Skip to main content
Disciplines
Automotive Business IT + Informatics Construction + Real Estate Electrical Engineering + Electronics Energy + Sustainability Insurance + Risk Finance + Banking Management + Leadership Marketing + Sales Mechanical Engineering + Materials
Events
DE
EN
Books
Journals
Topic Page
Marketing
Start single access now
Access for companies
EXTENDED SEARCH
Log in
Top
Published in:
Rough Sets and Other Mathematics: Ten Research Programs Read chapter Read first chapter

2015 | OriginalPaper | Chapter

Approximate Reasoning Under Type-2 Fuzzy Logics

Authors : Sudin Mandal, Namrata Bhattacharyya, Swapan Raha

Published in: Facets of Uncertainties and Applications

Publisher: Springer India

Log in

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

In this paper, we have made a study of approximate reasoning based on a Type-2 fuzzy set theory. We have focused upon two typical rules of inference used mostly in ordinary approximate reasoning methodology based on Type-1 fuzzy set theory. Similarity is inherent in approximate reasoning. The concept of similarity between Type-2 fuzzy sets is discussed and a similarity-based approximate reasoning technique is proposed. The proposal is illustrated with a typical artificial example. Prediction is the causal basis for decision making. Different measures leading to prediction under uncertainty are proposed for a better understanding of the power of Type-2 fuzzy set theory.

Dont have a licence yet? Then find out more about our products and how to get one now:

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!

inform now

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!

inform now

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!

inform now
previous chapter Open World Models: A View from Rough Set Theory
next chapter Approximation Dialectics of Proto-Transitive Rough Sets
Literature
1.
Chen, S.M.: A weighted fuzzy reasoning algorithm for medical diagnosis. Decis. Support. Syst. 11, 37–43 (1994)CrossRef
2.
Hajĕk, P.: Metamathematics of Fuzzy Logic. Kluwer Academic Press, Dordrecht (1998)CrossRef
3.
Helgason, C.M., Jobe, T.H.: Causal efficacy in the fuzzy hypercube: representation of concomitant mechanisms for stroke. Neural Netw. 11, 548–555 (1998)CrossRef
4.
Mendel, J.M., John, R.I.B.: Type-2 fuzzy sets made simple. IEEE Trans. Fuzzy Syst. 10(1), 117–127 (2002)CrossRef
5.
6.
Nieminen, J.: On the Algebraic Structure of Fuzzy Sets of Type-2, vol. 13. Kybernetica, New York (1977)MATH
7.
Raha, S., Pal, N.R., Ray, K.S.: Similarity based approximate reasoning: methodology and application. IEEE Trans. Syst. Man Cybern.—Part A: Syst. Hum. 32(4), 541–547 (2002)CrossRef
8.
Raha, S., Hossain, A., Ghosh, S.: Similarity based approximate reasoning: fuzzy control. J. Appl. Log. 6(1), 47–71 (2008)MathSciNetCrossRef
9.
Xuechang, L.: Entropy, distance measure and similarity measures of fuzzy sets and their relations. Fuzzy Sets Syst. 52, 171–174 (1992)MathSciNet
10.
Yager R.R.: Measurement of properties on fuzzy sets and possibility distribution. In: Klement, E.P. (ed.) Proceedings of the 3rd International Seminar on Fuzzy Set Theory, pp. 211–222. Johannes Kepler University of Linz
11.
Yager, R.R.: An Introduction to applications of possibility theory. Hum. Syst. Manag. 3, 246–253 (1983)
12.
Yang, M.S., Lin, D.C.: On similarity and inclusion measures between type-2 fuzzy sets with an application to clustering. Comput. Math. Appl. 57, 896–907 (2009)MathSciNetCrossRef
13.
14.
Zadeh, L.A.: The concept of linguistic variable and its application to approximate reasoning—I. Inf. Sci. 8, 199–249 (1975)MathSciNetCrossRef
15.
Zadeh, L.A.: A computational approach to fuzzy quantifiers in natural languages. Comput. Math. Appl. 9, 149–184 (1983)MathSciNetCrossRef
16.
Zadeh, L.A.: A theory of approximate reasoning. In: Hayes, J.E., Mitchie, D., Mikulich, L.I. (eds.) Machine Intelligence. A theory of approximate reasoning, vol. 9, pp. 149–194 (1979)
Metadata
Title
Approximate Reasoning Under Type-2 Fuzzy Logics
Authors
Sudin Mandal
Namrata Bhattacharyya
Swapan Raha
Copyright Year
2015
Publisher
Springer India
Book
Facets of Uncertainties and Applications

Print ISBN: 978-81-322-2300-9

Electronic ISBN: 978-81-322-2301-6

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-81-322-2301-6_7

Premium Partner

    Image Credits