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A New Exponential Fuzzy Entropy of Order-\((\alpha , \beta )\) and its Application in Multiple Attribute Decision-Making Problems

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Abstract

Fuzzy entropy is an important concept to measure the fuzzy information. Measure of fuzziness of a fuzzy set is the measure of its fuzziness. In the present communication, we have defined an exponential fuzzy entropy of order-\((\alpha , \beta )\). Besides establishing the validity of the proposed measure, we have also discussed some of its properties. At last, we have given the application of the proposed measure in multiple attribute decision-making problems. In this section, we have considered two cases for the weights of attributes: One is the case when weights are completely unknown to us, and the other is the case when weights are partially known to us.

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References

  1. Bhandari, D., Pal, N.R.: Some new information measures for fuzzy sets. Inf. Sci. 67(3), 204–228 (1993)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  3. Ebanks, B.R.: On measure of fuzziness and their representation. J. Math. Anal. Appl. 94, 301–312 (1983)

    Article  MathSciNet  Google Scholar 

  4. Higashi, M., Klir, G.J.: On measures of fuzziness and fuzzy complements. Int. J. Gen. Syst. 8, 169–180 (1982)

    Article  MathSciNet  MATH  Google Scholar 

  5. Hung, W.L., Yang, M.S.: Fuzzy entropy on intuitionistic fuzzy sets. Int. J. Intell. Syst. 21, 443–451 (2006)

    Article  MATH  Google Scholar 

  6. Joshi, Rajesh, Kumar, Satish: A new approach in multiple attribute decision making using \(R\)-norm entropy and Hamming distance measure. Int. J, Inf. Manag. Sci. 27, 253–268 (2016)

    Google Scholar 

  7. Kapur, J.N.: Measures of Fuzzy Information. Mathematical Science Trust Society, New Delhi (1997)

    Google Scholar 

  8. Kaufman, A.: Fuzzy Subsets: Fundamental Theoretical Elements, vol. 3. Academic press, New York (1980)

    Google Scholar 

  9. Kvalseth, T.O.: On exponential entropies. IEEE Int. Conf. Syst. Man Cybernet. 4, 2822–2826 (2000)

    Google Scholar 

  10. Liu, Manfeng, Ren, Haiping: A new intuitionistic fuzzy entropy and application in multi-attribute decision-making. Information 5, 587–601 (2014)

    Article  Google Scholar 

  11. Pal, N.R., Pal, S.K.: Object background segmentation using new definition of entropy. Proc. Inst. Elec. Eng. 136, 284–295 (1989)

    Google Scholar 

  12. Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27, 378623 (1948)

    Article  MathSciNet  Google Scholar 

  13. Verma, R., Sharma, B.D.: On generalized exponential fuzzy entropy. World Acad. Sci. Eng. Technol. 60, 1402–1405 (2011)

    Google Scholar 

  14. Verma, R., Sharma, B.D.: On generalized exponential fuzzy entropy. World Acad. Sci. Eng. Technol. 5(12), 1895–1898 (2011)

    Google Scholar 

  15. Wang, J., Wang, P.: Intuitionistic linguistic fuzzy multi-critria decision-making method based on intuitionistic fuzzy entropy. Control. Decis. 27, 1694–1698 (2012)

    MathSciNet  Google Scholar 

  16. Yager, R.R.: On the measure of fuzziness and negation. Part 1: membership in the unit interval. Int. J. Gen. Syst. 5, 221–229 (1979)

    Article  MATH  Google Scholar 

  17. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 221–229 (1965)

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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Acknowledgements

I am thankful to anonymous reviewers for their valuable and constructive suggestions.

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Authors and Affiliations

  1. Department of Mathematics, Maharishi Markandeshwar University Mullana, Ambala, 133207, India

    Rajesh Joshi & Satish Kumar

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  1. Rajesh Joshi
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  2. Satish Kumar
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Correspondence to Rajesh Joshi.

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Joshi, R., Kumar, S. A New Exponential Fuzzy Entropy of Order-\((\alpha , \beta )\) and its Application in Multiple Attribute Decision-Making Problems. Commun. Math. Stat. 5, 213–229 (2017). https://doi.org/10.1007/s40304-017-0109-6

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  • DOI: https://doi.org/10.1007/s40304-017-0109-6

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