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Fuzzy Set Membership Approach

A fuzzy set membership approach recasts values into a statement of set membership (Eastman 1997). A fuzzy set is a set 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]. A fuzzy number is a fuzzy set defined on the domain of real numbers. The concept of a fuzzy number provides us with the basis for defining linguistic or fuzzy variables (Klir and Yuan 1995). Specifically, the fuzzy numbers are states of a linguistic variable. The states are represented by linguistic concepts such as "very steep," "steep," "moderate," "shallow." Given the fuzzy numbers, linguistic terms can be assigned to a spatial unit to represent the different degree of "slope steepness." A number of numerical approximation systems have been proposed to convert linguistic terms systematically to their correspondign fuzzy numbers (Bonissone 1982; Chen and Hwang 1992).

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