Implementation of Fuzzy Cognitive Maps Using Fuzzy Neural Network and Application in Prediction of Time Series

Abstract

The fuzzy cognitive map (FCM) has gradually emerged as a powerful paradigm for knowledge representation and a simulation mechanism that is applicable to numerous research and application fields. However, since efficient methods to determine the states of the investigated system and to quantify causalities that are the very foundations of FCM theory are lacking, constructing FCMs for complex causal systems greatly depends on expert knowledge. The manually developed models have a substantial shortcoming due to the model subjectivity and difficulties with assessing its reliability. In this paper, we proposed a fuzzy neural network to enhance the learning ability of FCMs. Our approach incorporates the inference mechanism of conventional FCMs with the determination of membership functions, as well as the quantification of causalities. In this manner, FCM models of the investigated systems can automatically be constructed from data and, therefore, operate with less human intervention. In the employed fuzzy neural network, the concept of mutual subsethood is used to describe the causalities, which provides more transparent interpretation for causalities in FCMs. The effectiveness of the proposed approach in handling the prediction of time series is demonstrated through many numerical simulations.Index Terms-Fuzzy cognitive maps (FCMs), fuzzy neural network, fuzzy-rule identification, mutual subsethood.

A Dynamic Temporal Neuro Fuzzy Inference System for Mining Medical Databases

“…The main objective of this work is to propose a dynamic neuro fuzzy inference system that builds a model named, Fuzzy Temporal Cognitive Map (FTCM) based on four layer fuzzy neural network (Song et al, 2010), with an identification of membership function in a prespecified time interval and computation of relationship among the concepts within that interval. Further, the causalities among the concepts are represented as a temporal relationship pattern with an integration of Allen's interval algebra (Allen, 1983).…”

“…The improved quality in learning process depends on the historical data. Enhancement in the learning process is suggested in (Song et al, 2010) by incorporating the inference mechanism of FCM with automatic identification of membership functions and quantification of causalities. (Miao et al, 2002;Leong and Miao, 2005) proposed fuzzy cognitive agents which deploy the fuzzy cognitive maps as decision making engines based on user preferences and domain knowledge.…”

“…Since no cause can cause itself, all w ii = 0, where: Genarally the FCMs are created manually and the reliability of it depends upon the experts' knowledge. Hence to overcome this problem, we construct a four layered fuzzy neural network as defined in (Song et al, 2010) with automatic identification of membership function.…”

“…Basically, FCMs are constructed manually based upon the domain experts' knowledge. The proposed approach makes use of a four layered fuzzy neural network for the generation of FTCM based on the structure given in (Song et al, 2010). A hybrid type causality, i.e., a combination of equality causality and difference causality is defined to present FTCM.…”

“…The linguistic terms which represent the output variable (y il ) are also described by symmetric Gaussian membership function. Layer 3 nodes are connected to layer 2 nodes with the help of fuzzy weights, which are calculated using mutual subsethood, ie., 1-ε (x il , y il ), Mutual subsethood (Song et al, 2010) measures the similarity between the input and output variables, which describes the causal-effect relationship from the input linguistic term to the output linguistic term. Also, it ensures that no concept will cause itself.…”