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Proceedings of the Third International Conference on Soft Computing for Problem Solving pp 535–538Cite as

Additive and Multiplicative Inverse of Generalized Fuzzy Numbers with Different Left Heights and Right Heights

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Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 258))

Abstract

In this paper, with the help of Zadeh’s extension principle, it is shown that there is error in the additive and multiplicative inverse of generalized fuzzy numbers with different left heights and right heights proposed by Lee and Chen [1]. To resolve the error, new additive and multiplicative inverse of generalized fuzzy numbers with different left heights and right heights are proposed. Also, it is shown that generalized fuzzy numbers with different left heights and right heights cannot be used for fuzzy risk analysis.

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References

  1. Lee, L.W., Chen, S.M.: Fuzzy risk analysis based on fuzzy numbers with different shapes and different deviations. Expert Syst. Appl. 34, 2763–2771 (2008)

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  2. Chang, J.R., Cheng, C.H., Kuo, C.Y.: Conceptual procedure for ranking fuzzy numbers based on adaptive two-dimensions dominance. Soft. Comput. 10, 94–103 (2006)

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  3. Chen, S.M., Munif, A., Chen, G.S., Liu, H.C., Kuo, B.C.: Fuzzy risk analysis based on ranking generalized fuzzy numbers with different left heights and right heights. Expert Syst. Appl. 39, 6320–6334 (2012)

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  4. Zimmermann, H.J.: Fuzzy Set Theory and Its Applications, 4th edn. Kluwer Academic Publisher, Dordrecht (2001)

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Acknowledgments

The second author, Dr. Amit Kumar, want to acknowledge the adolescent inner blessings of Mehar (lovely daughter of his cousin sister). He believes that Mata Vaishno Devi has appeared on the earth in the form of Mehar and without her blessings it was not possible to think the ideas presented in this paper. The first and third authors would like to acknowledge for financial assistant given by University Grant Commission (F. No. 39–49/2010 (SR)).

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Authors and Affiliations

  1. School of Mathematics and Computer Applications, Thapar University, Patiala, Punjab, India

    Gourav Gupta, Amit Kumar & M. K. Sharma

Authors
  1. Gourav Gupta
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  2. Amit Kumar
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  3. M. K. Sharma
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Corresponding author

Correspondence to Gourav Gupta .

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Editors and Affiliations

  1. Department of Paper Technology, Indian Institute of Technology Roorkee, Roorkee, Uttarakhand, India

    Millie Pant

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

    Kusum Deep

  3. Department of Mathematics and Computer Science, Liverpool Hope University, Liverpool, United Kingdom

    Atulya Nagar

  4. Department of Applied Mathematics, South Asian University, New Delhi, India

    Jagdish Chand Bansal

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Gupta, G., Kumar, A., Sharma, M.K. (2014). Additive and Multiplicative Inverse of Generalized Fuzzy Numbers with Different Left Heights and Right Heights. In: Pant, M., Deep, K., Nagar, A., Bansal, J. (eds) Proceedings of the Third International Conference on Soft Computing for Problem Solving. Advances in Intelligent Systems and Computing, vol 258. Springer, New Delhi. https://doi.org/10.1007/978-81-322-1771-8_47

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  • DOI: https://doi.org/10.1007/978-81-322-1771-8_47

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  • Publisher Name: Springer, New Delhi

  • Print ISBN: 978-81-322-1770-1

  • Online ISBN: 978-81-322-1771-8

  • eBook Packages: EngineeringEngineering (R0)

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