Hierarchical Architectures of Fuzzy Models: From Type-1 fuzzy sets to Information Granules of Higher Type

Granular Data Aggregation: An Adaptive Principle of the Justifiable Granularity Approach

The design of information granules assumes a central position in the discipline of Granular Computing and its applications. The principle of justifiable granularity offers a conceptually and algorithmically attractive way of designing information granule completed on a basis of some experimental evidence (especially present in the form of numeric data). This paper builds upon the existing principle and presents its significant generalization, referred here as an adaptive principle of justifiable information granularity. The method supports a granular data aggregation producing an optimal information granule (with the optimality expressed in terms of the criteria of coverage and specificity commonly used when characterizing quality of information granules). The flexibility of the method stems from an introduction of the adaptive weighting scheme of the data leading to a vector of weights used in the construction of the optimal information granule. A detailed design procedure is provided along with the required optimization vehicle (realized with the aid of the population-based optimization techniques, such as particle swarm optimization and differential evolution). Two direct application areas in which the principle becomes of direct usage include prediction of time series and prediction of spatial data. In both cases, it is advocated that the results formed by the principle are reflective of the precision (quality) of the prediction process.