Design of Interval Type-2 Information Granules Based on the Principle of Justifiable Granularity

Information granules are concise abstract descriptors of data supported by experimental evidence. They summarize the data by forming a small collection of well justified information granule. Fuzzy sets of type-2 generalize type-1 fuzzy sets. In this article, we present an original design of interval type-2 information granules based on a collection of type-1 fuzzy sets by engaging the principle of justifiable granularity. This principle generates an information granule by maximizing a product of two generic characteristics of the granule, such as coverage and specificity. Given a collection of type-1 fuzzy sets, the result of the principle comes in a form of a single type-2 information granule. In general, we emphasize the effect of type elevation of information granules by stressing that a family of type-n information granules gives rise to a single type-(n+1) information granule. The overall optimization process is discussed along with a series of related optimization procedures. A series of experimental studies is included to illustrate the essence of the approach.