# Fuzzy Set Operations

Posted By on May 16, 2016

## Definitions.

Universe of DiscourseThe Universe of Discourse is the range of all possible values for an input to a fuzzy system. Fuzzy SetA Fuzzy Set is any set that allows its members to have different grades of membership (membership function) in the interval [0,1]. SupportThe Support of a fuzzy set F is the crisp set of all points in the Universe of Discourse U such that the membership function of F is non-zero. Crossover pointThe Crossover point of a fuzzy set is the element in U at which its membership function is 0.5. Fuzzy SingletonA Fuzzy singleton is a fuzzy set whose support is a single point in U with a membership function of one.

## Fuzzy Set Operations.

### Union

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
The Union operation in Fuzzy set theory is the equivalent of the OR operation in Boolean algebra.

### Complement

The membership function of the Complement of a Fuzzy set A with membership function is defined as

The following rules which are common in classical set theory also apply to Fuzzy set theory.

,

### Distributivity

#### Posted by Akash Kurup

Founder and C.E.O, World4Engineers Educationist and Entrepreneur by passion. Orator and blogger by hobby

Website: http://world4engineers.com