A Fuzzy Petri Nets Model for Computing With Words

TL;DR

This paper introduces fuzzy Petri nets for computing with words, integrating concurrency and fuzzy logic to enhance the modeling and reasoning capabilities in computing with linguistic information.

Contribution

It proposes a novel fuzzy Petri nets model for computing with words, combining concurrency with fuzzy set theory, and compares its expressiveness with fuzzy automata.

Findings

Fuzzy Petri nets extend computing with words to concurrent systems.

The model supports reasoning with more words through fuzzy logic.

Comparison shows different expressiveness levels between models.

Abstract

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.