2,553 research outputs found
A Bibliography on Fuzzy Automata, Grammars and Lanuages
This bibliography contains references to papers on fuzzy formal languages, the generation of fuzzy languages by means of fuzzy grammars, the recognition of fuzzy languages by fuzzy automata and machines, as well as some applications of fuzzy set theory to syntactic pattern recognition, linguistics and natural language processing
Fuzzy Automata: A Quantitative Review
Classical automata theory cannot deal with the system uncertainty. To deal with the system uncertainty the concept of fuzzy finite automata was proposed. Fuzzy automata can be used in diverse applications such as fault detection, pattern matching, measuring the fuzziness between strings, description of natural languages, neural network, lexical analysis, image processing, scheduling problem and many more. In this paper, a methodical literature review is carried out on various research works in the field of Fuzzy automata and explained the challenging issues in the field of fuzzy automata
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
Fuzzy graphs: Algebraic structure and syntactic recognition
© Springer Science+Business Media Dordrecht 2013. Directed fuzzy hypergraphs are introduced as a generalization of both crisp directed hypergraphs and directed fuzzy graphs. It is proved that the set of all directed fuzzy hypergraphs can be structured into a magmoid with operations graph composition and disjoint union. In this framework a notion of syntactic recognition inside magmoids is defined. The corresponding class is proved to be closed under boolean operations and inverse mor-phisms of magmoids. Moreover, the language of all strongly connected fuzzy graphs and the language that consists of all fuzzy graphs that have at least one directed path from the begin node to the end node through edges with membership grade 1 are recognizable. Additionally, a useful characterization of recognizability through left derivatives is also achieved
Observability and Decentralized Control of Fuzzy Discrete Event Systems
Fuzzy discrete event systems as a generalization of (crisp) discrete event
systems have been introduced in order that it is possible to effectively
represent uncertainty, imprecision, and vagueness arising from the dynamic of
systems. A fuzzy discrete event system has been modelled by a fuzzy automaton;
its behavior is described in terms of the fuzzy language generated by the
automaton. In this paper, we are concerned with the supervisory control problem
for fuzzy discrete event systems with partial observation. Observability,
normality, and co-observability of crisp languages are extended to fuzzy
languages. It is shown that the observability, together with controllability,
of the desired fuzzy language is a necessary and sufficient condition for the
existence of a partially observable fuzzy supervisor. When a decentralized
solution is desired, it is proved that there exist local fuzzy supervisors if
and only if the fuzzy language to be synthesized is controllable and
co-observable. Moreover, the infimal controllable and observable fuzzy
superlanguage, and the supremal controllable and normal fuzzy sublanguage are
also discussed. Simple examples are provided to illustrate the theoretical
development.Comment: 14 pages, 1 figure. to be published in the IEEE Transactions on Fuzzy
System
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