Learning Opposites with Evolving Rules

The idea of opposition-based learning was introduced 10 years ago. Since then a noteworthy group of researchers has used some notions of oppositeness to improve existing optimization and learning algorithms. Among others, evolutionary algorithms, reinforcement agents, and neural networks have been reportedly extended into their opposition-based version to become faster and/or more accurate. However, most works still use a simple notion of opposites, namely linear (or type- I) opposition, that for each $x\in[a,b]$ assigns its opposite as $\breve{x}_I=a+b-x$. This, of course, is a very naive estimate of the actual or true (non-linear) opposite $\breve{x}_{II}$, which has been called type-II opposite in literature. In absence of any knowledge about a function $y=f(\mathbf{x})$ that we need to approximate, there seems to be no alternative to the naivety of type-I opposition if one intents to utilize oppositional concepts. But the question is if we can receive some level of accuracy increase and time savings by using the naive opposite estimate $\breve{x}_I$ according to all reports in literature, what would we be able to gain, in terms of even higher accuracies and more reduction in computational complexity, if we would generate and employ true opposites? This work introduces an approach to approximate type-II opposites using evolving fuzzy rules when we first perform opposition mining. We show with multiple examples that learning true opposites is possible when we mine the opposites from the training data to subsequently approximate $\breve{x}_{II}=f(\mathbf{x},y)$.