Our purpose is to provide a set-theoretical frame to clustering fuzzy relational data basically based on the cardinality of the fuzzy subsets and their complementaries that represent the objects under study, without applying any crisp property when the various elements that compose the process are fuzzified.
　　From this perspective we define a family of fuzzy similarity indexes which includes a set of fuzzy indexes introduced by Tolias et al, and we analyze under which conditions a fuzzy proximity relation is defined. Following an original idea due to S. Miyamoto we evaluate the similarity between objects and between clusters by means the same mathematical procedure. Joining these concepts and methods we establish an algorithm to clustering fuzzy relational data. Finally, we present an example to make clear the whole process.