Hi Reza,

It's good to see your question, thank you for asking it! Your question requires a few different responses:

Firstly, you have to work out whether your crisp number is in a discrete universe (such as integers) or in a continuous universe (such as infinitesimally defined real numbers). From my experience it is usual to have a continuous universe of numbers for the definition of fuzzy numbers, even if you're dealing with integers. However, I add it here in order for you to contemplate on it.

Secondly, a crisp number can't really be fuzzified as it is defined in a binary fashion, that is to say that the membership of the crisp number is only 1 when the value is equal to your crisp number, and 0 at all other times. In other words:

if number == X then

    mu(X) = 1

else

    mu(X) = 0

Third, if you're going to fuzzify it to be a triangular or trapezoidal membership function, then you need to relate it to its particular domain. For example “About 50” might be defined differently within the domain of “Human Age”, than say, “About 50” in the domain of “Vehicle Speed”. What I mean by this is that the support (that is the width of the function at the base) and the core (that is the width of the function at the top) will vary based on the domain.

Forth, fuzzy numbers which have been defined from crisp numbers, such as “about 50” are usually (although not always) defined as triangular membership functions.

Finally, if you're looking for an automatic method, then it really depends on what systems or programming languages you're using. There are a variety of libraries for different programming languages (including my “X-mu library” for Python: https://github.com/danieljohnlewis/xmu-python ), and different fuzzy control systems. It's also quite simple to build you're own fuzzy handlers in whichever programming language you choose.

I hope that answers your question, and please do let me know how you get on. Feel free to ask for any clarifications, I'll do my best to help.

Daniel Lewis

Hi Reza,

It's good to see your question, thank you for asking it! Your question requires a few different responses:

Firstly, you have to work out whether your crisp number is in a discrete universe (such as integers) or in a continuous universe (such as infinitesimally defined real numbers). From my experience it is usual to have a continuous universe of numbers for the definition of fuzzy numbers, even if you're dealing with integers. However, I add it here in order for you to contemplate on it.

Secondly, a crisp number can't really be fuzzified as it is defined in a binary fashion, that is to say that the membership of the crisp number is only 1 when the value is equal to your crisp number, and 0 at all other times. In other words:

if number == X then

    mu(X) = 1

else

    mu(X) = 0

Third, if you're going to fuzzify it to be a triangular or trapezoidal membership function, then you need to relate it to its particular domain. For example “About 50” might be defined differently within the domain of “Human Age”, than say, “About 50” in the domain of “Vehicle Speed”. What I mean by this is that the support (that is the width of the function at the base) and the core (that is the width of the function at the top) will vary based on the domain.

Forth, fuzzy numbers which have been defined from crisp numbers, such as “about 50” are usually (although not always) defined as triangular membership functions.

Finally, if you're looking for an automatic method, then it really depends on what systems or programming languages you're using. There are a variety of libraries for different programming languages (including my “X-mu library” for Python: https://github.com/danieljohnlewis/xmu-python ), and different fuzzy control systems. It's also quite simple to build you're own fuzzy handlers in whichever programming language you choose.

I hope that answers your question, and please do let me know how you get on. Feel free to ask for any clarifications, I'll do my best to help.

Daniel Lewis

Dubois & Prade (1987), in order to converting crisp numbers to trapezoidal fuzzy numbers suggested the mean value method.