Deriving Relative Weights from Ratio Comparisons
As it was mentioned in Chapter 3, an important issue in MCDM methods is to be able to determine the relative weights of importance of a collection of entities (such as the alternatives to be studied in terms of a single decision criterion). This task is similar and closely related to the problem of determining the degree of membership of the elements of a fuzzy set. Usually, such values are between 0 and 1 and they add up to 1. Such weights of degrees of membership are supposed to be a good model of the way people perceive categories [Dubois and Prade, 1980]. Often, the most representative members in the set are assigned to the value of 1 and non-members to the value of 0. Then, the main problem is to determine the degree of membership (i.e., a number between 0 and 1) of the between members. Psychologists [Lakoff, 1973] have found that people can easily identify representative members in a fuzzy set, while they have difficulties in identifying the other members. The importance of evaluating the membership degrees in applications of fuzzy set theory in engineering and scientific fields is best illustrated in the more than 1,800 references given in [Gupta, et al., 1979] (see also Chapter 12 for discussions on some related problems).
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