Fuzzy Logic in Stock Market Analysis
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Traditional sorts of mathematical analysis generally yield hard yes or no answers. A number is, say, greater than 7 or it is not. There is another type of commonly asked question, however, which cannot readily be answered in this way. Suppose, for example, we wish to ask whether a given number is "a lot" less than 7, or "a lot" more, or is "rather close" to 7? Such questions cannot be properly answered by a simple yes or no. Suppose that we say that 6 and 8 are close to 7. Does that mean, however, that 5.9 and 8.1 are no longer "close" to 7? Intuitively, we may sense that this is not what we intend, but the conventional mathematics of set theory, and computer programs applying such mathematics, compel us to set such artificial boundaries. Yet in a great many practical situations, however, we are not looking for yes or no answers, or seeking to define absolute boundaries, but are looking for characteristics that are less sharpely defined. Stock market analysis is one area in which we frequently encounter such situations. We can give an exact yes or no answer to some questions, such as whether a given stock is outperforming its industry group's average, or whether a given company's price/earnings ratio is above or below average for its group. But the stock analyst is seldom content with such a simple division of stocks into sheep or goats. He or she may want to ask questions with less distinct answers; is a stock "a lot" above or "a lot" below its group average?
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fference. If, for example, we choose to buy stocks with a membership value of greater than 0.75, this is merely making a yes-or-no decision to buy stocks in the upper quartile of those outperforming the average. But in practice, we do not want to use a single measure alone; we want to combine several measures in our analysis. Suppose that we wanted to measure both overall performance relative to the group and a stock's individual performance relative to its own thirty-day moving average?
If we simply rejected a stock from consideration because it was not in the upper quartile of above-market performers, we might miss a stock that is just below that upper quartile, but which has been breaking sharply above its own moving average. By applying fuzzy logic to both of our measures, we can avoid this sort of blanket rejection, and allow particularly good performance by one measure to counterbalance modest performance by the other.
In this simple example, the desired results might also be obtained by a simple weighted addition of measures. Fuzzy systems, however, can adapt themselves to more complex analyses involving consideration of multiple dimensions, and membership functions more subtle than the simple linear function used
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Approximate Word count = 1678
Approximate Pages = 7 (250 words per page)
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