Classifying through a fuzzy algebraic structure

The properties of a fuzzy algebraic structure are investigated and the existence and uniqueness of the operators for the elements of the structure is formally proved. Afterwards the problem of generating appropriate classifications in a universe of discourse in which the characteristics of the elements are defined through attributes whose values are linguistic labels is analyzed and a method based on the fuzzy structure is introduced. A simple example is used to show how the new method works and results are compared to the ones given on the same data set by better-known clustering algorithm, in order to prove feasibility. Finally, an application of the fuzzy clustering in the context of a real medical diagnosis will be shown and main features of the method discussed.