We provide two methodologies in the area of computation theory to solve optimal strategies for games such as Watermelon chess and Go. From experimental results, we find relevance to graph theory, group representation, and mathematical consciousness. We prove that the decision strategy of movement for Watermelon chess and Chinese checker games belongs to a matrix that is a noncommutative ring or an abelian group over set Y={-1,0,1}. Additionally, the movement for any chess game with two players belongs to a noncommutative ring or an abelian group from Occam’s razor principle. We derive the closed form of the transition matrix for any chess game with two players and discover that the element of the transition matrix belongs to a rational number. We propose a different methodology based on abstract algebra to analyze the complexity of chess games in their entirety, instead of being limited solely to endgame results. It is probable that similar decision processes of people may also belong to a noncommutative ring or an abelian group.

We present a Boolean algebra based algorithm to extract if-then classification rules from supervised learning feedforward neural networks to solve the black-box problem of the decision process of the neural networks. This algorithm is called the BAB-G rule extraction algorithm, which stands for Boolean Algebra Based for General inputs. According to the concept of discretizing continuous hidden neuron activation values, we present the BAB-G rule extraction algorithm, which can be applied to three-layer feedforward neural networks with discrete, continuous, or mixed inputs. The antecedent parts of the if-then rules obtained from this algorithm are slanting hyperplanes. During the rule extraction procedure, redundant hidden neurons can be removed without affecting the functionality of the neural networks. Some empirical results on the data sets from the UCI repository of machine learning database are given for comparing our rule extraction algorithm and C5.0 decision tree algorithm. For these datasets, statistical hypothesis tests show that the rules obtained from our algorithm achieve the same classification accuracy as the neural networks. Moreover, our rules are better than the C5.0 decision tree both on comprehensibility and on accuracy for these datasets.

For classification problems, neural networks are well known for high accuracy in comparison to traditional statistical methods such as logistic regression and discriminant analysis. It is even better than other algorithms such as decision trees and Bayesian networks. However, the knowledge learned by the neural networks is stored in the hierarchical functional mapping of the structures of neural networks and the weight and bias parameters. It is not easy for people to understand its black-box decision process. In this research, we extract probabilistic Boolean classification rules from neural networks. The ruleset model can be tuned to a specified sensitivity according to different thresholds. In addition, we can compute a weighted important factor for each attribute that composes the Boolean rules. The weighted important factor is a numeric number between 0 and 1. If the weighted important factor is 0, it means the corresponding attribute is a noise signal. Hence, the weighted important features can be filtered out with a given threshold. From the linearly and nonlinearly separable simulation datasets, we find that the accuracy of PBCR1 and PBCR2 are better than neural networks even with a 1/10 training ratio. From UCI machine learning datasets, we find that the AUC of PBCR1 and PBCR2 will be a little lower than the AUC of neural networks. However, on the accuracy metric, from red wine and white wine datasets, PBCR1 and PBCR2 are almost the same with neural networks. The accuracies of PBCR1 and PBCR2 are superior to DT by a statistically significant margin. For the F1 score, PBCR1 and PBCR2 are statistically significantly better than DT on red wine, white wine, and PID datasets.

This research discusses the kamma, the eighth consciousness, ¯alaya-vijñ¯ana, and the relationship to quantum consciousness proposed by Penrose and Hameroff. We name it the quantum kamma hypothesis, which is the extension of quantum consciousness and the basis of engergy medical science.