Division Charts as Granules and Their Merging Algorithm for Rule Generation in Nondeterministic Data

We have been proposing a framework rough Nondeterministic information analysis, which considers granular computing concepts in tables with incomplete and nondeterministic information, as well as rule generation. We have recently defined an expression named division chart with respect to an implication and a subset of objects. Each division chart takes the role of the minimum granule for rule generation, and it takes the role of contingency table in statistics. In this paper, we at first define a division chart in deterministic information systems (DISs) and clarify the relation between a division chart and a corresponding implication. We also consider a merging algorithm for two division charts and extend the relation in DISs to nondeterministic information systems. The relation gives us the foundations of rule generation in tables with nondeterministic information

2012 IEEE International Conference on Granular Computing Uncertainty and Knowledge Theories New Era in Granular Computing

Abstract-LNS is a generalization of topological neighborhood system(TNS) by simply dropping all axioms of topology but the superset axiom. The goal of this paper is to show that LNS is the "correct " granule for granular computing (GrC) and Granular Mathematics (GrM). Here are some high lights 1) Zadeh(1996)suggested that if classical mathematics is viewed as Math(point), GrM is Math(granule). The axiomatization of LNS in GrC2011 shows that GrM = Math(granule), point free. 2) Crisp LNS = Fuzzy LNS (when in terms of alpha-cuts). item TNS, a special LNS, models the uncertainty of "nearness" 3) Infinitesimals can be defined by TNS in hyperreals. 4) LNS includes all generalized rough sets and fuzzy sets (when rough degree/fuzzy are ignored.) 5) GrC/GrM provide the infrastructure for probability, possibility and belief measures. Index Terms-largest neighborhood system, granular computing, uncertainty, central knowledg