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
Fuzzy Optimization and Decision Making
Erschienen in: Fuzzy Optimization and Decision Making 3/2019

30.11.2018

Applying the concept of null set to solve the fuzzy optimization problems

verfasst von: Hsien-Chung Wu

Erschienen in: Fuzzy Optimization and Decision Making | Ausgabe 3/2019

Einloggen

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

search-config
loading …

Abstract

The concept of null set in the space of fuzzy numbers is introduced. Based on this concept, we can define two partial orderings according to the subtraction and Hukuhara difference between any two fuzzy numbers. These two partial orderings will be used to define the solution concepts of fuzzy optimization problems. On the other hand, we transform the fuzzy optimization problems into a conventional vector optimization problem. Under these settings, we can apply the technique of scalarization to solve this transformed vector optimization problem. Finally, we show that the optimal solution of the scalarized problem is also the optimal solution of the original fuzzy optimization problem.
Vorheriger Artikel Uncertain time series analysis with imprecise observations
Nächster Artikel Numerical solution of linear inhomogeneous fuzzy delay differential equations

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
Literatur
Bellmam, R. E., & Zadeh, L. A. (1970). Decision-making in a fuzzy environment. Management Sciences, 17, 141–164.MathSciNetCrossRef
Chalco-Cano, Y., Lodwick, W. A., Osuna-Gómez, R., & Rufian-Lizana, A. (2016). The Karush–Kuhn–Tucker optimality conditions for fuzzy optimization problems. Fuzzy Optimization and Decision Making, 15, 57–73.MathSciNetCrossRefMATH
Chalco-Cano, Y., Lodwick, W. A., & Rufian-Lizana, A. (2013). Optimality conditions of type KKT for optimization problem with interval-valued objective function via generalized derivative. Fuzzy Optimization and Decision Making, 12, 305–322.MathSciNetCrossRefMATH
Chalco-Cano, Y., Silva, G. N., & Rufian-Lizana, A. (2015). On the Newton method for solving fuzzy optimization problems. Fuzzy Sets and Systems, 272, 60–69.MathSciNetCrossRefMATH
Delgado, M., Kacprzyk, J., Verdegay, J.-L., & Vila, M. A. (Eds.). (1994). Fuzzy optimization: Recent advances. New York: Physica-Verlag.MATH
Diamond, P. (1991). Congruence classes of fuzzy sets form a banach space. Journal of Mathematical Analysis and Applications, 162, 144–151.MathSciNetCrossRefMATH
Herrera, F., Kovács, M., & Verdegay, J. L. (1993). Optimality for fuzzified mathematical programming problems: A parametric approach. Fuzzy Sets and Systems, 54(1993), 279–285.MathSciNetCrossRefMATH
Inuiguchi, M. (2007). Necessity measure optimization in linear programming problems with fuzzy polytopes. Fuzzy Sets and Systems, 158, 1882–1891.MathSciNetCrossRefMATH
Inuiguchi, M., & Ichihashi, H. (1990). Relative modalities and their use in possibilistic linear programming. Fuzzy Sets and Systems, 35, 303–323.MathSciNetCrossRefMATH
Inuiguchi, M., Ichihashi, H., & Kume, Y. (1993). Modality constrained programming problems: A unified approach to fuzzy mathematical programming problems in the setting of possibility theory. Information Sciences, 67, 93–126.MathSciNetCrossRefMATH
Inuiguchi, M., & Ramík, J. (2000). Possibilistic linear programming: A brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem. Fuzzy Sets and Systems, 111, 3–28.MathSciNetCrossRefMATH
Jamison, K. D. (2000). Possibilities as cumulative subjective probabilities and a norm on the space of congruence classes of fuzzy numbers motivated by an expected utility functional. Fuzzy Sets and Systems, 111, 331–339.MathSciNetCrossRefMATH
Jayswal, A., Stancu-Minasian, I., & Ahmad, I. (2011). On sufficiency and duality for a class of interval-valued programming problems. Applied Mathematics and Computation, 218, 4119–4127.MathSciNetCrossRefMATH
Lai, Y.-J., & Hwang, C.-L. (1992). Fuzzy mathematical programming: Methods and applications., Lecture notes in economics and mathematical systems New York: Springer.CrossRefMATH
