nach oben

Soft Computing

Erschienen in:

01.08.2013 | Foundations

Symmetric fuzzy numbers and additive equivalence of fuzzy numbers

verfasst von: Dong Qiu, Weiquan Zhang

Erschienen in: Soft Computing | Ausgabe 8/2013

Einloggen

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

search-config

KI-gestützte Suche

Aus

Abstract

To obtain the group properties of fuzzy quantities, Mareš introduced an equivalence relation between fuzzy quantities. However, the Mareš’s method used to prove his main theorems demands to limit the investigation to fuzzy quantities with finite support. In this paper, we discuss the properties of symmetric fuzzy numbers, show an equivalent characterization of convex fuzzy sets, and present a way to construct a symmetric convex fuzzy set with a convex fuzzy set. Based on these results, we restrict ourselves to fuzzy numbers and prove Mareš’s results without the limitation to fuzzy numbers with finite support using the refined equivalence relation due to Hong and Do. Our results prove one of Mareš’s open questions in the literature.

Vorheriger Artikel A congruence modular variety that is neither congruence distributive nor 3-permutable

Nächster Artikel Fitness approximation for bot evolution in genetic programming

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

Anastassiou GA (2002) On H-fuzzy differentiation. Math Balkanica 16:155–193MathSciNet

Aytar S (2004) Statistical limit points of sequences of fuzzy numbers. Inf Sci 165:129–138MathSciNetMATHCrossRef

Báez-Sánchez AD, Moretti AC, Rojas-Medar MA (2012) On polygonal fuzzy sets and numbers. Fuzzy Sets Syst. doi:10.1016/j.fss.2012.04.003

Bede B, Gal SG (2005) Generalizations of the differentiability of fuzzy-number-valued functions with applications to fuzzy differential equations. Fuzzy Sets Syst 151:581–599MathSciNetMATHCrossRef

Bica AM (2007) Algebraic structures for fuzzy number from categorial point of view. Soft Comput 11:1099–1105MATHCrossRef

Diamond P, Kloeden P (1990) Metric spaces of fuzzy sets. Fuzzy Sets Syst 35:241–249MathSciNetMATHCrossRef

Diamond P, Kloeden P (1994) Metric spaces of fuzzy sets: theory and applications. World Scientific, Singapore

Dubois D, Prade H (1978) Operations on fuzzy numbers. Int J Syst Sci 9:613–626MathSciNetMATHCrossRef

Dubois D, Prade H (1980) Fuzzy sets and systems. Academic Press, New York

Dubois D, Prade H (1981) Additions of interactive fuzzy numbers. IEEE Trans Autom Control 26:926–936MathSciNetCrossRef

Dubois D, Prade H (1984) Fuzzy-set-theoretic differences and inclusions and their use in the analysis of fuzzy equations. Control Cybernet (Warsaw) 13:129–146MathSciNetMATH

Dubois D, Prade H (1987) Fuzzy numbers: an overview. In: Bezdek J (ed) Analysis of fuzzy information, vol f. CRS, Boca Raton, pp 3–39

Höhle U (1988) Quotients with respect to similarity relations. Fuzzy Sets Syst 27:31–44MATHCrossRef

Hong D, Do H (1996) Additive decomposition of fuzzy quantities. Inf Sci 88:201–207MathSciNetMATHCrossRef

Hong D (2003) An additive decomposition of fuzzy numbers. Kybernetika 39:289–294MathSciNetMATH

Hong D, Lee S (2002) Some algebraic properties and a distance measure for interval-valued fuzzy numbers. Inf Sci 148:1–10MathSciNetMATHCrossRef

Hukuhara M (1967) Integration des applications measurables dont la valeur est un compact convexe. Funkcialaj Ekvacioj 10:205–223MathSciNetMATH

Kaleva O (1987) Fuzzy differential equations. Fuzzy Sets Syst 24:301–317MathSciNetMATHCrossRef

Kovács M (1992) A stable embedding of ill-posed linear systems into fuzzy systems. Fuzzy Sets Syst 45:305–312MATHCrossRef

Makó Z (2012) Real vector space of LR-fuzzy intervals with respect to the shape-preserving t-norm-based addition. Fuzzy Sets Syst 200:136–149MATHCrossRef

Mareš M (1983) Fuzzy quantities in networks. Fuzzy Sets Syst 10:123–134MATHCrossRef

Mareš M (1988) How to satisfy fuzzy manager. Ekonomickomatematicky Obzor 24:396–404MATH

Mareš M (1989) Addition of fuzzy quantities: disjunction-conjunction approach. Kybernetika 25:104–116MathSciNetMATH

Mareš M (1992) Additive decomposition of fuzzy quantities. Fuzzy Sets Syst 47:341–346MATHCrossRef

Maturo A (2009) On some structures of fuzzy numbers. Iranian J Fuzzy Syst 6:49–59MathSciNetMATH

