An application of this concept to the formulation of a class of problems in pattern classification is described in RAND Memorandum RM-4307-PR, "Ab- straction and Pattern Classification," by R. Bellman, R. Kalaba and L. A. Zadeh, October, 1964.
More generally, the domain of definition of fA (x) may be restricted to a sub- set of X
In a more general setting, the range of the membership function can be taken to be a suitable partially ordered set P. For our purposes, it is convenient and sufficient to restrict the range of f to the unit interval. If the values of f~ (x) are interpreted as truth values, the latter case corresponds to a multivalued Logic with a continuum of
truth values in the interval [0, 1]