An Optimization of Allocation of Information Granularity in the Interpretation of Data Structures: Toward Granular Fuzzy Clustering

Abstract

Clustering forms one of the most visible conceptual and algorithmic framework of developing information granules. In spite of the algorithm being used, the representation of information granules-clusters is predominantly numeric (coming in the form of prototypes, partition matrices, dendrograms, etc.). In this paper, we consider a concept of granular prototypes that generalizes the numeric representation of the clusters and, in this way, helps capture more details about the data structure. By invoking the granulation-degranulation scheme, we design granular prototypes being reflective of the structure of data to a higher extent than the representation that is provided by their numeric counterparts (prototypes). The design is formulated as an optimization problem, which is guided by the coverage criterion, meaning that we maximize the number of data for which their granular realization includes the original data. The granularity of the prototypes themselves is treated as an important design asset; hence, its allocation to the individual prototypes is optimized so that the coverage criterion becomes maximized. With this regard, several schemes of optimal allocation of information granularity are investigated, where interval-valued prototypes are formed around the already produced numeric representatives. Experimental studies are provided in which the design of granular prototypes of interval format is discussed and characterized.

DCC: a framework for dynamic granular clustering

“…Granular computing is motivated by human problem solving strategies which are often based on information granules rather than on precise data (Pedrycz 2013). If one takes the present state of evolution of mankind, such a strategy seems to be more successful than alternative strategies that are directly based on the underlying real data.…”

“…In each single step, representations of the data on higher levels of granulation are possible, e.g., a cluster can be considered as granular representation of its members (Pedrycz 2013).…”

Granular computing, computational intelligence, and the analysis of non-geometric input spaces

“…Here IGs find a one-to-one mapping with clusters, which are typically endowed with some mathematical construct in order to offer a synthetic description of the data together with its characteristic uncertainty. IG constructs (mostly fuzzy sets) have been used also in problems of optimization and decision-making (Liang and Liao 2007;Kahraman et al 2006;Pedrycz 2014;Wang et al 2014a, b;Pedrycz and Bargiela 2012). In fact, both problems are typically affected by uncertainty at different levels: in the problem definition (e.g., constraints) or by considering the output (e.g., decision variables).…”

Concepts and Design Aspects of Granular Models of Type-1 and Type-2

“…As a result, we can talk about interval-valued fuzzy sets, fuzzy fuzzy sets (or fuzzy 2 sets, for brief), probabilistic sets and alike. [12] in which fuzzy clusters of type-2 have been investigated [5] or they are used to better characterize a structure in the data and could be based upon the existing clusters [13].…”