Abstract
Three-way decision model (3WDM) with decision-theoretical rough sets (DTRSs) always addresses precise cost parameters and precise attribute values in uncertain problem solving. However, intuitionistic fuzzy sets (IFSs), as extensions of fuzzy sets, are described by dual parameters, namely the membership and nonmembership degrees. Therefore, under intuitionistic fuzzy environments, the 3WDM confronted great challenges when intuitionistic fuzzy number (IFN) cost parameters and IFN attribute values arise together. In this paper, by considering the impacts of both the IFN cost parameters and the IFN attribute values, new 3WDMs with IFNs are constructed from the membership degree and nonmembership degree perspectives, respectively. Then optimistic and pessimistic 3WDMs with IFNs are, respectively, established based on different risk preferences for more accurate decisions. Subsequently, by introducing a sequential strategy, the presented models are applied to address attribute increments in practical problems. Finally, we present a numerical example and some experiments to validate the efficiency of sequential 3WDMs.
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