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

Decision Making in the Medical Domain: Comparing the Effectiveness of GP-Generated Fuzzy Intelligent Structures

ABSTRACT: In this work, we examine the effectiveness of two intelligent models in medical domains. Namely, we apply grammar-guided genetic programming to produce fuzzy intelligent structures, such as fuzzy rule-based systems and fuzzy Petri nets, in medical data mining tasks. First, we use two context-free grammars to describe fuzzy rule-based systems and fuzzy Petri nets with genetic programming. Then, we apply cellular encoding in order to express the fuzzy Petri nets with arbitrary size and topology. The models are examined thoroughly in four real-world medical data sets. Results are presented in detail and the competitive advantages and drawbacks of the selected methodologies are discussed, in respect to the nature of each application domain. Conclusions are drawn on the effectiveness and efficiency of the presented approach

A new approach to adaptive fuzzy control: the controller output error method

The controller output error method (COEM) is introduced and applied to the design of adaptive fuzzy control systems. The method employs a gradient descent algorithm to minimize a cost function which is based on the error at the controller output. This contrasts with more conventional methods which use the error at the plant output. The cost function is minimized by adapting some or all of the parameters of the fuzzy controller. The proposed adaptive fuzzy controller is applied to the adaptive control of a nonlinear plant and is shown to be capable of providing good overall system performance

Supervisory Control of Fuzzy Discrete Event Systems: A Formal Approach

Fuzzy {\it discrete event systems} (DESs) were proposed recently by Lin and Ying [19], which may better cope with the real-world problems with fuzziness, impreciseness, and subjectivity such as those in biomedicine. As a continuation of [19], in this paper we further develop fuzzy DESs by dealing with supervisory control of fuzzy DESs. More specifically, (i) we reformulate the parallel composition of crisp DESs, and then define the parallel composition of fuzzy DESs that is equivalent to that in [19]; {\it max-product} and {\it max-min} automata for modeling fuzzy DESs are considered; (ii) we deal with a number of fundamental problems regarding supervisory control of fuzzy DESs, particularly demonstrate controllability theorem and nonblocking controllability theorem of fuzzy DESs, and thus present the conditions for the existence of supervisors in fuzzy DESs; (iii) we analyze the complexity for presenting a uniform criterion to test the fuzzy controllability condition of fuzzy DESs modeled by max-product automata; in particular, we present in detail a general computing method for checking whether or not the fuzzy controllability condition holds, if max-min automata are used to model fuzzy DESs, and by means of this method we can search for all possible fuzzy states reachable from initial fuzzy state in max-min automata; also, we introduce the fuzzy $n$-controllability condition for some practical problems; (iv) a number of examples serving to illustrate the applications of the derived results and methods are described; some basic properties related to supervisory control of fuzzy DESs are investigated. To conclude, some related issues are raised for further consideration

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 review of applications of fuzzy sets to safety and reliability engineering

Safety and reliability are rigorously assessed during the design of dependable systems. Probabilistic risk assessment (PRA) processes are comprehensive, structured and logical methods widely used for this purpose. PRA approaches include, but not limited to Fault Tree Analysis (FTA), Failure Mode and Effects Analysis (FMEA), and Event Tree Analysis (ETA). In conventional PRA, failure data about components is required for the purposes of quantitative analysis. In practice, it is not always possible to fully obtain this data due to unavailability of primary observations and consequent scarcity of statistical data about the failure of components. To handle such situations, fuzzy set theory has been successfully used in novel PRA approaches for safety and reliability evaluation under conditions of uncertainty. This paper presents a review of fuzzy set theory based methodologies applied to safety and reliability engineering, which include fuzzy FTA, fuzzy FMEA, fuzzy ETA, fuzzy Bayesian networks, fuzzy Markov chains, and fuzzy Petri nets. Firstly, we describe relevant fundamentals of fuzzy set theory and then we review applications of fuzzy set theory to system safety and reliability analysis. The review shows the context in which each technique may be more appropriate and highlights the overall potential usefulness of fuzzy set theory in addressing uncertainty in safety and reliability engineering