonferroni mean” (PFDWBM), “picture fuzzy Dombi geometric Bonferroni mean” (PFDGBM), and picture fuzzy Dombi weighted geometric Bonferroni mean” (PFDWGBM) operators. Some appropriate characteristics and special cases of our proposed methodologies are also presented. An algorithm of the MAGDM problem is also characterized to resolve complex real-life situations. Moreover, we also determined a practical example of the waste materials to evaluate a suitable recycling machine using our developed methodologies. To ratify the reliability and versatility of our current approaches, by contrasting the findings of existing approaches with the results of developed techniques.