We present an algebraic structure as a complete methodology of classification. Utilizing this structure, we apply an algebraic approximation to the problem of generating appropriate clusters of objects characterized by fuzzy attributes. More precisely, the values of the attributes are expressed in terms of linguistic labels, and thus are handled as fuzzy numbers. This opens new possibilities in all those fields for which the need to describe the population under analysis by means of more natural terms becomes crucial. In fact, in these cases, the application of resolution strategies based on the adoption of “standard” methods, such as a distance matrix, appears as a brutal effort to adapt quantitative methods to qualitative problems

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