nach oben

Fuzzy Optimization and Decision Making

Erschienen in:

09.02.2016

Intuitionistic fuzzy linear programming and duality: a level sets approach

verfasst von: Jaroslav Ramík, Milan Vlach

Erschienen in: Fuzzy Optimization and Decision Making | Ausgabe 4/2016

Einloggen

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

search-config

KI-gestützte Suche

Aus

Abstract

The paper is concerned with linear programming problems whose input data may be intuitionistic fuzzy (IF) while the values of variables are always real numbers. We propose rather general approach to this type of problems based on level sets, and present recent results for problems in which the notions of feasibility and optimality are based on the IF relations. Special attention is devoted to the weak and strong duality.

Vorheriger Artikel Parametric computation of a fuzzy set solution to a class of fuzzy linear fractional optimization problems

Nächster Artikel Reliability analysis in uncertain random system

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

Atanassov, K. T. (1986). Intutionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87–96.MathSciNetCrossRef

Bector, C. R., & Chandra, C. (2002). On duality in linear programming under fuzzy environment. Fuzzy Sets and Systems, 125, 317–325.MathSciNetCrossRefMATH

Bellman, R. E., & Zadeh, L. E. (1970). Decision making in a fuzzy environment. Management Science, 17, B141–B164.MathSciNetCrossRefMATH

Dubois, D. (2011). The role of fuzzy sets in decision sciences: Old techniques and new directions. Fuzzy Sets and Systems, 184, 3–28.MathSciNetCrossRefMATH

Dubey, D., Chandra, S., & Mehra, A. (2012). Fuzzy linear programming under interval uncertainty based on IFS representation. Fuzzy Sets and Systems, 188(1), 68–87.MathSciNetCrossRefMATH

Dubois, D., & Prade, H. (1983). Ranking fuzzy numbers in the setting of possibility theory. Information Sciences, 30, 183–224.MathSciNetCrossRefMATH

Dubois, D. (1987). Linear programming with fuzzy data. In J. Bezdek (Ed.), Analysis of fuzzy information. USA: CRC Press—Technology and Engineering Taylor and Francis Group.

Dubois, D., Gottwald, S., Hajek, P., Kacprzyk, J., & Prade, H. (2005). Terminological difficulties in fuzzy set theory the case of intuitionistic fuzzy sets. Fuzzy Sets and Systems, 156(3), 485–491.MathSciNetCrossRefMATH

Gupta, S. K., & Dangar, D. (2014). Duality for a class of fuzzy nonlinear optimization problem under generalized convexity. Fuzzy Optimization and Decision Making, 13, 131–150.MathSciNetCrossRef

Hamacher, H., Lieberling, H., & Zimmermann, H.-J. (1978). Sensitivity analysis in fuzzy linear programming. Fuzzy Sets and Systems, 1, 269–281.MathSciNetCrossRefMATH

Inuiguchi, M. (2007). On possibilistic/fuzzy optimization: Foundations of fuzzy logic and soft computing. In P. Melin et al. (Eds.) Proceedings LNAI4529 12th International fuzzy systems association world congress IFSA (pp. 351–360). Mexico: Cancun.

Inuiguchi, M., Ichihashi, H., & Kume, Y. (1992). Some properties of extended fuzzy preference relations using modalities. Information Sciences, 61, 187–209.MathSciNetCrossRefMATH

Inuiguchi, M., Ichihashi, H., & Kume, Y. (1992). Relationships between modality constrained programming problems and various fuzzy mathematical programming problems. Fuzzy Sets and Systems, 49(3), 243–259.MathSciNetCrossRefMATH

Inuiguchi, M., Ramík, J., Tanino, T., & Vlach, M. (2003). Satisficing solutions and duality in interval and fuzzy linear programming. Fuzzy Sets and Systems, 135, 151–177.MathSciNetCrossRefMATH

Kuhn H. W. (1976). Nonlinear programming: A historical view. In Proceedings SIAM–AMS, vol. 9 (pp.1–26). Rhode Island: AMS Providence.