Lai, Y.-J., & Hwang, C.-L. (1994). Fuzzy multiple objective decision making: Methods and applications., Lecture notes in economics and mathematical systems New York: Springer.CrossRefMATH
Li, L., Liu, S., & Zhang, J. (2015). On fuzzy generalized convex mappings and optimality conditions for fuzzy weakly univex mappings. Fuzzy Sets and Systems, 280, 107–132.MathSciNetCrossRefMATH
Lodwick, W. A., & Bachman, K. A. (2005). Solving large-scale fuzzy and possibilistic optimization problems. Fuzzy Optimization and Decision Making, 4, 257–278.MathSciNetCrossRefMATH
Lodwick, W. A., & Jamison, K. D. (2007). Theoretical and semantic distinctions of fuzzy, possibilistic, and mixed fuzzy/possibilistic optimization. Fuzzy Sets and Systems, 158, 1861–1872.MathSciNetCrossRefMATH
Lodwick, W. A., & Jenkins, O. A. (2013). Constrained intervals and interval spaces. Soft Computing, 17, 1393–1402.CrossRefMATH
Lodwick, W. A., & Kacprzyk, J. (Eds.). (2010). Fuzzy optimization: Recent advances and applications. Berlin: Springer.MATH
Luhandjula, M. K., Ichihashi, H., & Inuiguchi, M. (1992). Fuzzy and semi-infinite mathematical programming. Information Sciences, 61, 233–250.MathSciNetCrossRefMATH
Markov, S. (2004). On quasilinear spaces of convex bodies and intervals. Journal of Computational and Applied Mathematics, 162, 93–112.MathSciNetCrossRefMATH
Osuna-Gomez, R., Chalco-Cano, Y., Hernandez-Jimenez, B., & Ruiz-Garzon, G. (2015). Optimality conditions for generalized differentiable interval-valued functions. Information Sciences, 321, 136–146.MathSciNetCrossRefMATH
Pirzada, U. M., & Pathak, V. D. (2013). Newton method for solving the multi-variable fuzzy optimization problem. Journal of Optimization Theorey and Applications, 156, 867–881.MathSciNetCrossRefMATH
Słowiński, R. (Ed.). (1998). Fuzzy sets in decision analysis. Operations research and statistics. Boston: Kluwer Academic Publishers.MATH
Słowiński, R., & Teghem, J. (Eds.). (1990). Stochastic versus fuzzy approaches to multiobjective mathematical programming under uncertainty. Boston: Kluwer Academic Publishers.MATH
Verdegay, J. L. (1984). A dual approach to solve the fuzzy linear programming problems. Fuzzy Sets and Systems, 14, 131–141.MathSciNetCrossRefMATH
Wu, H.-C. (2007). Duality theorems and saddle point optimality conditions in fuzzy nonlinear programming problems based on different solution concepts. Fuzzy Sets and Systems, 158, 1588–1607.MathSciNetCrossRefMATH
Wu, H.-C. (2008). The optimality conditions for optimization problems with fuzzy-valued objective functions. Optimization, 57, 473–489.MathSciNetCrossRefMATH
Wu, H.-C. (2009). The Karush–Kuhn–Tucker optimality conditions for multi-objective programming problems with fuzzy-valued objective functions. Fuzzy Optimization and Decision Making, 8, 1–28.MathSciNetCrossRefMATH
Wu, H.-C. (2010). Duality theory for optimization problems with interval-valued objective functions. Journal of Optimization Theory and Applications, 144, 615–628.MathSciNetCrossRefMATH
Zimmermann, H.-J. (1976). Description and optimization of fuzzy systems. International Journal of General Systems, 2, 209–215.CrossRefMATH
Zimmermann, H.-J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems, 1, 45–55.MathSciNetCrossRefMATH
Metadaten
Titel
Applying the concept of null set to solve the fuzzy optimization problems
verfasst von
Hsien-Chung Wu
Publikationsdatum
30.11.2018
Verlag
Springer US
Erschienen in
Fuzzy Optimization and Decision Making / Ausgabe 3/2019
Print ISSN: 1568-4539
Elektronische ISSN: 1573-2908
DOI
https://doi.org/10.1007/s10700-018-9299-y

Weitere Artikel der Ausgabe 3/2019

Fuzzy Optimization and Decision Making 3/2019 Zur Ausgabe

OriginalPaper

A bibliometric analysis of Fuzzy Optimization and Decision Making (2002–2017)

OriginalPaper

Uncertain time series analysis with imprecise observations

OriginalPaper

Numerical solution of linear inhomogeneous fuzzy delay differential equations

OriginalPaper

Group decision making based on DEA cross-efficiency with intuitionistic fuzzy preference relations

OriginalPaper

On a class of fuzzy parametric variational inequality controlled differential equation problems in finite dimension spaces

Premium Partner

    Bildnachweise