On algebraic foundations of information granulation
Technologies for constructing intelligent systems
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In his paper 驴Towards a theory of fuzzy information granulation and its centrality in human reasoning and fuzzy logic驴 L.A. ZADEH writes 驴There are three basic concepts that underline human cognition: granulation, organization and causation. Informally, granulation involves decomposition of whole into parts; organization involves integration of parts into whole; and causation involves association of causes with effects. Granulation of an object A leads to a collection of granules of A, with a granule being a clump of points (objects) drawn together by indistinguishability, similarity, proximity or functionality.驴 Furthermore, he writes: 驴Modes of information granulation (IG) in which the granules are crisp (c-granular) play important roles in a wide variety of methods, approaches and techniques. Crisp IG, however, does not reflect the fact that in almost all of human reasoning and concept formation the granules are fuzzy (f-granular)驴.Besides others, the paper presented is a further step to develop a systematic mathematical theory fitting ZADEH's approach. In particular, the paper deals with further conceptual considerations and mathematical investigations of the approach suggested by Y. HATA and M. MUKAIDONO for defining 驴some classes of fuzzy information granularity and their representations驴.