This paper proposed a self-learning, self-adapting algorithm (ANN-GA-Cascades) for extracting fuzzy rules, which is based on fusion of soft computing. We could use it to attain the fuzzy rules of oiliness in oil exploration: firstly, supervised learning of training sample is performed by using neural networks, with the inputs being the simplest well-logging attribute set which is relevant to the oiliness attributes, and the outputs being the corresponding oiliness partition Ck (dry layer, water layer, inferiority layer and oil layer). When the neural network attained precision or the maximum iteration steps, the kth output node of neural network will be the corresponding partition of decision character, with the output function being ψk = f(xi, (WG1)ij, (WG2)jk), in which (WG1)ij are the connection weights between input layer and hidden layer, (WG2)jk are the connection weights between hidden layer and output layer. Then, the genetic algorithm (GA) was used to randomly assemble the input character and ψk as the fitness function. In this way, the optimal chromosome will be the fuzzy rule of partition Ck. Finally, the empirical study application of this algorithm on oil well oilsk81 and oilsk83 of Jianghan oilfield in China has proved to be satisfactory.
There are much raw data in the procedure of oil exploration, which covers certain information that could become knowledge and even be formed to if–then fuzzy rules, thus is helpful for a better decision-making. Artificial neural networks and genetic algorithms are both commonly used in extracting fuzzy rules. When the input and output variables as well as the fuzzy partition of the variables become too much, fuzzy rules extracted by neural networks will be obtained and at the same time the rules will be exponentially growing (Benitez & Castro, 1996). Using genetic algorithms to extract fuzzy rules (Lim, Rahardja, & Gwee, 1996) could, on the one hand, achieve the global optimization search, and, on the other hand, be hard to get the expression of chromosome and conformation of fitness function.
At the same time, two main goals should be considered in extracting fuzzy rules: one is the maximizing accuracy; and the other is the minimizing complexity, which means a good interpretability for fuzzy rules. But the two goals are often conflicted with each other. Based on the tradeoff of accuracy and interpretability, the main consideration of fuzzy rule sets should be accuracy maximization and complexity minimization. Then, fuzzy rules selection should be considered based on the following three main parameters (Ishibuchi et al., 1997, Ishibuchi et al., 2001 and Ishibuchi and Yamamoto, 2004): f1(S), f2(S) and f3(S), where S is the set of fuzzy rules, f1(S) being the number of correctly classified training patterns by S, f2(S) is the number of fuzzy rules in S and f3(S) is the total number of antecedent conditions of fuzzy rules in S. The larger value of f1(S) denotes the higher recognition accuracy of fuzzy rules set, and the smaller value of f2(S), f3(S) denotes the better interpretability of fuzzy rules set.
This paper presents an algorithm of extracting fuzzy rules from trained neural network using genetic algorithm (Wang and Cao, 2002 and Guo and Chen, 2001), which is ANN-GA-Cascades. The ANN is trained on the encoded vectors of the input attributes and the corresponding vectors of the output classes. The training of ANN is processed until the convergence rate between the actual and the desired outputs will be achieved. Then we obtain the function of the kth output node of ANN ψk = f(xi, (WG1)ij, (WG2)jk) which will be the corresponding partition of decision character, where (WG1)jk is the connection weights of the input layer to the hidden layer and (WG2)jk is the connection weights of the hidden layer to the output layer. The function ψk represents the input patterns of the kth cluster. Finally, we use genetic algorithms to obtain the best chromosome which maximizes the fitness function ψk. For extracting the rule of kth cluster (classk), the best chromosome must be decoded as follows:
(1)
The attribute values exist if the corresponding bits in the best chromosome equal one and vice versa.
(2)
The operators “OR” and “AND” are used to correlate the existing values of the same attribute and the different attributes, respectively.
(3)
The set of rules makes rule refinement and cancels redundant attributes, e.g. if an attribute has three values, such as A, B and C, the rule will be as follows:
If the kth attribute has a value A or B or C, then classk attribute can be dropped (redundant).
A novel machine learning algorithm for extracting comprehensive rules has been presented in this paper. The algorithm combines ANN with GA, which provides a soft computing fusion model for extracting fuzzy rules in the oil exploration; also, this algorithm can be applied to the oil reservoir lithology identification. The future work should consist more experiments with other data sets, as well as more elaborated experiments to optimize the GA parameters of the proposed algorithm.