Mesiar R (1996) Anote to the T-sum of L-R fuzzy numbers. Fuzzy Sets Syst 79:259–261MathSciNetMATHCrossRef

Michta M (2011) On set-valued stochastic integrals and fuzzy stochastic equations. Fuzzy Sets Syst 177:1–19MathSciNetMATHCrossRef

Negoita CV, Ralescu D (1975) Representation theorems for fuzzy concepts. Kybernetes 4:169–174MATHCrossRef

Panda G, Panigrahi M, Nanda S (2006) Equivalence class in the set of fuzzy numbers and its application in decision-making problems. Int J Math Math Sci. Article ID 74165

Pushkov SG (2008) Fuzzy modules with respect to t-norm and some of their properties. J Math Sci 154:374–378MathSciNetMATHCrossRef

Qiu D, Shu L (2008) Notes on “On the restudy of fuzzy complex analysis: part I and part II". Fuzzy Sets Syst 159:2185–2189MathSciNetMATHCrossRef

Qiu D, Shu L, Mo Z (2009a) Notes on fuzzy complex analysis. Fuzzy Sets Syst 160:1578–1589MathSciNetMATHCrossRef

Qiu D, Shu L, Mo Z (2009b) On starshaped fuzzy sets. Fuzzy Sets Syst 160:1563–1577MathSciNetMATHCrossRef

Qiu D, Yang F, Shu L (2010) On convex fuzzy processes and their generalizations. Int J Fuzzy Syst 12:268–273MathSciNet

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

Stefanini L, Sorini L, Guerra ML (2006) Paremetric representation of fuzzy numbers and application to fuzzy calculus. Fuzzy Sets Syst 157:2423–2455MathSciNetMATHCrossRef

Tripathy BC, Baruah A (2009) New type of difference sequence spaces of fuzzy real numbers. Math Model Anal 14:391–397MathSciNetMATHCrossRef

Tripathy BC, Baruah A (2010a) Norlund and Riesz mean of sequences of fuzzy real numbers. Appl Math Lett 23:651–655MathSciNetMATHCrossRef

Tripathy BC, Baruah A (2010b) Lacunary statistically convergent and lacunary strongly convergent generalized difference sequences of fuzzy real numbers. Kyungpook Math J 50:565–574MathSciNetMATHCrossRef

Tripathy BC, Borgogain S (2008) The sequence space m(M, ϕ, ▵ _n ^m , p)^F. Math Model Anal 13:577–586MathSciNetMATHCrossRef

Tripathy BC, Borgogain S (2011) Some classes of difference sequence spaces of fuzzy real numbers defined by Orlicz function. Adv Fuzzy Syst. Article ID 216414

Tripathy BC, Dutta AJ (2007) On fuzzy real-valued double sequence spaces. Math Comput Model 46:1294–1299MathSciNetMATHCrossRef

Tripathy BC, Dutta AJ (2010) Bounded variation double sequence space of fuzzy real numbers. Comput Math Appl 59:1031–1037MathSciNetMATHCrossRef

Tripathy BC, Sarma B (2008) Sequence spaces of fuzzy real numbers defined by Orlicz functions. Mathematica Slovaca 58:621–628MathSciNetMATHCrossRef

Tripathy BC, Sarma B (2011) Double sequence spaces of fuzzy numbers defined by Orlicz function. Acta Mathematica Scientia 31:134–140MathSciNetMATHCrossRef

Tripathy BC, Sarma B (2012) On I-convergent double sequences of fuzzy real numbers. Kyungpook Math J 52:189–200MathSciNetCrossRef

Tripathy BC, Sen M, Nath S (2012) I-convergence in probabilistic n-normed space. Soft Comput 16:1021–1027MATHCrossRef

Wang G, Li Y, Wen C (2007) On fuzzy n-cell numbers and n-dimension fuzzy vectors. Fuzzy Sets Syst 158:71–84MathSciNetMATHCrossRef

Zadeh LA (1975) The concept of alinguistic variable and its applications to approximate reasoning. Parts I, II, III. Inf Sci 8:199–251, 301–357; 9:43–80

Titel: Symmetric fuzzy numbers and additive equivalence of fuzzy numbers
verfasst von: Dong Qiu
Weiquan Zhang
Publikationsdatum: 01.08.2013
Verlag: Springer Berlin Heidelberg
Erschienen in: Soft Computing / Ausgabe 8/2013
Print ISSN: 1432-7643
Elektronische ISSN: 1433-7479
DOI: https://doi.org/10.1007/s00500-013-1000-3

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 8/2013

Orders on intervals over partially ordered sets: extending Allen’s algebra and interval graph results

Outer enclosures to the parametric AE solution set

A congruence modular variety that is neither congruence distributive nor 3-permutable

Special issue on “uncertainty modeling and analysis with intervals: foundations, tools, applications”

Error bounds for initial value problems by optimization

FRASel: a consensus of feature ranking methods for time series modelling

Premium Partner