15-06-2012, 12:01 PM
A DYNAMIC FUZZY-COGNITIVE-MAP APPROACH
BASED ON RANDOM NEURAL NETWORKS
A DYNAMIC FUZZY-COGNITIVE-MAP APPROACH.pdf (Size: 206.35 KB / Downloads: 35)
Abstract.
A fuzzy cognitive map is a graphical means of representing
arbitrarily complex models of interrelations between concepts.
The purpose of this paper is to describe a dynamic fuzzy cognitive
map based on the random neural network model. Previously, we have
developed a random fuzzy cognitive map and illustrated its application
in the modeling of processes. The adaptive fuzzy cognitive map
changes its fuzzy causal web as causal patterns change and as experts
update their causal knowledge.
Introduction
Modeling a dynamic system can be hard in a computational sense. Many
quantitative techniques exist. Well-understood systems may be amenable to
any of the mathematical programming techniques of operations research. Insight
into less well-defined systems may be found from the statistically based
methods of data mining. These approaches offer the advantage of quantified
results but suffer from two drawbacks. First, developing the model typically
requires a great deal of effort and specialized knowledge outside the domain
of interest.
The Random Neural Network Model.
The RNN model has been
introduced by Gelenbe [9, 10, 11] in 1989. This model has a remarkable
property called “product form” which allows the computation of joint probability
distributions of the neurons of the network. The model consists of a
network of n neurons in which positive and negative signals circulate. Each
neuron accumulates signals as they arrive, and can fire if its total signal
count at a given instant of time is positive. Firing then occurs at random
according to an exponential distribution of constant rate, and signals are
sent out to other neurons or to the outside of the network. Each neuron
i of the network is represented at any time t by its input signal potential
ki(t). Positive and negative signals have different roles in the network. A
negative signal reduces by 1 the potential of the neuron to which it arrives
(inhibition) or has no effect on the signal potential if it is already zero; while
an arriving positive signal adds 1 to the neuron potential.
The Dynamic Random Fuzzy Cognitive Maps
Our RFCM improves the conventional FCM by quantifying the probability
of activation of the concepts and introducing a nonlinear dynamic function
to the inference process [3]. Similar to a FCM, concepts in RFCM can
be causes or effects that collectively represent the system’s state.
Conclusions
FCMs are an interesting yet isolated decision support tool. Their implicitly
qualitative nature is at odds with general practice in the automation
of decision support tools. In this paper, we have proposed a dynamic FCM
based on the RNN, the DRFCM. We show fusing the RFCM with a traditional
reinforced learning algorithm can yield excellent results. The DRFCM
may be rapidly adapted to changes in the modeled behavior.