The paper is devoted to a survey of work done in fuzzy clustering, mainly during the first decade of the 21st century, and that with emphasis on various approachesto the problem, as well as various formulations of the very problem. That is why not only the classical formulations are treated, but several other problems, related to (the use of) clustering, like feature selection, inference systems, three-way clustering, and, on the other hand, such formulations of clustering as the possibilistic one or the one involving intuitionistic fuzzy sets. These are treated as the background for presentation of some specific ideas of the main author, concerning definite heuristic algorithms for effective solving of some of these problems.
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