ABSTRACT

The membership function (MF) is a curve that defines how each point in the input space maps to a membership value (or a membership level) between 0 and 1. The input space is sometimes referred to as the world of discourse. The only condition that the membership function must actually meet is that it must vary between 0 and 1. By convention, all membership features have an mf character at the end of their name. The simplest membership feature is formed using straight lines. The simplest of these is the trigonometric membership function, and the function name is trimf. It is nothing more than a set of three points that form a triangle. The trapezoidal membership function trapmf has a flat top and is actually a truncated triangular curve. These linear membership functions have the advantage of simplicity. Fuzzy sets describe vague concepts. The fuzzy set acknowledges the possibility of being a partial member within it. The membership function associated with a given fuzzy set maps the input values to the appropriate membership values. The type 2 fuzzy set is reduced to the type 1 fuzzy set, which is similar to the probability of decreasing determinism when the unpredictability disappears. Type 2 fuzzy sets and systems generalize to standard type 1 purge sets and systems to handle more uncertainty. From the very beginning of the fuzzy set, there has been criticism for the fact that there is no associated uncertainty in the membership function of the type 1 fuzzy set. The use of the word “fuzzy” in one place seems to contradict its use in other place because it can have a lot of other meanings. The membership function of a generic type 2 fuzzy set is three-dimensional (3D). A cross section of one 3D piece is displayed. Cross sections and others are located in the Footprint of Uncertainty (FOU), assuming that the level of information is not adequate to accurately specify the member function. For example, we can only know the upper and lower limits of the membership level for each element of the universe for the fuzzy set. These fuzzy sets are described as interval value membership functions.