nach oben

Soft Computing

Erschienen in:

01.11.2012 | Original Paper

A comparison index for interval ordering based on generalized Hukuhara difference

verfasst von: Maria Letizia Guerra, Luciano Stefanini

Erschienen in: Soft Computing | Ausgabe 11/2012

Einloggen

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

search-config

KI-gestützte Suche

Aus

Abstract

Interval methods is one option for managing uncertainty in optimization problems and in decision management. The precise numerical estimation of coefficients may be meaningless in real-world applications, because data sources are often uncertain, vague and incomplete. In this paper we introduce a comparison index for interval ordering based on the generalized Hukuhara difference; we show that the new index includes the commonly used order relations proposed in literature. The definition of a risk measure guarantees the possibility to quantify a worst-case loss when solving maximization or minimization problems with intervals.

Vorheriger Artikel E-perfect effect algebras

Nächster Artikel Type-2 hierarchical fuzzy system for high-dimensional data-based modeling with uncertainties

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

Bellman RE, Zadeh LA (1970) Decision-making in a fuzzy environment. Manag Sci 17(4):141–164MathSciNetCrossRef

Chalco-Cano Y, Román-Flores H, Jiménez-Gamero MD (2011) Generalized derivative and π-derivative for set-valued functions. Inf Sci 181(11):2177–2188. doi:10.1016/j.ins.2011.01.023

Dantzig GB (1963) Linear programming and extensions. Princeton University Press, Princeton

Dubois D (2010) Representation, propagation, and decision issues in risk analysis under incomplete probabilistic information. Risk Anal 30(3):361–368CrossRef

Dubois D, Prade H (1980) Fuzzy sets and systems: theory and applications. Academic Press, New YorkMATH

Dubois, D, Prade, H (eds) (2000) Fundamentals of fuzzy sets. The handbooks of fuzzy sets series. Kluwer, Boston

Guerra ML, Stefanini L (2011) A comparison index for interval ordering. IEEE SSCI 2011, symposium series on computational intelligence (FOCI 2011), pp 53–58

Inuiguchi M, Ramik J (2000) Possibilistic linear programming: a brief review of fuzzy mathematical programming and a comparison with stochastic programming in portfolio selection problem. Fuzzy Sets Syst 111:3–28MathSciNetMATHCrossRef

Ishibuchi H, Tanaka H (1990) Multiobjective programming in optimization of the interval objective function. Eur J Oper Res 48:219–225MATHCrossRef

Jiang C, Han X, Liu GR, Liu GP (2008) A nonlinear interval number programming method for uncertain optimization problems. Eur J Oper Res 188:1–13MathSciNetMATHCrossRef

Kaburlasos VG (2006) Towards a unified modelling and knowledge-representation based on lattice theory. Springer, Berlin

Kehagias A (2011) Some remarks on the lattice of fuzzy intervals. Inf Sci 181(10):1863–1873MathSciNetMATHCrossRef

Markov S (1977) A non-standard subtraction of intervals. Serdica 3:359–370MathSciNetMATH

Markov S (1979) Calculus for interval functions of a real variable. Computing 22:325–337MathSciNetMATHCrossRef

Moore RE (1979) Methods and applications of interval analysis. Society for Industrial and Applied Mathematics, PhiladelphiaMATHCrossRef

Moore RE, Kearfott RB, Cloud MJ (2009) Introduction to interval analysis. Society for Industrial and Applied Mathematics, PhiladelphiaMATHCrossRef

Negoita CV, Ralescu D (1975) Applications of fuzzy sets to systems analysis. Birkhauser, BaselMATH

Oliveira C, Henggeler Antunes C (2007) Multiple objective linear programming models with interval coefficients—an illustrated overview. Eur J Oper Res 181:1434–1463MATHCrossRef

Papadakis SE, Kaburlasos VG (2010) Piecewise-linear approximation of nonlinear models based on probabilistically/possibilistically interpreted intervals’ Numbers (INs). Inf Sci 180(24):5060–5076MATHCrossRef

Plotnikova NV (2005) Systems of linear differential equations with p-derivative and linear differential inclusions. Sbornik: Math 196:1677–1691MathSciNetMATHCrossRef

Ramik J (2007) Optimal solutions in optimization problem with objective function depending on fuzzy parameters. Fuzzy Sets Syst 158(11):1873–1881MathSciNetMATHCrossRef

Sengupta A, Pal TK (2000) On comparing interval numbers. Eur J Oper Res 127:28–43MathSciNetMATHCrossRef

Sengupta A, Pal TK (2009) Fuzzy preference ordering of interval numbers in decision problems. Springer, BerlinMATHCrossRef

Stefanini L (2010) A generalization of Hukuhara difference and division for interval and fuzzy arithmetic. Fuzzy Sets Syst 161(11):1564–1584MathSciNetMATHCrossRef

Tanaka H, Okuda T, Asai K (1974) On fuzzy mathematical programming. J Cybern 3:37–46MathSciNet

Tong S (1994) Interval number and fuzzy number linear programming. Fuzzy Sets Syst 66:301–306CrossRef

Wang X, Kerre EE (2001a) Reasonable properties for the ordering of fuzzy quantities (I). Fuzzy Sets Syst 118:375–385MathSciNetMATHCrossRef

Wang X, Kerre EE (2001b) Reasonable properties for the ordering of fuzzy quantities (II). Fuzzy Sets Syst 118:387–405MathSciNetMATHCrossRef

Zadeh LA (1965) Fuzzy sets. Inf Control 8:338–353MathSciNetMATHCrossRef

Zimmermann HJ (1987) Fuzzy sets, decision making and expert systems. Kluwer, BostonCrossRef

Titel: A comparison index for interval ordering based on generalized Hukuhara difference
verfasst von: Maria Letizia Guerra
Luciano Stefanini
Publikationsdatum: 01.11.2012
Verlag: Springer-Verlag
Erschienen in: Soft Computing / Ausgabe 11/2012
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-012-0866-9

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 11/2012

An adaptive heuristic to the bounded-diameter minimum spanning tree problem

Extended-order algebras and fuzzy implicators

Geometrical aspects of possibility measures on finite domain MV-clans

Bipedal robot walking control on inclined planes by fuzzy reference trajectory modification

Vagueness: where degree-based approaches are useful, and where we can do without

Noetherian and Artinian BL-algebras