Petri net model with fuzzy timing and fuzzy-metric temporal logic

Abstract

This paper is concerned with a Petri net model having fuzzy timing and fuzzy real-time temporal logic. In an earlier paper, we introduced a Petri net model with four fuzzy set theoretic functions of time but no algorithms were given for computing the two important operators called, earliest and latest. In this paper, we first present algorithms for performing these two operations on fuzzy functions of time. Then we extend the existing concept of (real-time) metric temporal logic to fuzzy metric temporal logic by expressing the metrics for state and time constraints in terms of fuzzy possibility distributions. Finally we combine the two concepts of fuzzy-timing Petri net and fuzzy metric temporal logic to introduce a new Petri net model called the temporal-logic fuzzy-timing Petri net (TLFTN). The paper concludes with an algorithm and illustrative example for model checking using TLFTNs. © 1999 John Wiley & Sons, Inc.