Fifty years have gone by since the publication of the first paper on clustering based on fuzzy sets theory. In 1965, L.A. Zadeh had published âFuzzy Setsâ [335]. After only one year, the first effects of this seminal paper began to emerge, with the pioneering paper on clustering by Bellman, Kalaba, Zadeh [33], in which they proposed a prototypal of clustering algorithm based on the fuzzy sets theory. Starting from this paper, several uncertain clustering methods based on different theoretical approaches for modeling the uncertainty have been proposed. The present paper presents a systematic literature review of these clustering approaches. In particular, with respect to the Statistical Reasoning System, we first illustrate the connection between Information and Uncertainty from the perspective of the so-called Informational Paradigm, according to which Information is constituted by âInformational ingredientsâ, specifically the âEmpirical Information,â represented by statistical data, and âTheoretical informationâ consisting of background knowledge and basic modeling assumptions. We then describe different kinds of uncertainty affecting the Information. Focusing on the uncertainty associated with a particular statistical methodology, i.e. Cluster Analysis, and adopting as theoretical platform the Informational Paradigm, we present a systematic literature review of different uncertainty-based clustering approaches -i.e. Fuzzy clustering, Possibilistic clustering, Shadowed clustering, Rough sets-based clustering, Intuitionistic fuzzy clustering, Evidential clustering, Credibilistic clustering, Type-2 fuzzy clustering, Neutrosophic clustering, Hesitant fuzzy clustering, Interval-based fuzzy clustering, and Picture fuzzy clustering. We thus show how all these clustering approaches are able of managing in different ways the uncertainty associated with the two components of the Informational Paradigm, i.e. the Empirical and Theoretical Information.
