Confidence Picture fuzzy hybrid aggregation operators and its application in multi criteria group decision making

A Picture fuzzy set (PFS) is a set used to quantify uncertainty with the condition that the sum of degrees of the membership, the neutral membership, and the non-membership is equal to or less than one. Utilizing PFS and decision makers’ degrees of familiarity with the decision making problem in terms of confidence level, the paper proposes some novel aggregating operators such as confidence Picture fuzzy weighted averaging, confidence Picture fuzzy ordered weighted averaging, confidence Picture fuzzy hybrid averaging, confidence Picture fuzzy weighted geometric, confidence Picture fuzzy ordered weighted geometric and confidence Picture fuzzy hybrid geometric. Some desirable properties are also discussed. Finally, a multi criteria group decision making method has been presented by utilizing the proposed aggregating operators and applying it to solve a green supplier selection problem. Sensitivity analysis has been conducted to examine the effect of different combinations of decision makers’ confidence levels on the aggregated values, while comparative analysis has also been conducted to validate the consistency of the proposed aggregation operators over some other existing operators. Results are computed, tabulated, and plotted graphically. Some concluding remarks are also provided.