A Fuzzy Petri Nets Model for Computing With Words

Motivated by Zadeh’s paradigm of computing with words rather than numbers, several formal models of computing with words have recently been proposed. These models are based on automata and thus are not well-suited for concurrent computing. In this paper, we incorporate the well-known model of concurrent computing, Petri nets, together with fuzzy set theory and thereby establish a concurrency model of computing with words–fuzzy Petri nets for computing with words (FPNCWs). The new feature of such fuzzy Petri nets is that the labels of transitions are some special words modeled by fuzzy sets. By employing the methodology of fuzzy reasoning, we give a faithful extension of an FPNCW which makes it possible for computing with more words. The language expressiveness of the two formal models of computing with words, fuzzy automata for computing with words and FPNCWs, is compared as well. A few small examples are provided to illustrate the theoretical development.

💡 Research Summary

The paper addresses a notable gap in the field of Computing with Words (CWW). While earlier CWW models have been built on automata, those formalisms are inherently sequential and therefore ill‑suited for representing concurrent processes, resource sharing, or the interleaving of events that are common in real‑world systems. To overcome this limitation, the authors propose a new formalism called Fuzzy Petri Nets for Computing with Words (FPNCW), which integrates the well‑established concurrency framework of Petri nets with fuzzy set theory.

An FPNCW is defined as a tuple (P, T, I, O, μ, λ) where P denotes places, T denotes transitions, I and O are the input and output arcs, μ assigns to each place a fuzzy marking in the interval