Fuzzy Logic

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  • Topic: Fuzzy logic, Fuzzy set, Multi-valued logic
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  • Published : September 23, 2010
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Fuzzy Logic

Electrical and Electronics Department, Rajalakshmi Engineering College Thandalam, Chennai, India

Fuzzy logic was developed by Lotfi A. Zadeh in the 1960s in order to provide mathematical rules and functions which permitted natural language queries. Fuzzy logic provides a means of calculating intermediate values between absolute true and absolute false with resulting values ranging between 0.0 and 1.0. With fuzzy logic, it is possible to calculate the degree to which an item is a member. Fuzzy logic has rapidly become one of the most successful of today's technologies for developing sophisticated control systems. The reason for which is very simple. Fuzzy logic addresses such applications perfectly as it resembles human decision making with an ability to generate precise solutions from certain or approximate information. It fills an important gap in engineering design methods left vacant by purely mathematical approaches (e.g. linear control design), and purely logic-based approaches (e.g. expert systems) in system design. While other approaches require accurate equations to model real-world behaviours, fuzzy design can accommodate the ambiguities of real-world human language and logic. It provides both an intuitive method for describing systems in human terms and automates the conversion of those system specifications into effective models.

Fuzzy Logic requires some numerical parameters in order to operate such as what is considered significant error and significant rate-of-change-of-error, but exact values of these numbers are usually not critical unless very responsive performance is required in which case empirical tuning would determine them. For example, a simple temperature control system could use a single temperature feedback sensor whose data is subtracted from the command signal to compute "error" and then time-differentiated to yield the error slope or rate-of-change-of-error, hereafter called "error-dot". Error might have units of degs F and a small error considered to be 2F while a large error is 5F. The "error-dot" might then have units of degs/min with a small error-dot being 5F/min and a large one being 15F/min. These values don't have to be symmetrical and can be "tweaked" once the system is operating in order to optimize performance. Generally, FL is so forgiving that the system will probably work the first time without any tweaking. III.FUZZY SETS

A fuzzy set is a set whose elements have degrees of membership. That is, a member of a set can be full member (100% membership status) or a partial member (e.g. less than 100% membership and greater than 0% membership). •A fuzzy subset F of a set S can be defined as a set of ordered pairs. The first element of the ordered pair is from the set S, and the second element from the ordered pair is from the interval [0, 1]. •The value zero is used to represent non-membership; the value one is used to represent complete membership and the values in between are used to represent degrees of membership.

The membership function of the Union of two fuzzy sets A and B with membership functions and respectively is defined as the maximum of the two individual membership functions. This is called the maximum criterion.

The Union operation in Fuzzy set theory is the equivalent of the OR operation in Boolean algebra. Intersection
The membership function of the Intersection of two fuzzy sets A and B with membership functions and respectively is defined as the minimum of the two individual membership functions. This is called the minimum criterion.

The Intersection operation in Fuzzy set theory is the equivalent of the AND operation in Boolean algebra Complement
The membership function of the Complement of a Fuzzy set A with membership function is defined as the negation of the specified membership function....
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