Shulou(Shulou.com)06/03 Report--

I. exact mathematics and fuzzy mathematics

In the current industrial production and the realization of science and technology, most of them use accurate mathematics, whether it is Newton's laws of physics or mathematical equations, calculus. Our existing production technology is basically based on accurate mathematics. This is a good way to solve the problem that is not sensitive to the change of initial and intermediate conditions. It is precisely because these problems are not sensitive to the changes of initial and intermediate conditions, people can carry out accurate measurement and operation, through a logical model to find the corresponding solution to the problem.

With the development of the times, when the problems we know and do have been solved in a variety of instrumental and quantitative ways, those problems that are sensitive to the changes of initial and intermediate conditions (also known as fuzzy problems) have become the focus of attention in people's field of vision, which is why statistical prediction, data analysis and other industries begin to burst into vitality.

So does our current technology support the solution of these fuzzy problems? I think this should be divided into two aspects, one is theory, the other is engineering technology.

First of all, in terms of theory, the study of fuzzy problems has begun since 1965, but fuzzy problems do not pop up all of a sudden, just like the graph model studied by Ni Gong, which is a modeling product of graph theory. and graph theory is only a part of combinatorial mathematics. When human beings study this problem based on stereo and multilateral mapping, we will find a lot of uncertain situations. For example, a graph can be divided into complete and incomplete graphs, and the factors of direction and weight should be added. This is already quite complicated. The key point is that there is no unified theory to regulate this phenomenon in different situations. On the one hand, there is no unified theory for this phenomenon. When studying these problems, mathematicians will give a lot of restrictions, do not consider the influence of external factors, and so on, so most of the mathematical theories we see are based on hypotheses, and the reality is that there are a lot of fuzzy problems running through them, affecting the direction of the results. In fact, in terms of engineering technology, how to transform theory into engineering language (way) to solve production problems, such as the proposal of various algorithms.

In this context, people began to choose to study this fuzzy problem, we know that discrete mathematics and engineering problems are a perfect match, it objectively reflects the nature of things, after all, the composition of matter is also particle. From the perspective of discrete mathematics, the first thing we need to transform is the extension of set theory, so fuzzy sets are proposed, just like Hadoop distributed nodes. In order to explore the law of interaction between these nodes, we have the concept of fuzzy logic. Fuzzy mathematics based on fuzzy set and fuzzy logic has been developed.

At present, fuzzy mathematics has made great progress in some applications. Because the concept of fuzziness has found the description of fuzzy set, the process of judgment, evaluation, reasoning, decision-making and control can also be described by the method of fuzzy mathematics. For example: fuzzy clustering analysis, fuzzy pattern recognition, fuzzy comprehensive evaluation, fuzzy decision and fuzzy prediction, fuzzy control, fuzzy information processing and so on.

Second, what is the fuzzy problem? How to solve the fuzzy problem?

To take a simple example, 30-year-old is young or middle-aged, usually the computer will judge according to the boundary between young and middle-aged, for example, 40-year-old is the boundary, then the computer will think that 39-year-old people are young, 40-year-old is middle-aged. In real life, whether we rely on our own feelings or mainstream cognition, we do not have a very clear distinction between youth and middle age. we judge on the basis of many aspects, such as mentality, appearance, physical condition, and so on.

So what do we do when we look at it in the way of fuzzy mathematics? First of all, we may need to know several indicators that need to be considered to determine which age a person belongs to, and give weights to the corresponding indicators (of course, this weight will also be affected by other factors), and then determine its age stage. Here is an example that is not very appropriate, but easy to understand.

3. Big data

I really have no say in big data. It may be helpful to briefly talk about my understanding here.

First of all, I think big data is still in a big stage, the data is big, just like the mine, the mineral content in the large ore point must not be too small, but the mine is also divided into rich ore and poor ore. It is very important to use different algorithms (mining methods) for different types of big data. After reading the relevant books of Hadoop these days, I have learned a little bit about big data. In fact, no matter whether neural network, analytic hierarchy process or statistical probability are used in data processing, most of the ways to solve the fuzzy problem of big data are based on exact mathematics (of course, it is not absolute, the concept of precision and fuzziness is also a relative concept. If you stand from a different angle, your understanding will be different.

Foreman, I agree with you that there will be something new when people in psychology and biology discuss together, but if it is simple psychology and biology, it is not very useful. I feel that this social education binds people and majors too tightly, and when innovation is needed, it must be cross-disciplinary and cross-disciplinary.

At this point, I just want to talk about my understanding of "big data." maybe nowadays people will say that there is a lot of data, how many hard drives have been used, these data are treasures, yes, these data are treasures, but it is completely meaningless to keep these data. for example, a person has an Apple computer, but he can't program with iso, in fact, he has wasted a lot of resources.

If the control of "big data" is very critical, on the one hand, we should dig up knowledge and laws from the data, and on the other hand, we should summarize the core essence and truth of various related fields since human development. This is like two lines, one is to draw the development trend according to the current data, the other is to use the core essence and truth to predict the development trend, reconcile and choose the two lines, we can make a better prediction.

4. Algorithm

In the past two days, I took a closer look at the neural network at home. Yes, as you said, he can actually fall into the category of Analytic hierarchy process. Now the neural network has been very popular. At the same time, I have also checked. In fact, many large IT companies have set up combinatorial mathematics and other related research institutions. The theory of fuzzy mathematics is gradually improving, and the relevant algorithms have also been developed. I feel that If you want to do something different, on the one hand, you should have a deep understanding of the current mainstream, but also control the trend of future development.

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