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.INDEX TERMS Fuzzy grey cognitive map, fuzzy cognitive map, uncertainty modeling, general grey number, grey system theory.

The Dynamic Extensions of Fuzzy Grey Cognitive Maps

“…FGGCM is the extension of FGCM, it aims to improve the uncertainty modeling capability of FGCM because FGCM does not exploit all uncertainty processing ability of GST [20]. FGGCM uses the general grey number (GGN) rather than the IGN as its basic element.…”

“…In this way, FGGCM extends the uncertainty modeling ability of the FGCM. The sigmoid and tanh activation functions are proven in [20] and shown in Eq. (26) and Eq.…”

“…Firstly, we will introduce the background of the experiment in Section V-A and then the experimental setting under the RBEM (Section V-B) and PREM (Section V-C) are shown. The relevant data are collected from [6]- [8], [20], [52]- [54].…”

“…The FGCM was exploited to analyze this problem in 2014 [9]. And recently, the FGGCM was also validated by this system [20]. Because it was widely applied in the field of FCM, we also use the industrial control problem as the background to validate the proposed DFGCM and DFGGCM.…”

“…The typical applications of FGCM includes: supply chain performance and organizational culture [32], empathic buildings [33], intervalvalued time series forecasting [34], process modeling [35] and so on. The Fuzzy General Grey Cognitive Map (FG-GCM) was recently introduced to improve the uncertainty modeling ability of FGCM [20]. As an extension of FGCM, FGGCM uses the general grey number (GGN), rather than the interval grey number (IGN).…”