Mielcova, E. (2015). Ordering relations over intuitionistic fuzzy quantities: Lecture notes in computer science. In I. Rojas, G. Joya, A. Catala (Ed.), International Work—Conference on Artificial Neural Networks (advances in computational intelligence) IWANN.

Nachammai, A. L., & Thangaraj, P. (2012). Solving intuitionistic fuzzy linear programming problem by using similarity measures. European Journal of Scientific Research, 72(2), 204–210.MATH

Ralescu, D. A. (1992). A generalization of the representation theorem. Fuzzy Sets and Systems, 51, 309–311.MathSciNetCrossRefMATH

Ramík, J. (2005). Duality in fuzzy linear programming: Some new concepts and results. Fuzzy Optimization and Decision Making, 4, 25–39.MathSciNetCrossRefMATH

Ramík, J. (2006). Duality in fuzzy linear programming with possibility and necessity relations. Fuzzy Sets and Systems, 157, 1283–1302.MathSciNetCrossRefMATH

Ramík, J., & Vlach, M. (2001). Generalized concavity in optimization and decision making. Boston, Dordrecht: Kluwer.MATH

Ramík, J., & Vlach, M. (2004). A non-controversial definition of fuzzy sets. Transactions on rough sets II: Rough sets and fuzzy sets (pp. 201–207). Berlin, Heidelberg: Springer.

Rödder, W., & Zimmermann, H.-J. (1980). Extremal methods and system analysis: Duality in fuzzy linear programming (pp. 415–429). New York: Berlin.

Rommelfanger, H., Slowinski, R. (1998). Fuzzy linear programming with single or multiple objective functions: The handbooks of fuzzy sets series. Fuzzy sets in decision analysis, operations research, and statistics.179–213. Boston-Dordrecht-London: Kluwer.

Soyster, A. L. (1974). A duality theory for convex programming with set-inclusive constraints. Operations Research, 22, 892–898.MathSciNetCrossRefMATH

Stanciulescu, C., Fortemps, P., Install, M., & Wertz, V. (2003). Multiobjective fuzzy linear programming problems with fuzzy decision variables. European Journal of Operational Research, 149, 654675.MathSciNetCrossRef

Thuente, D. J. (1980). Duality theory for generalized linear programs with computational methods. Operations Research, 28, 1005–1011.MathSciNetCrossRefMATH

Verdegay, J. L. (1984). A dual approach to solve the fuzzy linear programming problem. Fuzzy Sets and Systems, 14, 131–141.MathSciNetCrossRefMATH

Wu, H.-C. (2003). Duality theory in fuzzy linear programming problems with fuzzy coefficients. Fuzzy Optimization and Decision Making, 2, 61–73.MathSciNetCrossRef

Yager, R. R. (2009). Some aspects of intuitionistic fuzzy sets. Fuzzy Optimization and Decision Making, 8, 67–90.MathSciNetCrossRefMATH

Zadeh, L. A. (1965). Fuzzy sets. Information and Control, 8, 338–353.MathSciNetCrossRefMATH

Zimmermann, H.-J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems, 1, 45–55.MathSciNetCrossRefMATH

Titel: Intuitionistic fuzzy linear programming and duality: a level sets approach
verfasst von: Jaroslav Ramík
Milan Vlach
Publikationsdatum: 09.02.2016
Verlag: Springer US
Erschienen in: Fuzzy Optimization and Decision Making / Ausgabe 4/2016
Print ISSN: 1568-4539
Elektronische ISSN: 1573-2908
DOI: https://doi.org/10.1007/s10700-016-9233-0

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

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

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Weitere Artikel der Ausgabe 4/2016

Parametric computation of a fuzzy set solution to a class of fuzzy linear fractional optimization problems

Blackwell type theorem for general T-related and identically distributed fuzzy variables

Reliability analysis in uncertain random system

Bilevel linear programming with ambiguous objective function of the follower

Fuzzy preorders: conditional extensions, extensions and their representations

Premium Partner