The Expected Value of a Fuzzy Number

ABSTRACT

Conjunction of two probability laws can give rise to a possibility law. Using two probability densities over two disjoint ranges, we can define the fuzzy mean of a fuzzy variable with the help of means two random variables in two disjoint spaces.

Conjunction of two probability laws can give rise to a possibility law. Using two probability densities over two disjoint ranges, we can define the fuzzy mean of a fuzzy variable with the help of means two random variables in two disjoint spaces.

KEYWORDS

Probability Density Function, Probability Distribution, Fuzzy Measure, Fuzzy Expected Value, Fuzzy Mean, Fuzzy Membership Function, Dubois-Prade Reference Functions

Probability Density Function, Probability Distribution, Fuzzy Measure, Fuzzy Expected Value, Fuzzy Mean, Fuzzy Membership Function, Dubois-Prade Reference Functions

Cite this paper

Shenify, M. and Mazarbhuiya, F. (2015) The Expected Value of a Fuzzy Number.*International Journal of Intelligence Science*, **5**, 1-5. doi: 10.4236/ijis.2015.51001.

Shenify, M. and Mazarbhuiya, F. (2015) The Expected Value of a Fuzzy Number.

References

[1] Zadeh, L.A. (1965) Fuzzy Sets as Basis of Theory of Possibility. Fuzzy Sets and Systems, 1, 3-28. http://dx.doi.org/10.1016/0165-0114(78)90029-5

[2] Aczel, M.J. and Ptanzagl, J. (1966) Remarks on the Measurement of Subjective Probability and Information. Metrica, 5, 91-105.

[3] Asai, K., Tanaka, K. and Okuda, T. (1977) On the Discrimination of Fuzzy States in Probability Space. Kybernetes, 6, 185-192. http://dx.doi.org/10.1108/eb005451

[4] Baldwin, J.F. and Pilsworth, B.W. (1979) Fuzzy Truth Definition of Possibility Measure for Decision Classification. International Journal of Man-Machine Studies, 11, 447-463.

[5] Kandel, A. (1979) On Fuzzy Statistics. In: Gupta, M.M., Ragade, R.K. and Yager, R.R., Eds., Advances in Fuzzy Set Theory and Application, North Holland, Amsterdam.

[6] Kandel, A. and Byatt, W.J. (1978) Fuzzy Sets, Fuzzy Algebra and Fuzzy Statistics. Proceedings of the IEEE 66, USA, January 1978, 1619-1639.

[7] Teran, P. (2014) Law of Large Numbers for Possibilistic Mean Value. Fuzzy Sets and Systems, 245, 116-124. http://dx.doi.org/10.1016/j.fss.2013.10.011

[8] Georgescu, I. and Kinnunen, J. (2011) Credibility Measures in Portfolio Analysis: From Possibilistic to Probabilistic Models. Journal of Applied Operational Research, 3, 91-102.

[9] Sam, P. and Chakraborty, S. (2013) The Possibilistic Safety Assessment of Hybrid Uncertain Systems. International Journal of Reliability, Quality and Safety Engineering, 20, 191-197.

[10] Zaman, K., Rangavajhala, S., Mc Donald, M. and Mahadevan, S. (2011) A Probabilistic Approach for Representation of Interval Uncertainty. Reliability Engineering and System Safety, 96, 117-130.

http://dx.doi.org/10.1016/j.ress.2010.07.012

[11] Baruah, H.K. (2010) The Randomness-Fuzziness Consistency Principle. International Journal of Energy, Information and Communications, 1, 37-48.

[12] 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.

[13] Baruah, H.K. (1999) Set Superimposition and Its Application to the Theory of Fuzzy Sets. Journal of Assam Science Society, 40, 25-31.

[14] Mazarbhuiya, F.A. (2014) Finding a Link between Randomness and Fuzziness. Applied Mathematics, 5, 1369-1374.

[15] Prade, H. (1983) Fuzzy Programming Why and How? Some Hints and Examples. In: Wang, P.P., Ed., Advances in Fuzzy Sets, Possibility Theory and Applications, Plenum Press, New York, 237-251.

http://dx.doi.org/10.1007/978-1-4613-3754-6_16

[16] Kandel, A. (1982) Fuzzy Techniques in Pattern Recognition. Wiley Interscience Publication, New York.

[1] Zadeh, L.A. (1965) Fuzzy Sets as Basis of Theory of Possibility. Fuzzy Sets and Systems, 1, 3-28. http://dx.doi.org/10.1016/0165-0114(78)90029-5

[2] Aczel, M.J. and Ptanzagl, J. (1966) Remarks on the Measurement of Subjective Probability and Information. Metrica, 5, 91-105.

[3] Asai, K., Tanaka, K. and Okuda, T. (1977) On the Discrimination of Fuzzy States in Probability Space. Kybernetes, 6, 185-192. http://dx.doi.org/10.1108/eb005451

[4] Baldwin, J.F. and Pilsworth, B.W. (1979) Fuzzy Truth Definition of Possibility Measure for Decision Classification. International Journal of Man-Machine Studies, 11, 447-463.

[5] Kandel, A. (1979) On Fuzzy Statistics. In: Gupta, M.M., Ragade, R.K. and Yager, R.R., Eds., Advances in Fuzzy Set Theory and Application, North Holland, Amsterdam.

[6] Kandel, A. and Byatt, W.J. (1978) Fuzzy Sets, Fuzzy Algebra and Fuzzy Statistics. Proceedings of the IEEE 66, USA, January 1978, 1619-1639.

[7] Teran, P. (2014) Law of Large Numbers for Possibilistic Mean Value. Fuzzy Sets and Systems, 245, 116-124. http://dx.doi.org/10.1016/j.fss.2013.10.011

[8] Georgescu, I. and Kinnunen, J. (2011) Credibility Measures in Portfolio Analysis: From Possibilistic to Probabilistic Models. Journal of Applied Operational Research, 3, 91-102.

[9] Sam, P. and Chakraborty, S. (2013) The Possibilistic Safety Assessment of Hybrid Uncertain Systems. International Journal of Reliability, Quality and Safety Engineering, 20, 191-197.

[10] Zaman, K., Rangavajhala, S., Mc Donald, M. and Mahadevan, S. (2011) A Probabilistic Approach for Representation of Interval Uncertainty. Reliability Engineering and System Safety, 96, 117-130.

http://dx.doi.org/10.1016/j.ress.2010.07.012

[11] Baruah, H.K. (2010) The Randomness-Fuzziness Consistency Principle. International Journal of Energy, Information and Communications, 1, 37-48.

[12] 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.

[13] Baruah, H.K. (1999) Set Superimposition and Its Application to the Theory of Fuzzy Sets. Journal of Assam Science Society, 40, 25-31.

[14] Mazarbhuiya, F.A. (2014) Finding a Link between Randomness and Fuzziness. Applied Mathematics, 5, 1369-1374.

[15] Prade, H. (1983) Fuzzy Programming Why and How? Some Hints and Examples. In: Wang, P.P., Ed., Advances in Fuzzy Sets, Possibility Theory and Applications, Plenum Press, New York, 237-251.

http://dx.doi.org/10.1007/978-1-4613-3754-6_16

[16] Kandel, A. (1982) Fuzzy Techniques in Pattern Recognition. Wiley Interscience Publication, New York.