Information granularity uncertainty principle: contingency tables and Petri net representations

This paper introduces an information granularity reduction principle in connection with the analysis of the component of uncertainty associated with data. This overall study is illustrated utilizing simple numerical studies dealing with dynamical systems with first order dynamics. Classical and fuzzy Petri models are introduced in the analysis of dynamical systems. The overall study is illustrated utilizing simple numeric studies. The agenda involves a number of essential development issues: (i) providing a constructive way to build Petri nets out of numerical experimental data from dynamical systems, (ii) analyzing the component of uncertainty associated with data and elaborating on its minimization via an optimal quantization of the variables involved in the model of construction, (iii) considering the role of set-theoretic and fuzzy set frameworks in the transformation of numeric quantities into their qualitative (symbolic) counterparts, and (iv) identifying the role of Petri nets in the analysis of dynamical systems.