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.
Highlights
Coping with the uncertainty data and information is one of the main tasks of soft computing
A more complexed situation where both nodes and weights values are two or more intervals is designed in Section IV-D to show the proposed algorithm’s availability, at the same time, we exploit the original Fuzzy Grey Cognitive Map (FGCM) multiple times to solve this situation, the results range of the original FGCM is consistent with the proposed model, but so many original FGCM’s runtime is too long to be tolerant
The FGCM is extended from the Fuzzy Cognitive Map (FCM) directly according to [40], and the FGCM using general grey number is obtained from FGCM directly
Summary
Coping with the uncertainty data and information is one of the main tasks of soft computing. Soft computing is different from the ‘‘hard computing’’, which need deterministic analytic techniques. Soft computing can deal with imprecision, uncertainty, partial truth, and approximations. The principal constituents of soft computing techniques are probabilistic reasoning, fuzzy logic, neuro-computing, genetic algorithms, belief networks, chaotic systems, as well as learning theory [1]. Fuzzy Cognitive Map (FCM) is one of the soft computing techniques [2]. Support of inconsistent knowledge, and circle causalities for knowledge modeling and inference [3], FCM has made many significant achievements in many research
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