Design of Interval Type-2 Information Granules Based on the Principle of Justifiable Granularity
Bowen Zhang, Witold Pedrycz, Xianmin Wang, Adam Gacek
Abstract
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- <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> information granules gives rise to a single type-( <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</i> +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.