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.Comment: double columns 14 pages, 8 figure

Learning Hybrid Process Models From Events: Process Discovery Without Faking Confidence

Process discovery techniques return process models that are either formal (precisely describing the possible behaviors) or informal (merely a "picture" not allowing for any form of formal reasoning). Formal models are able to classify traces (i.e., sequences of events) as fitting or non-fitting. Most process mining approaches described in the literature produce such models. This is in stark contrast with the over 25 available commercial process mining tools that only discover informal process models that remain deliberately vague on the precise set of possible traces. There are two main reasons why vendors resort to such models: scalability and simplicity. In this paper, we propose to combine the best of both worlds: discovering hybrid process models that have formal and informal elements. As a proof of concept we present a discovery technique based on hybrid Petri nets. These models allow for formal reasoning, but also reveal information that cannot be captured in mainstream formal models. A novel discovery algorithm returning hybrid Petri nets has been implemented in ProM and has been applied to several real-life event logs. The results clearly demonstrate the advantages of remaining "vague" when there is not enough "evidence" in the data or standard modeling constructs do not "fit". Moreover, the approach is scalable enough to be incorporated in industrial-strength process mining tools.Comment: 25 pages, 12 figure

Variable grouping in multivariate time series via correlation

The decomposition of high-dimensional multivariate time series (MTS) into a number of low-dimensional MTS is a useful but challenging task because the number of possible dependencies between variables is likely to be huge. This paper is about a systematic study of the “variable groupings” problem in MTS. In particular, we investigate different methods of utilizing the information regarding correlations among MTS variables. This type of method does not appear to have been studied before. In all, 15 methods are suggested and applied to six datasets where there are identifiable mixed groupings of MTS variables. This paper describes the general methodology, reports extensive experimental results, and concludes with useful insights on the strength and weakness of this type of grouping metho

A Reliable Energy-Efficient Multi-Level Routing Algorithm for Wireless Sensor Networks Using Fuzzy Petri Nets

A reliable energy-efficient multi-level routing algorithm in wireless sensor networks is proposed. The proposed algorithm considers the residual energy, number of the neighbors and centrality of each node for cluster formation, which is critical for well-balanced energy dissipation of the network. In the algorithm, a knowledge-based inference approach using fuzzy Petri nets is employed to select cluster heads, and then the fuzzy reasoning mechanism is used to compute the degree of reliability in the route sprouting tree from cluster heads to the base station. Finally, the most reliable route among the cluster heads can be constructed. The algorithm not only balances the energy load of each node but also provides global reliability for the whole network. Simulation results demonstrate that the proposed algorithm effectively prolongs the network lifetime and reduces the energy consumption

Fuzzy-Petri-Net Reasoning Supervisory Controller and Estimating States of Markov Chain Models

Markov chain models are efficient tools for representing stochastic discrete event processes with wide applications in decision and control. A novel approach to fuzzy-Petri-net reasoning generated solution to initial or another state in Markov-chain models is proposed. Reasoning is performed by a fuzzy-Petri-net supervisory controller employing a fuzzy-rule production system design and a fuzzy-Petri-net reasoning algorithm, which has been developed and implemented in C++. The reasoning algorithm implements calculation of the degrees of fulfilment for all the rules and their appropriate assignment to places of Petri net representation structure. The reasoning process involves firing active transitions and calculating degrees of fulfilment for the output places, which represent propositions in the knowledge base, and determining of fuzzy-distributions for output variables as well as their defuzzified values. Finally, these values are transferred to assign the state of Markov-chain decision model in terms of transition probabilities