Uncertainty and knowledge theories new era in Granular Computing

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.