FINDING STANDARD DEVIATIONOFA FUZZY NUMBER
DOI:
https://doi.org/10.29121/granthaalayah.v4.i1.2016.2844Keywords:
Probability Density Function, Probability Distribution, Fuzzy Measure, Fuzzy Mean, Fuzzy Variance, Fuzzy Standard Deviation, Fuzzy Membership Function, Dubois-Prade Reference FunctionsAbstract [English]
Two probability laws can be root of a possibility law. Considering two probability densities over two disjoint ranges, we can define the fuzzy standard deviation of a fuzzy variable with the help of the standard deviation two random variables in two disjoint spaces.
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Zadeh, L. A., (1965); Fuzzy Sets as Basis of Theory of Possibility, Fuzzy Sets and Systems 1, 3-28. DOI: https://doi.org/10.1016/0165-0114(78)90029-5
Aczel, M. J., and Ptanzagl, J, (1966); Remarks on the measurement of subjective probability and information, Metrica, 5, 91-105. DOI: https://doi.org/10.1007/BF02613579
Asai, K., Tanaka, K., and Okuda, T, (1977); On the discrimination of Fuzzy states in probability space, Kybernetes, 6, 185-192. DOI: https://doi.org/10.1108/eb005451
Baldwin, J. F., and Pilsworth, B. W, (1979); A theory of Fuzzy probability,9th. Int. Symp. On Multivalued Logic, Beth., U. K.
Kandel, A, (1979); On Fuzzy Statistics, in Advances in Fuzzy Set Theory and Application (M. M. Gupta, R. K. Ragade, and R. R. Yager, Eds), North Holland, Amsterdam.
Kandel, A. and Byatt, W. J. (1978); Fuzzy Sets, Fuzzy Algebra and Fuzzy Statistics, Proceedings of the IEEE 66, 1619-1639. DOI: https://doi.org/10.1109/PROC.1978.11171
Pedro Teran, (2014); Law of large numbers for possibilistic mean value, Fuzzy Sets and Systems. DOI: https://doi.org/10.1016/j.fss.2013.10.011
C. Carlsson and R. Fuller (2001); On Possibilistic Mean Value and Variance of Fuzzy Numbers, Fuzzy Sets and Systems 122 (2001), pp. 315-326.
F. A. Mazarbhuiya, M. Abulaish (2012), Clustering Periodic Patterns using Fuzzy Statistical Parameters. International Journal of Innovative Computing Information and Control (IJICIC), Vol. 8, No. 3(b), 2012, pp. 2113-2124.
Md. Husamuddin and F. A. Mazarbhuiya (2015); Clustering of Locally Frequent Patterns over Fuzzy Temporal Datasets, International Journal of Computer Trends and Technology (IJCTT) Vol.28 (3), October 2015, pp. 131-134.
Georgescu, I. and Kinnunen, J, (2011); Credibility measures in portfolio analysis: From possibilistic to probabilistic models, Journal of Applied Operational Research, Vol. 3(2), 91-102.
Sam, P, Chakraborty, S, (2013); The possibilistic Safety Assessment of hybrid Uncertain Systems, International Journal of Reliability, Quality and Safety Engineering, Vol. 20(1), 1350002, 191-197.
Zaman K., Rangavajhala, S., Mc Donald, M., and Mahadevan, S., (2011), A probabilistic approach for representation of interval uncertainty, Reliability Engineering and System Safety, Vol. 96(1), 117-130.
Baruah, H. K., (2010); The Randomness—Fuzziness Consistency Principle. International Journal of Energy, Information and Communications, 1, 37-48.
Baruah, H. K., (2012); An Introduction to the Theory of Imprecise Sets: The Mathematics of Partial Presence. Journal of Mathematical and Computational Science, 2, 110-124.
Baruah, H. K., (1999); Set superimposition and its application to the Theory of Fuzzy Sets, Journal of Assam Science Society, Vol.40 No. 1 and 2, 25-31.
Mazarbhuiya, F. A., (2014); Finding a link between Randomness and Fuzziness, Applied Mathematics, Vol. 5, 1369-1374.
M. Shenify and F. A. Mazarbhuiya (2015); The Expected Value of a Fuzzy Number, International Journal of Intelligence Science (IJIS), Scientific research publishing, Vol. 5, pp. 1-5.. DOI: https://doi.org/10.4236/ijis.2015.51001
Prade, H. (1983); Fuzzy Programming Why and How ? Some Hints and Examples, in Advances in Fuzzy Sets, Possibility Theory and Applications, Ed. Paul P. Wang, 237-251, Plenum Press, N. Y. DOI: https://doi.org/10.1007/978-1-4613-3754-6_16
Kandel, A., (1982); Fuzzy Techniques in Pattern Recognition, Wiley Interscience Publication.
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