Intuitionistic fuzzy cognitive map (IFCM), an extension of fuzzy cognitive map (FCM), forms a graph-oriented fuzzy model describing both causal relationships among concepts and the states of concepts through intuitionistic fuzzy sets (IFSs). In contrast with FCM, IFCM provides much more flexibility in system modeling. However, IFCMs may lead to confusing or unreasonable results in system modeling, since IFCMs have not fully considered the negative influence from conventional operations on IFSs and the activation process of concepts, and the problem of aggregating knowledge with different importance levels. To overcome the limitations of IFCMs, we propose a high-order IFCM based on evidential reasoning (ER) theory (IFCMR) in this study. Firstly, we introduce an evidential intuitionistic fuzzy aggregation (EIFA) operator and a multiplication operation on IFSs using ER theory. Secondly, we establish the theory of IFCMR based on the EIFA operator and the newly multiplication operation on IFSs. Thirdly, we propose a scheme of aggregating IFCMRs with different importance levels using the EIFA operator, which can also be utilized to aggregate conflict knowledge and to determine objective causal weights in terms of evidential cognitive map (ECM). Finally, a number of numerical examples are utilized to validate the feasibility and validity of IFCMRs in comparison with both IFCMs and ECMs.

Hesitant fuzzy set has been an important tool in dealing with multiple attribute decision making (MADM) problems, especially for the decision making situation when only some values of membership are possible for an alternative on attributes. However, determining attributes weights in hesitant fuzzy MADM is still an open problem. In this paper, we propose an objective weighting approach based on Shannon information entropy, which expresses the relative intensities of attribute importance to signify the average intrinsic information transmitted to the decision maker. Furthermore, we construct a hesitant fuzzy MADM approach based on the TOPSIS method and a weighted correlation coefficient proposed in this paper. Finally, we utilize a supplier selection example to validate the objective attributes weights determining method and the proposed hesitant fuzzy MADM approach.

Multiattribute decision making (MADM) is one of the central problems in artificial intelligence, specifically in management fields. In most cases, this problem arises from uncertainty both in the data derived from the decision maker and the actions performed in the environment. Fuzzy set and high-order fuzzy sets were proven to be effective approaches in solving decision-making problems with uncertainty. Therefore, in this paper, we investigate the MADM problem with completely unknown attribute weights in the framework of interval-valued intuitionistic fuzzy (IVIF) set (IVIFS). We first propose a new definition of IVIF entropy and some calculation methods for IVIF entropy. Furthermore, we propose an entropy-based decision-making method to solve IVIF MADM problems with completely unknown attribute weights. Particular emphasis is put on assessing the attribute weights based on IVIF entropy. Instead of the traditional methods, which use divergence among attributes or the probabilistic discrimination of attributes to obtain attribute weights, we utilize the IVIF entropy to assess the attribute weights based on the credibility of the decision-making matrix for solving the problem. Finally, a supplier selection example is given to demonstrate the feasibility and validity of the proposed MADM method.