3,101 research outputs found
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
Algebraic Aspects of Families of Fuzzy Languages
We study operations on fuzzy languages such as union, concatenation, Kleene , intersection with regular fuzzy languages, and several kinds of (iterated) fuzzy substitution. Then we consider families of fuzzy languages, closed under a fixed collection of these operations, which results in the concept of full Abstract Family of Fuzzy Languages or full AFFL. This algebraic structure is the fuzzy counterpart of the notion of full Abstract Family of Languages that has been encountered frequently in investigating families of crisp (i.e., non-fuzzy) languages. Some simpler and more complicated algebraic structures (such as full substitution-closed AFFL, full super-AFFL, full hyper-AFFL) will be considered as well.\ud
In the second part of the paper we focus our attention to full AFFL's closed under iterated parallel fuzzy substitution, where the iterating process is prescribed by given crisp control languages. Proceeding inductively over the family of these control languages, yields an infinite sequence of full AFFL-structures with increasingly stronger closure properties
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
Introducing synchrony in fuzzy automata
This paper introduces a sort of automata and associated languages, often arising in modelling natural
phenomena, in which both vagueness and simultaneity are taken as first class citizens. This requires a fuzzy
semantics assigned to transitions and a precise notion of a synchronous product to enforce the simultaneous
occurrence of actions. The expected relationships between automata and languages are revisited in this
setting; in particular it is shown that any subset of a fuzzy synchronous language with the suitable signature
forms a synchronous Kleene algebra.NORTE-01-0145-FEDER-000037. POCI-01-0145-FEDER-030947. ERDF – European Regional Development Fund through the Operational Programme for Competitiveness and Internationalisation - COMPETE 2020 Programme and by National Funds through the Portuguese funding
agency, FCT - Funda¸c˜ao para a Ciˆencia e a Tecnologia, within projects POCI-01-0145-FEDER-030947 and UID/MAT/04106/2019.
The second author is supported in the scope of the framework contract foreseen in the numbers 4, 5 and 6 of the article
23, of the Decree-Law 57/2016, of August 29, changed by Portuguese Law 57/2017, of July 19. This paper is also a result
of the project SmartEGOV: Harnessing EGOV for Smart Governance (Foundations, Methods, Tools) NORTE-01-0145-
FEDER-000037, supported by Norte Portugal Regional Operational Programme (NORTE 2020), under the PORTUGAL
2020 Partnership Agreement, through the European Regional Development Fund (EFDR). It received further support from
the PT-FLAD Chair in Smart Cities & Smart Governanc
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
- …