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# Membership Function in Fuzzy Logic | Artificial Intelligence

In this tutorial, we will learn about the membership function in fuzzy logic under artificial intelligence? By Monika Sharma Last updated : April 15, 2023

## Membership Function in Fuzzy Logic

The membership function is the backbone of the Inference Engine. It is a function which quantifies the data and represents a Fuzzy Set, which is defined over the range 0 to 1 (both inclusive). The input space that the Membership Function works in is known as the Universe of Discourse and the data that it takes as input are usually linguistic terms.

### Linguistic Terms

The Linguistic terms can be defined as the words which define the physical characteristics of a function. For example, if we are defining the temperature of a body, then we use the terms which define the characteristics of it, like high, low, very high, moderate, etc. These are the linguistic terms here.

## Membership Function Formula

The membership function for a fuzzy set P on the universe of discourse X is defined as: µP: X → [0, 1]

Where,

• 'µ' denotes the membership function,
• 'P' denoted the Fuzzy Set,
• and 'X' denotes the universe of discourse, i.e. input space.