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
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)
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)
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)
Zimmermann, H.J.: Fuzzy Set Theory and Its Applications, 4th edn. Kluwer Academic Publisher, Dordrecht (2001)
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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© 2014 Springer India
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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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