Fermatean fuzzy multi-criteria group decision making approach based on reliability of decision information

There are various uncertainties in the multi-criteria group decision making (MCGDM) process, including the definition of the importance of decision information and the assignment of criterion assessment values, etc., which cause decision makers to be unconfident in their decisions. In this paper, an MCGDM approach based on the reliability of decision information is proposed in Fermatean fuzzy (FF) environment, allowing a decision to be made with confidence that the alternative chosen is the best performing alternative under the range of probable circumstances. First, we prove that the FF Yager weighted averaging operator is monotone with respect to the total order and note the inconsistency between the monotonicity of some FF aggregation operators and their application in MCGDM. Second, we extend the divergence measure of FFS to order sigma for calculating the variance of decision information and accordingly develop an exponential FF entropy measure to measure the uncertainty of decision information. Then, the reliability of decision information is defined, which accounts for the degree of variance of decision information across criteria from the criterion dimension and the uncertainty of the decision information from the alternative dimension. Following that, an integrated MCGDM framework is completed. Finally, the applications to a numerical example and comparisons with previous approaches are conducted to illustrate the validity of the established approach.