25,213 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
Analysis, filtering, and control for Takagi-Sugeno fuzzy models in networked systems
Copyright © 2015 Sunjie Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.The fuzzy logic theory has been proven to be effective in dealing with various nonlinear systems and has a great success in industry applications. Among different kinds of models for fuzzy systems, the so-called Takagi-Sugeno (T-S) fuzzy model has been quite popular due to its convenient and simple dynamic structure as well as its capability of approximating any smooth nonlinear function to any specified accuracy within any compact set. In terms of such a model, the performance analysis and the design of controllers and filters play important roles in the research of fuzzy systems. In this paper, we aim to survey some recent advances on the T-S fuzzy control and filtering problems with various network-induced phenomena. The network-induced phenomena under consideration mainly include communication delays, packet dropouts, signal quantization, and randomly occurring uncertainties (ROUs). With such network-induced phenomena, the developments on T-S fuzzy control and filtering issues are reviewed in detail. In addition, some latest results on this topic are highlighted. In the end, conclusions are drawn and some possible future research directions are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grants 61134009, 61329301, 11301118 and 61174136, the Natural Science Foundation of Jiangsu Province of China under Grant BK20130017, the Fundamental Research Funds for the Central Universities of China under Grant CUSF-DH-D-2013061, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany
Diagnosability of Fuzzy Discrete Event Systems
In order to more effectively cope with the real-world problems of vagueness,
{\it fuzzy discrete event systems} (FDESs) were proposed recently, and the
supervisory control theory of FDESs was developed. In view of the importance of
failure diagnosis, in this paper, we present an approach of the failure
diagnosis in the framework of FDESs. More specifically: (1) We formalize the
definition of diagnosability for FDESs, in which the observable set and failure
set of events are {\it fuzzy}, that is, each event has certain degree to be
observable and unobservable, and, also, each event may possess different
possibility of failure occurring. (2) Through the construction of
observability-based diagnosers of FDESs, we investigate its some basic
properties. In particular, we present a necessary and sufficient condition for
diagnosability of FDESs. (3) Some examples serving to illuminate the
applications of the diagnosability of FDESs are described. To conclude, some
related issues are raised for further consideration.Comment: 14 pages; revisions have been mad
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
Unsharp Quantum Reality
The positive operator (valued) measures (POMs) allow one to generalize the notion of observable beyond the traditional one based on projection valued measures (PVMs). Here, we argue that this generalized conception of observable enables a consistent notion of unsharp reality and with it an adequate concept of joint properties. A sharp or unsharp property manifests itself as an element of sharp or unsharp reality by its tendency to become actual or to actualize a specific measurement outcome. This actualization tendency-or potentiality-of a property is quantified by the associated quantum probability. The resulting single-case interpretation of probability as a degree of reality will be explained in detail and its role in addressing the tensions between quantum and classical accounts of the physical world will be elucidated. It will be shown that potentiality can be viewed as a causal agency that evolves in a well-defined way
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