Representing non-fuzzy memberships

I'm trying to model an input for a FIS in Matlab, unlike other inputs this value is a boolean Yes / No

Do I use two membership functions that do not overlap but cover the entire domain e.g

NO (0 - 0.49) YES (0.50 - 1)

Or

Do I use a single membership function for YES which covers the entire domain and use the complement to represent NO

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1 Answer

A non-fuzzy input is generally modeled as a number with fuzzy membership function of 1 and support 0. By "support" I mean the extremum values of the graphical representation of the number.(3 numbers for a triangular fuzzy number and 4 for a trapezoidal one for instance). Let's take as example fuzzy triangular numbers: fuzzy numbers are defined by the 3 values [a,b,c]; to represent a crisp (non-fuzzy) value, a and c are set equal to b. Below is the representation of a triangular fuzzy number. This should make it clearer what a, b and c are.

http://stackoverflow.com/questions/14874444/extracting-vertices-of-a-triangle-which-is-in-y-coordinate-matrix-format

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