nach oben

Fuzzy Optimization and Decision Making

Erschienen in:

16.03.2016

Limit properties and derivative operations in the metric space of intuitionistic fuzzy numbers

verfasst von: Zhenghai Ai, Zeshui Xu, Qian Lei

Erschienen in: Fuzzy Optimization and Decision Making | Ausgabe 1/2017

Einloggen

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

search-config

KI-gestützte Suche

Aus

Abstract

Intuitionistic fuzzy numbers (IFNs) are a useful tool to depict the uncertain information in real life. Based on IFNs, the intuitionistic fuzzy calculus (IFC) has been put forward recently. To further develop the IFC theory, in this paper, we investigate the limit properties of IFCs, and study the intuitionistic fuzzy infinitesimals and their orders. We also discuss the continuity, the derivatives and the differentials of intuitionistic fuzzy functions in detail, and reveal their relationships. Additionally, we define the metric space of the IFNs, based on which, a series of desirable results are obtained. These results are similar to the ones in the classical calculus.

Vorheriger Artikel Exponential distance-based fuzzy clustering for interval-valued data

Nächster Artikel A fuzzy extension of Analytic Hierarchy Process based on the constrained fuzzy arithmetic

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. (1986). Intuitionistic fuzzy set. Fuzzy Sets and Systems, 20, 87–96.MathSciNetCrossRefMATH

Atanassov, K. (2012). On intuitionistic fuzzy sets theory. Berlin: Springer.CrossRefMATH

Bustince, H., Herrera, F., & Montero, J. (2008). Fuzzy sets and their extensions: Representation, aggregation and models. Berlin: Springer.CrossRefMATH

Das, D., & De, P. K. (2014). Ranking of intuitionistic fuzzy numbers by new distance measure. ArXiv preprint arXiv:1410.7155.

De, S. K., Biswas, R., & Roy, A. R. (2001). An application of intuitionistic fuzzy sets in medical diagnosis. Fuzzy Sets and Systems, 117, 209–213.CrossRefMATH

Gerstenkron, T., & Mafiko, J. (1991). Correlation of intuitionistic fuzzy sets. Fuzzy Sets and Systems, 44, 39–43.MathSciNetCrossRef

Hung, W. L., Lee, J. S., & Fuh, C. D. (2004). Fuzzy clustering based on intuitionistic fuzzy relations. International Journal of Uncertainly, 12, 513–529.MathSciNetCrossRefMATH

Lei, Q., & Xu, Z. S. (2015a). Chain and substitution rules of intuitionistic fuzzy calculus. IEEE Transactions on Fuzzy Systems. doi:10.1109/TFUZZ.2015.2450832.

Lei, Q., & Xu, Z. S. (2015b). Derivative and differential operations of intuitionistic fuzzy numbers. International Journal of Intelligent Systems, 30, 468–498.CrossRef

Lei, Q., & Xu, Z. S. (2015). Fundamental properties of intuitionistic fuzzy calculus. Knowledge-based Systems, 76, 1–16.CrossRef

Li, D. F. (2014). Decision and game theory in management with intuitionistic fuzzy sets. Berlin: Springer.CrossRefMATH

Mitchell, H. B. (2005). Pattern recognition using type-II fuzzy sets. Information Sciences, 170, 409–418.CrossRef

Raquel, U., Francisco, C., Fujita, H., & Herrera-Viedma, Enrique. (2015). Confidence-consistency driven group decision making approach with incomplete reciprocal intuitionistic preference relations. Knowledge-Based Systems, 89, 86–96.CrossRef

Rudin, W. (1964). Principles of mathematical analysis (2nd ed.). New York: McGraw-Hill.MATH

Song, Y. F., Wang, X. D., Lei, L., & Xue, A. J. (2015). A novel similarity measure on intuitionistic fuzzy sets with its applications. Applied Intelligence, 42, 252–261.CrossRef

Szmidt, E., & Kacprzyk, J. (2004). A similarity measure for intuitionistic fuzzy sets and its application in supporting medical diagnostic reasoning. Lecture Notes in Artificial Intelligence (Vol. 3070, pp. 388–393).

Szmidt, E., & Kacprzyk, J. (2000). Distances between intuitionistic fuzzy sets. Fuzzy Sets and Systems, 114, 505–518.MathSciNetCrossRefMATH

Wu, J., & Francisco, C. (2014). Multiplicative consistency of intuitionistic reciprocal preference relations and its application to missing values estimation and consensus building. Knowledge-Based Systems, 71, 187–200.CrossRef

Xu, Z. S., & Cai, X. Q. (2012). Intuitionistic fuzzy information aggregation: Theory and applications. Beijing: Science Press; and Berlin: Springer.

Xu, Z. S. (2013a). Intuitionistic fuzzy preference modeling and interactive decision making. Berlin: Springer.

Xu, Z. S. (2013b). Intuitionistic fuzzy aggregation and clustering. Berlin: Springer.MATH

Xu, Z. S., & Chen, J. (2008). An overview of distance and similarity measure of intuitionistic fuzzy sets. International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 16, 529–555.MathSciNetCrossRefMATH

Yager, R. R., & Kacprzyk, J. (1997). The ordered weighted averaging operators: Theory and applications. Norwell, MA: Kluwer.CrossRefMATH

Yu, S., Xu, Z. S., Xu, J. P., & Liu, H. F. (2015). Indefinite integrals of generalized intuitionistic multiplicative functions. Fuzzy Optimization and Decision Making. doi:10.1007/s10700-015-9209-5.

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

Titel: Limit properties and derivative operations in the metric space of intuitionistic fuzzy numbers
verfasst von: Zhenghai Ai
Zeshui Xu
Qian Lei
Publikationsdatum: 16.03.2016
Verlag: Springer US
Erschienen in: Fuzzy Optimization and Decision Making / Ausgabe 1/2017
Print ISSN: 1568-4539
Elektronische ISSN: 1573-2908
DOI: https://doi.org/10.1007/s10700-016-9239-7

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 1/2017

A fuzzy extension of Analytic Hierarchy Process based on the constrained fuzzy arithmetic

Fuzzy cross-efficiency evaluation: a possibility approach

Exponential distance-based fuzzy clustering for interval-valued data

An original approach to ranking fuzzy numbers by inclusion index and Bitset Encoding

Belief structures, weight generating functions and decision-making

Premium Partner