Skip to main content
SpringerLink
Log in

New Fuzzy Divergence Measure and Its Applications in Multi-criteria Decision-Making Using New Tool

  • Conference paper
  • First Online:
Mathematical Analysis II: Optimisation, Differential Equations and Graph Theory (ICRAPAM 2018)

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 307))

Abstract

Fuzzy set theory is well suited for dealing with uncertainty and vagueness. In this research paper, we introduced new convex function, new fuzzy divergence measure and its generalization with the proof of its validity. Further, we established relations between new and well-known fuzzy divergence measures. Also, we discussed applications of new fuzzy divergence measure in multi-criteria decision-making using a new tool and its comparison with the TOPSIS method.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. R.K. Bajaj, D.S. Hooda, On some new generalized measures of fuzzy information. World Acad. Sci. Eng. Technol. 62, 747–753 (2010)

    Google Scholar 

  2. D. Bhandari, N.R. Pal, Some new information measures for fuzzy sets. Inf. Sci. 67(3), 209–228 (1993)

    Article  MathSciNet  Google Scholar 

  3. P.K. Bhatia, S. Singh, A new measure of fuzzy directed divergence and its application in image segmentation. Int. J. Intell. Syst. Appl. 4, 81–89 (2013)

    Google Scholar 

  4. M. Emami, K. Nazari, H. Fardmanesh, Application of fuzzy TOPSIS technique for strategic management decision. J. Appl. Basic Sci. Res. 2(1), 685–689 (2012)

    Google Scholar 

  5. C. Ferrari, Hyperentropy and related heterogeneity divergence and information measures. Statistica 40(2), 155–168 (1980)

    MathSciNet  Google Scholar 

  6. M. Ghosh, D. Das, C. Chakraborty, A.K. Roy, Automated leukocyte recognition using fuzzy divergence. Micron 41, 840–846 (2010)

    Article  Google Scholar 

  7. D.S. Hooda, D. Jain, The generalized fuzzy measures of directed divergence, total ambiguity and information improvement. Investig. Math. Sci. 2, 239–260 (2012)

    MATH  Google Scholar 

  8. G.R. Jahanshahloo, L.F. Hosseinzadeh, M. Izadikhah, Extension of TOPSIS method for decision making problems with fuzzy data. Appl. Math. Comput. 181, 1544–1551 (2006)

    MATH  Google Scholar 

  9. K.C. Jain, R.N. Saraswat, A new information inequality and its application in establishing relation among various F-divergence measures. J. Appl. Math. Stat. Inform. 8(1), 17–32 (2012)

    Article  Google Scholar 

  10. K.C. Jain, R.N. Saraswat, Some bounds of information divergence measure in terms of Kullback-Leibler divergence measure. Antarct. J. Math. 9(7), 613–623 (2012)

    Google Scholar 

  11. K.C. Jain, R.N. Saraswat, Series of information divergence measures using new F-divergences, convex properties and inequalities. Int. J. Mod. Eng. Res. 2(5), 3226–3231 (2012)

    Google Scholar 

  12. J.N. Kapur, Measures of Fuzzy Information (Mathematical Sciences Trust Society, New Delhi, 1997)

    Google Scholar 

  13. S. Kullback, R.A. Leibler, On information and sufficiency. Ann. Math. Stat. 22(1), 79–86 (1951)

    Article  MathSciNet  Google Scholar 

  14. A.D. Luca, S. Termini, A definition of non-probabilistic entropy in the setting of fuzzy set theory. Inf. Control 20(4), 301–312 (1972)

    Article  Google Scholar 

  15. S. Montes, I. Couso, P. Gil, C. Bertoluzza, Divergence measure between fuzzy sets. Int. J. Approx. Reason. 30, 91–105 (2002)

    Article  MathSciNet  Google Scholar 

  16. A. Ohlan, R. Ohlan, Generalizations of Fuzzy Information Measures (Springer International Publishing, Switzerland, 2016)

    Book  Google Scholar 

  17. A. Ohlan, R. Ohlan, Parametric generalized exponential fuzzy divergence measure and strategic decision making, in Generalizations of Fuzzy Information Measures, ed. by A. Ohlan, R. Ohlan (Springer International Publishing, Switzerland, 2016), pp. 53–69

    Chapter  Google Scholar 

  18. O. Parkash, P.K. Sharma, S. Kumar, Two new measures of fuzzy divergence and their properties. SQU J. Sci. 11, 69–77 (2006)

    Article  Google Scholar 

  19. C.E. Shannon, A mathematical theory of comunication. Bell Syst. Tech. J. 27(3), 379–423 (1948)

    Article  Google Scholar 

  20. D. Stanujkic, N. Magdalinovic, S. Tojanovic, R. Jovanovic, Extension of ratio system part of MOORA method for solving decision making problems with interval data. Informatica 23(1), 141–154 (2012)

    MATH  Google Scholar 

  21. R. Verma, B.D. Sharma, On generalized exponential fuzzy entropy. World Acad. Sci. Eng. Technol. 69, 1402–1405 (2011)

    Google Scholar 

  22. L.A. Zadeh, Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Manipal University Jaipur, Jaipur, 303007, Rajasthan, India

    Ram Naresh Saraswat & Adeeba Umar

Authors
  1. Ram Naresh Saraswat
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Adeeba Umar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Adeeba Umar .

Editor information

Editors and Affiliations

  1. Department of Applied Mathematics, Delhi Technological University, New Delhi, India

    Naokant Deo

  2. Department of Mathematics, Netaji Subhas University of Technology, New Delhi, India

    Vijay Gupta

  3. Department of Mathematics, Lucian Blaga University of Sibiu, Sibiu, Romania

    Ana Maria Acu

  4. Department of Mathematics, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    P. N. Agrawal

Rights and permissions

Reprints and permissions

Copyright information

© 2020 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Saraswat, R.N., Umar, A. (2020). New Fuzzy Divergence Measure and Its Applications in Multi-criteria Decision-Making Using New Tool. In: Deo, N., Gupta, V., Acu, A., Agrawal, P. (eds) Mathematical Analysis II: Optimisation, Differential Equations and Graph Theory. ICRAPAM 2018. Springer Proceedings in Mathematics & Statistics, vol 307. Springer, Singapore. https://doi.org/10.1007/978-981-15-1157-8_17

Download citation

Publish with us

Policies and ethics

Search

Navigation