What are Angular Fuzzy Sets?

Angular Fuzzy Sets

Angular fuzzy sets differ from normal standard fuzzy sets only in the their coordinate description. Angular fuzzy sets are defined on a universe of angles, hence they are of repeating shapes for every 2π cycles. Angular fuzzy sets are used in the quantitative description of the linguistic variables, which are known as “truth values”.

For example, let’s consider that pH values of water samples are taken from a contaminated pond. We know that,

  • If pH=7, it is a neutral solution.
  • Levels of pH between 14 and 7 are labeled as absolute basic (AB), very basic (VB), basic, fairly basic (FB), neutral (N) drawn from θ=π/2 to θ=0
  • Levels of pH between 7 to 0 are called neutral, fairly acidic (FA), acidic (A), very acidic (VA), absolutely acidic (AA), are drawn from θ=0 to θ=(-π/2).

Linguistic values vary with θ and their membership values are given by the equation

Angular Membership Value Equation

here ‘t’ is the horizontal projection of the radial vector.

Angular Fuzzy Set Membership Values