A three-cycle decision-making selection mechanism with intuitionistic trapezoidal fuzzy preference relations

Preference relations as information representation form are widely used to manage complexity and uncertainty in practical decision-making cases. Intuitionistic trapezoidal fuzzy numbers (ITrFNs) can convey more fuzzy messages than other fuzzy numbers. This paper defines intuitionistic trapezoidal fuzzy preference relations (ITrFPRs) to adequately describe the preferences of decision makers (DMs). To optimize the decision-making selection process, this paper constructs a three-cycle decision-making selection mechanism with ITrFPRs. To build this mechanism, firstly, a possibility degree formula is presented to rank ITrFNs. Secondly, ITrFPRs, consistent ITrFPRs, acceptable consistent ITrFPRs and a new consistency index are defined. Thirdly, a novel consistency transformation method is built to elevate the consistency of ITrFPRs. Fourthly, considering the relationship between consistency conditions and priority weight, a priority weight derivation method is exploited to derive intuitionistic trapezoidal fuzzy weights. Ultimately, a three cycle selection mechanism integrated with consistency checking, consistency improvement and priority weight derivation procedures is constructed and applied into the case of trip itinerary selection. Sensitive and comparative analyses are carried out to illustrate the effectiveness and applicability of the proposed mechanism.