An Fermatean fuzzy programming method for group decision making with interval-valued Fermatean fuzzy preference relations and application to financing alternative selection

Financing alternative selection is central to enterprise financial planning, directly impacting capital chain stability and long-term strategy implementation. Interval-valued Fermatean fuzzy preference relations (IVFFPRs) offer higher freedom and represent broader uncertain information. This paper proposes an Fermatean fuzzy programming method for group decision making with IVFFPRs and applies it to financing alternative selection. A novel consistency index for Fermatean fuzzy preference relations (FFPRs) is presented to examine the additive consistency of an FFPR. By decomposing an IVFFPR into two FFPRs, the definition of additive consistency for an IVFFPR is formulated. When facing multiple IVFFPRs failing additive consistency, a goal programming model is built to improve IVFFPRs consistency, simultaneously. The information uncertainty weights and consensus deviation weights of decision makers (DMs) are calculated by the entropy measurements and Hamming distance, respectively. The combined weights of DMs are obtained through the combination weighting approach of game theory. These weights are utilized to aggregate individual IVFFPRs into a collective one. An Fermatean fuzzy programming model is constructed to obtain alternatives’ priority weights. Three approaches grounded in DMs’ risk attitudes are devised to resolve the constructed model. A case of financing alternative selection is analyzed to confirm the efficacy of the proposed method.