9,637 research outputs found
Retraction and Generalized Extension of Computing with Words
Fuzzy automata, whose input alphabet is a set of numbers or symbols, are a
formal model of computing with values. Motivated by Zadeh's paradigm of
computing with words rather than numbers, Ying proposed a kind of fuzzy
automata, whose input alphabet consists of all fuzzy subsets of a set of
symbols, as a formal model of computing with all words. In this paper, we
introduce a somewhat general formal model of computing with (some special)
words. The new features of the model are that the input alphabet only comprises
some (not necessarily all) fuzzy subsets of a set of symbols and the fuzzy
transition function can be specified arbitrarily. By employing the methodology
of fuzzy control, we establish a retraction principle from computing with words
to computing with values for handling crisp inputs and a generalized extension
principle from computing with words to computing with all words for handling
fuzzy inputs. These principles show that computing with values and computing
with all words can be respectively implemented by computing with words. Some
algebraic properties of retractions and generalized extensions are addressed as
well.Comment: 13 double column pages; 3 figures; to be published in the IEEE
Transactions on Fuzzy System
Supervisory Control of Fuzzy Discrete Event Systems
In order to cope with situations in which a plant's dynamics are not
precisely known, we consider the problem of supervisory control for a class of
discrete event systems modelled by fuzzy automata. The behavior of such
discrete event systems is described by fuzzy languages; the supervisors are
event feedback and can disable only controllable events with any degree. The
concept of discrete event system controllability is thus extended by
incorporating fuzziness. In this new sense, we present a necessary and
sufficient condition for a fuzzy language to be controllable. We also study the
supremal controllable fuzzy sublanguage and the infimal controllable fuzzy
superlanguage when a given pre-specified desired fuzzy language is
uncontrollable. Our framework generalizes that of Ramadge-Wonham and reduces to
Ramadge-Wonham framework when membership grades in all fuzzy languages must be
either 0 or 1. The theoretical development is accompanied by illustrative
numerical examples.Comment: 12 pages, 2 figure
Fuzzy cellular model for on-line traffic simulation
This paper introduces a fuzzy cellular model of road traffic that was
intended for on-line applications in traffic control. The presented model uses
fuzzy sets theory to deal with uncertainty of both input data and simulation
results. Vehicles are modelled individually, thus various classes of them can
be taken into consideration. In the proposed approach, all parameters of
vehicles are described by means of fuzzy numbers. The model was implemented in
a simulation of vehicles queue discharge process. Changes of the queue length
were analysed in this experiment and compared to the results of NaSch cellular
automata model.Comment: The original publication is available at http://www.springerlink.co
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 -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
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
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