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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]


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

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