Skip to main content

Mathematical Interpretation of Fuzzy Information Model

  • Conference paper
  • First Online:
Soft Computing: Theories and Applications

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1380))

  • 883 Accesses

Abstract

One of the important attributes of human thinking and reasoning is fuzziness or vagueness, which mostly arises due to imprecise information. To tackle such kinds of situations, the fuzzy theory came into existence. Keeping in consideration the instances of imprecise data and related situations, we have developed a new generalized two-parametric fuzzy entropy measure that is presented in this paper. A detailed proof of the properties of the new fuzzy entropy model is also discussed in this paper. Further, a deep mathematical evaluation of all the well-known axioms for fuzziness measures is carried out in this research paper.

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

Access this chapter

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 189.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 249.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Similar content being viewed by others

References

  1. Arora, H.D., Dhiman, A.: Application of fuzzy information measure to coding theory. Int. J. Adv. Technol. Eng. Sci. 2, 678–687 (2014)

    Google Scholar 

  2. Baig, M.A.K., Dar, M.J.: Some coding theorems on fuzzy entropy function depending upon parameter R and V. IOSR J. Math. 9:119–123

    Google Scholar 

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

    Google Scholar 

  4. Bhat, A.H., Baig, M.A.K.: Some coding theorems on new generalized fuzzy entropy of order alpha and type beta. Appl. Math. Inf. Sci. Lett. 5, 63–69 (2017)

    Article  Google Scholar 

  5. Ebanks, B.R.: On measures of fuzziness and their representations. J. Math. Anal. Appl. 94, 24–37 (1983)

    Article  MathSciNet  Google Scholar 

  6. Hartley, R.T.V.: Transmission of information. Bell Syst. Tech. J. 7, 535–563 (1928)

    Article  Google Scholar 

  7. Kapur, J.N.: Generalized entropy of order α and type β. In: Maths Seminar, Delhi, vol. 4, pp. 78–94 (1967)

    Google Scholar 

  8. Kaufmann, A.: Fuzzy Subsets; Fundamental Theoretical Elements, 3rd edn. Academic , New Delhi (1980)

    Google Scholar 

  9. Klir, G., Boyuan, U.C.: Fuzzy set theory foundations and applications. Prentice Hall (1988)

    Google Scholar 

  10. Kosko, B.: Fuzzy entropy and conditioning. Inf. Sci. 40, 165–174 (1986)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  12. Nyquist, H.: Certain factors affecting telegraph speed. Bell Syst. Tech. J. 3, 324–346 (1924)

    Article  Google Scholar 

  13. Nyquist, H.: Certain topics in telegraphy transmission theory. J. Am. Inst. Electr. Eng. 47, 617–619 (1928)

    Google Scholar 

  14. Ohlan, A., Ohlan, R.: Generalizations of Fuzzy Information Measures. Springer International Publishing, Berlin (2016)

    Google Scholar 

  15. Parkash, O., Sharma, P.K.: A new class of fuzzy coding theorems. Caribb. J. Math. Comput. Sci. 12, 1–10 (2002)

    MathSciNet  MATH  Google Scholar 

  16. Peerzada, S., Sofi, S.M., Nisa, R.: A new generalized fuzzy information measure and its properties. Int. J. Adv. Res. Sci. Eng. 6, 1647–1654 (2017)

    Google Scholar 

  17. Renyi, A.: On measure of entropy and information. In: Proceedings of 4th Berkeley Symposium on Mathematics, Statistics and Probability, vol. 1, pp. 547–561 (1961)

    Google Scholar 

  18. Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 423–467 (1948)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  20. Zadeh, L.A.: Probability measures of fuzzy events. J. Math. Anal. Appl. 23, 421–427 (1968)

    Article  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Qayoom, B., Baig, M.A.K. (2022). Mathematical Interpretation of Fuzzy Information Model. In: Sharma, T.K., Ahn, C.W., Verma, O.P., Panigrahi, B.K. (eds) Soft Computing: Theories and Applications. Advances in Intelligent Systems and Computing, vol 1380. Springer, Singapore. https://doi.org/10.1007/978-981-16-1740-9_37

Download citation

Publish with us

Policies and ethics