# Fuzzy sets as a basis for a theory of possibility

**Lotfi A. Zadeh**

CiteWeb id: 19990000018

CiteWeb score: 10207

DOI: 10.1016/S0165-0114(99)80004-9

The theory of possibility described in this paper is related to the theory of fuzzy sets by defining the concept of a possibility distribution as a fuzzy restriction which acts as an elastic constraint on the values that may be assigned to a variable. More specifically, if F is a fuzzy subset of a universe of discourse U = {u} which is characterized by its membership function/~r, then a proposition of the form "X is F," where X is a variable taking values in U, induces a possibility distribution Hx which equates the possibility of X taking the value u to/~r.(u)--the compatibility of u with F. In this way, X becomes a fuzzy variable which is associated with the possibility distribution Fix in much the same way as a random variable is associated with a probability distribution. In general, a variable may be associated both with a possibility distribution and a probability distribution, with the weak connection between the two expressed as the possibility/probability consistency principle. A thesis advanced in this paper is that the imprecision that is intrinsic in natural languages is, in the main, possibilistic rather than probabilistic in nature. Thus, by employing the concept of a possibility distribution, a proposition, p, in a natural language may be translated into a procedure which computes the probability distribution of a set of attributes which are implied by p. Several types of conditional translation rules are discussed and, in particular, a translation rule r,~r propositions of the form"X is F is ~-possible, "~ where ~ is a number in the interval [**0**, ! ], is formulate~ and illustrated by examples.

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- www.cs.berkeley.edu/~zadeh/papers/Fuzzy%20sets%20as%20a%20basis%20for%20a%20theory%20of%20possibility-1978.pdf
- www.eecs.berkeley.edu/~zadeh/papers/Fuzzy%20sets%20as%20a%20basis%20for%20a%20theory%20of%20possibility-1978.pdf
- www.sciencedirect.com/science/article/pii/S0165011499800049
- dl.acm.org/citation.cfm?id=310820
- connections-qj.org/article/fuzzy-sets-basis-theory-possibility
- en.journals.sid.ir/ViewPaper.aspx?ID=300903

Lotfi A. Zadeh,

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