## Fuzzy System & Neural Networks Notes

**FUZZY LOGIC**

**Q: What is a fuzzy set?**

A fuzzy set is a set that is defined by a membership function. A membership function assigns to each element in the set under consideration (the universal space) a membership grade, which is a value in the interval [0, 1]. In classical sets, objects either belong to a set or do not belong to a set; there is no other choice. By defining a set using a membership function, it is possible for an element to belong partially to a set. For example, if a door is slightly open, one might say that the door is open, with a membership grade of 0.2 to indicate that the door is slightly open. We might also say that the door is closed, with a membership grade of 0.8. By using a fuzzy set, we are able to indicate that the door is partially open or partially closed. Using classical logic, we would not be able to do this; the door would be considered either open or closed with no in-between.

- Fuzzy logic is a concept of `certain degree’.
- Who is the founder of fuzzy logic?

Answer: D. Zadeh Lotfi. - The only ambiguity in founder of fuzzy logic that may occur is Buddha. because Fuzzy logic was inspired by Buddha but was only officially found in the 60s including the word `fuzzy` itself.
- The idea of fuzzy logic was first advanced by Dr. Lotfi Zadeh of the University of California at Berkeley in the 1960s. Dr. Zadeh was working on the problem of computer understanding of natural language. Natural language (like most other activities in life and indeed the universe) is not easily translated into the absolute terms of 0 and 1. (Whether everything is ultimately describable in binary terms is a philosophical question worth pursuing, but in practice much data we might want to feed a computer is in some state in between and so, frequently, are the results of computing.)
- FUZZY LOGIC SUGGESTS inaccuracy and imprecision. Webster’s dictionary defines the word fuzzy as “not clear, distinct, or precise; blurred.” In a broad sense, fuzzy logic refers to fuzzy sets, which are sets with blurred boundaries, and, in a narrow sense, fuzzy logic is a logical system that aims to formalize approximate reasoning.
- Fuzzy logic is an approach to computer science that mimics the way a human brain thinks and solves problems. The idea of fuzzy logic is to approximate human decision making using natural language terms instead of quantitative terms.
- It is formally defined as a form of knowledge representation suitable for notions that cannot be defined precisely, but which depend upon their contexts. It enables computerized devices to reason more like humans.
- The idea of fuzzy logic is to approximate human decision-making using natural-language terms instead of quantitative terms. Fuzzy logic is similar to neural networks, and one can create behavioral systems with both methodologies. A good example is the use of fuzzy logic for automatic control: a set of rules or a table is constructed that specifies how an effect is to be achieved, provided input and the current system state. Using fuzzy arithmetic, one uses a model and makes a subset of the system components fuzzy so that fuzzy arithmetic must be used when executing the model. In a broad sense, fuzzy logic refers to fuzzy sets, which are sets with blurred boundaries, and, in a narrow sense, fuzzy logic is a logical system that aims to formalize approximate reasoning.
- Fuzzy logic differs to Boolean logic in a sense that something can be true to a certain extent and does not have to be just true or false.
- Japan is currently the most active users of fuzzy logic. When it was founded in the 60s the Americans and the rest of the world totally ignored the idea. Instead, it was adopted by the Japanese followed by Korea and other parts of the East. Currently 70% of Japanese products use fuzzy logic.