Quantitative reachability analysis of generalized possibilistic decision processes

Abstract

The verification of reachability properties of fuzzy systems is usually based on the fuzzy Kripke structure or possibilistic Kripke structure. However, fuzzy Kripke structure or possibilistic Kripke structure is not enough to describe nondeterministic and concurrent fuzzy systems in real life. In this paper, firstly, we propose the generalized possibilistic decision process as the model of nondeterministic and concurrent fuzzy systems, and deduce the possibilities of sets of paths of the generalized possibilistic decision process relying on defining of schedulers. Then, we give fuzzy matrices calculation methods of the maximal possibilities and the minimal possibilities of eventual reachability, always reachability, constrained reachability, repeated reachability and persistent reachability. Finally, we propose a model checking approach to convert the verification of safety property into the analysis of reachabilities.