Finding a Link between Randomness and Fuzziness
Author(s)
Fokrul Alom Mazarbhuiya
ABSTRACT
If sample realizations are intervals, if the upper and the lower boundaries of such intervals are realizations of two independently distributed random variables, the two probability laws together lead to some interesting assertions. In this article, we shall attempt to remove certain confusions regarding the relationship between probability theory and fuzzy mathematics.
KEYWORDS
Probability, Possibility, Fuzzy Sets, Possibilistic Events, Uniform Probability Law, Triangular Fuzzy Number, Order Statistics
Probability, Possibility, Fuzzy Sets, Possibilistic Events, Uniform Probability Law, Triangular Fuzzy Number, Order Statistics
Cite this paper
Mazarbhuiya, F. (2014) Finding a Link between Randomness and Fuzziness. Applied Mathematics, 5, 1369-1374. doi: 10.4236/am.2014.59128.
Mazarbhuiya, F. (2014) Finding a Link between Randomness and Fuzziness. Applied Mathematics, 5, 1369-1374. doi: 10.4236/am.2014.59128.
References
[1] Zadeh, L.A. (1965) Fuzzy Sets as a Basis of Theory of Possibility. Fuzzy Sets and Systems, 1, 3-28.
http://dx.doi.org/10.1016/0165-0114(78)90029-5 [2] Chen, G.Q., Lee, S.C. and Yu, E.S.H. (1983) Application of Fuzzy Set Theory to Economics, In: Wang, P.P., Ed., Advances in Fuzzy Sets, Possibility Theory, and Application, Plenum Press, New York, 277-305.
http://dx.doi.org/10.1007/978-1-4613-3754-6_18 [3] Dubois, D. and Prade, H. (1983) Ranking Fuzzy Number in the Setting of Possibility Theory. Information Sciences, 3, 183-224.
http://dx.doi.org/10.1016/0020-0255(83)90025-7 [4] Prade, H. (1983) Fuzzy Programming: Why and How? Some Hints and Examples, in Advances in Fuzzy Sets, Possibility Theory and Application. [5] Baruah, H.K. (1999) Set Superimposition and Its Application to the Theory of Fuzzy Sets. Journal of the Assam Science Society, 40, 25-31. [6] Mazarbhuiya, F.A., Mahanta, A.K. and Baruah, H.K. (2003) Fuzzy Arithmetic without Using the Method of α-Cut. Bulletin of Pure and Applied Sciences, 22E, 45-54. [7] Mazarbhuiya, F.A., Mahanta, A.K. and Baruah, H.K. (2011) Solution of the Fuzzy Equation A+X= B Using the Method of Superimposition. Applied Mathematics, 2, 1039-1045.
http://dx.doi.org/10.4236/am.2011.28144 [8] Mahanta, A.K., Mazarbhuiya, F.A. and Baruah, H.K. (2008) Finding Calendar-Based Periodic Patterns. Pattern Recognition Letters, 29, Elsevier Publication, USA, 1274-1284. [9] Mazarbhuiya, F.A. and Abulaish, M. (2012) