Skip to main content
Fachgebiete
Automobil + Motoren Bauwesen + Immobilien Business IT + Informatik Elektrotechnik + Elektronik Energie + Nachhaltigkeit Finance + Banking Management + Führung Marketing + Vertrieb Maschinenbau + Werkstoffe Versicherung + Risiko
DE
EN
Bücher
Zeitschriften
Themenseiten
Organisationspsychologie Projektmanagement Marketing Smart Manufacturing
Weitere Formate
Podcasts Webinare Technik Webinare Wirtschaft Kongresse Veranstaltungskalender Awards
Jetzt Einzelzugang starten
Zugang für Unternehmen
Referenzkunden
SLX-Digitalkonferenz: Zukunftswerkstatt 2024

Mehr Umsatz mit Top-Kontakten

Am 7. Mai erfahren Sie, wie Vertriebsteams Leadgenerierung, Leadnurturing und Leadstrategien effizient steuern können.
Erweiterte Suche
Anmelden
nach oben
Soft Computing
Erschienen in: Soft Computing 11/2009

01.09.2009 | Original Paper

Inductive semimodules and the vector modules over them

verfasst von: Feng Feng, Young Bae Jun

Erschienen in: Soft Computing | Ausgabe 11/2009

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config
loading …

Abstract

The notion of an inductive semimodule over an ordered *-semiring is introduced and some related properties are investigated. Inductive semimodules are extensions of several important algebraic structures such as Kleene modules, Kleene algebras and inductive *-semirings. We prove that an inductive semimodule over an ordered *-semiring K is a Kleene module if and only if K is a Kleene algebra. Moreover, we establish that the vector module of an inductive semimodule over an ordered Conway semiring is again an inductive semimodule over the matrix semiring. Consequently, in an inductive semimodule over an ordered Conway semiring, least solutions to linear inequation systems can be denoted by linear expressions, avoiding the least fixed point operator. In addition, we also introduce a related notion called weak inductive semimodules, and propose several open problems on them.
Vorheriger Artikel Fuzzy boundary layer tuning for sliding mode systems as applied to the control of a direct drive robot

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Jetzt informieren
Fußnoten
1
Note that a more restrictive notion of *-semirings is discussed in Lehmann (1977) and is also known as Lehmann semirings (Golan 2003).
 
2
Note that a more restrictive notion of Kleene (left-) modules is given by Ehm et al. (2004).
 
Literatur
Aho AV, Hopcroft JE, Ullman JD (1975) The design and analysis of computer algorithms. Addison-Wesley, Reading
Akram M, Dudek WA (2008) Intuitionistic fuzzy left k-ideals of semirings. Soft Comput 12:881–890MATHCrossRef
Ahsan J, Saifullah K, Farid Khan M (1993) Fuzzy semirings. Fuzzy Sets Syst 60:309–320MATHCrossRef
Backhouse RC (1975) Closure algorithms and the star-height problem of regular languages. Ph.D. thesis, Imperial College, London
Bloom SL, Ésik Z (1993a) Iteration theories. Springer, BerlinMATH
Bloom SL, Ésik Z (1993b) Matrix and matrical iteration theories, part I. J Comput Syst Sci 46:381–408MATHCrossRef
Bloom SL, Ésik Z (1997) The equational logic of fixed points. Theor Comput Sci 179:1–60MATHCrossRef
Conway JH (1971) Regular algebra and finite machines. Chapman & Hall, LondonMATH
Dudek WA (2008) Special types of intuitionistic fuzzy left h-ideals of hemirings. Soft Comput 12:359–364MATHCrossRef
Dutta TK, Biswas BK (1994) Fuzzy prime ideals of a semiring. Bull Malays Math Soc 17:9–16MATH
Ehm T, Mö ller B, Struth G (2004) Kleene modules. In: Berghammer R et al (eds) Relational and Kleene-algebraic methods in computer science, Lecture notes in computer science, vol 3051. Springer, Berlin, pp 112–123
Eilenberg S (1974) Automata, languages, and machines, vol A. Academic Press, New YorkMATH
Glazek K (2002) A guide to the literature on semirings and their applications in mathematics and information sciences. Kluwer, DordrechtMATH
Golan JS (2003) Semirings and affine equations over them: theory and applications. Kluwer, DordrechtMATH
Jun YB, Öztürk MA, Song SZ (2004) On fuzzy h-ideals in hemirings. Inf Sci 162:211-226MATHCrossRef
Kim CB (2000) Isomorphism theorems and fuzzy k-ideals of k-semirings. Fuzzy Sets Syst 112:333–342MATHCrossRef
Kleene SC (1956) Representation of events in nerve nets and finite automata. In: Shannon CE, McCarthy J (eds) Automata studies. Princeton University Press, Princeton, pp 3–41
Kozen D (1981) On induction vs *-continuity. In: Kozen D (ed) Proceedings of the workshop on logics of programs. Lecture notes in computer science, vol 131. Springer, Berlin, pp 167–176
Kozen D (1990) On Kleene algebras and closed semirings. In: Rovan B (ed) In: Proceedings of MFCS’90. Lecture notes in computer science, vol 452. Springer, Berlin, pp 26–47
Kuich W (1987) The Kleene and Parikh theorem in complete semirings. In: Ottmann T (ed) Proceedings of the 14th colloquium automata, languages, and programming. Lecture notes in computer science, vol 267. Springer, Berlin, pp 212–225
Kuich W, Salomaa A (1986) Semirings, automata, and languages. Springer, Berlin
Leiß H (1991) Towards Kleene algebra with recursion. In: Bö rger E et al (eds) Computer science logic, 5th workshop, CSL’91. Lecture notes in computer science, vol 626. Springer, Berlin, pp 242–256
Ng KC (1984) Relation algebras with transitive closure. Ph.D. thesis, University of California, Berkeley
Pratt V (1988) Dynamic algebras as a well-behaved fragment of relation algebras. In: Pigozzi D (ed) Proceedings of the conference on algebra and computer science. Lecture notes in computer science, vol 425. Springer, Berlin, pp 77–110
Tarski A (1955) A lattice theoretical fixpoint theorem and its applications. Pacific J Math 5:285–309MATHMathSciNet
Metadaten
Titel
Inductive semimodules and the vector modules over them
verfasst von
Feng Feng
Young Bae Jun
Publikationsdatum
01.09.2009
Verlag
Springer-Verlag
Erschienen in
Soft Computing / Ausgabe 11/2009
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-008-0384-y

Weitere Artikel der Ausgabe 11/2009

Soft Computing 11/2009 Zur Ausgabe

Original Paper

Computational complexities of axiomatic extensions of monoidal t-norm based logic

Original Paper

Fuzzy boundary layer tuning for sliding mode systems as applied to the control of a direct drive robot

Original Paper

Self-spawning neuro-fuzzy system for rule extraction

Original Paper

Monte Carlo methods in fuzzy queuing theory

Original Paper

Design principles of adaptive cellular immunity for artificial immune systems

Original Paper

On very true operators on pocrims