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.
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.
