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In mathematics, fuzzy sets are sets whose elements have degrees of membership. 
In classical set theory, the membership of elements in a set is assessed in binary 
terms according to a bivalent condition — an element either belongs or does not 
belong to the set. By contrast, fuzzy set theory permits the gradual assessment of 
the membership of elements in a set; this is described with the aid of a 
membership function valued in the real unit interval [0, 1]. Fuzzy sets generalize 
classical sets.

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Decision-Making in a Fuzzy Environment 
R. E. Bellman, L. A. Zadeh
Permalink: http://dx.doi.org/10.1287/mnsc.17.4.B141
Published Online: December 1, 1970

Abstract
By decision-making in a fuzzy environment is meant a decision process in 
which the goals and/or the constraints, but not necessarily the system 
under control, are fuzzy in nature. This means that the goals and/or the 
constraints constitute classes of alternatives whose boundaries are not 
sharply defined.
Fuzzy goals and fuzzy constraints can be defined precisely as fuzzy sets in 
the space of alternatives. A fuzzy decision, then, may be viewed as an 
intersection of the given goals and constraints. A maximizing decision is 
defined as a point in the space of alternatives at which the membership 
function of a fuzzy decision attains its maximum value.
The use of these concepts is illustrated by examples involving multistage 
decision processes.

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