Fuzzification is the process where we convert our input and output to linguistic variables using ranges and membership functions.In this example, we want to convert our input, project funding and staffing, and output risk into linguistic variables:

• Project funding: Inadequate, marginal and adequate. These are the three linguistic variables we have for project funding. We will use a fuzzy cone membership function.
• Project staffing: Small and large, a fuzzy cone membership function
• Risk:  low, normal and high.

We need some more defintions:

• Linguistic Variable: Variables whose values are words in a natural language. Let us take the example of Project Funding, the actual values of project funding in this example are percentages. So if we say the project funding is 50% then, 50% of the funding is still available. This 50% is now transalated to the linguistic variable, adequate, marginal or inadequate. The fuzzy system will use only these linguistc variables and not the original value.
• Crisp Values: The real values an input or output can take is a crisp value. For example, 50% is the crisp value Project funding can take.
• Membership Function: Its a function which defines how the crisp values are mapped to a membership value (degree of membership). These functions can be either linear or curved. For example,let us again take project funding,

Crisp input value for project funding is 60%

Membership function will translate this value into degree of membership for each of the linguistic variables. We will not show here the detail of how the membership function converts our crisp input values to linguistic variables, but will give a simple example to follow.

Let us say we are trying to evaluate the risk for the following crisp values,

Project funding = 35%

Project staffing = 60%

When we pass these values to the respective membership function we get the following results, Inadequate = 0.5, adequate = 0.0 and marginal = 0.2; similarly for project staffing we get small = 0.1 and large =0.7

The crisp input value for project funding 35%, cannot be represented by the linguistic variable adequate, hence membership value for adequate is 0.0. It does not belong completely to marginal linguistic variable, and hence we have 0.2 as the value.

Similarly 70% of project staffing has a high degree of membership with linguistic variable large, hence the value 0.7.

As you saw, fuzzification converts the crisp input values to fuzzy membership values to linguistic variables.