Enhance the Uncertainty Modeling Ability of Fuzzy Grey Cognitive Maps by General Grey Number

Abstract

In real-life systems, people cannot get precise data. The data are represented in the forms of interval or multiple intervals in many cases. Most intelligent algorithms are designed for precise data in algorithm research. People always use a real number contained in the interval or multiple intervals as the candidate for the precise data. However, such a measure will lose lots of information contained in the interval or multiple intervals. Fuzzy Cognitive Map (FCM) is one of the famous intelligent algorithms. The Fuzzy Grey Cognitive Map (FGCM) was proposed to enable FCM to do interval computation. But FGCM can only deal with a single interval, as for multiple intervals, the FGCM is powerless. Thus, this paper aims to enhance the FGCM to make it can cope with multiple intervals. The paper introduces the general grey number and deduces the new activation functions according to Grey System Theory (GST) and Taylor series. Finally, an industrial process control problem is applied to verify the new algorithm. The results show that the new algorithm is not only compatible with the original FGCM and FCM, but can process more uncertain knowledge and data. In general, the new algorithm inherits most of FGCM's characteristics and can cope with the data expressed by multiple intervals, which means it can be used in environments with more uncertain knowledge and data.

Keywords

• Fuzzy grey cognitive map
• fuzzy cognitive map
• uncertainty modeling
• general grey number
• grey system theory