Temporal fuzzy cognitive maps

This paper is concerned with the design, implementation, and evaluation of a novel extension of FCMs, temporal fuzzy cognitive maps (tFCMs). FCMs have advantages such as simplicity, supporting of inconsistent knowledge, and circle causalities for knowledge modeling and inference. However, the lack of the time dimension limits the usage of FCMs from the long term inference and the time related knowledge modeling. In order to narrow down the gap, a temporalized FCM is proposed to define a complete discrete temporal extension of the FCM. To reduce the complexities brought by the temporalization, a design approach is also introduced to construct the map, using simplified patterns and fuzzy logic based effect functions to capture fuzzy knowledge from domain experts. The paper also discusses how the errors in the fuzzy knowledge affect the result. Two different causality models are studied in theory and experiments to compare the error effects during the inferring. The result shows a significant difference in error accumulation in different causality models and gives a guideline to help users balance the error accumulation and sensitivities of their maps.