Granular reasoning proposed by Murai et al. is a mechanism for reasoning using granular computing, and the concept of “focus” has been proposed as a key concept of granular reasoning. On the other hand, the authors have proposed another concept of granularity, called “visibility”. In this paper, we try to capture the concepts of visibility and focus as modalities of modal logics by introducing ...

Granular computing is an emerging field of study that attempts to formalize and explore methods and heuristics of human problem solving with multiple levels of granularity and abstraction. A fundamental issue of granular computing is the representation and utilization of granular structures. The main objective of this article is to examine a logic approach to address this issue. Following the c...

Granular computing as a paradigm is an area frequently studied within the Approximate Reasoning paradigm. Proposed by L. A.Zadeh granular computing has been studied within fuzzy as well as rough set approaches to uncertainty. It is manifest that both theories are immanently related to granulation as fuzzy set theory begins with fuzzy membership functions whose inverse images are prototype granu...

Granular computing is an emerging field of study focusing on structured thinking, structured problem solving and structured information processing with multiple levels of granularity [1, 2, 7, 8, 13, 17, 19, 20, 21, 22, 24, 25, 29]. Many theories may be interpreted in terms of granular computing. The main objective of this chapter is to examine the granular structures and approximations used in...

Covering model provides a general framework for granular computing in that overlapping among granules are almost indispensable. For any given covering, both intersection and union of covering blocks containing an element are exploited as granules to form granular worlds at different abstraction levels, respectively, and transformations among these different granular worlds are also discussed. A...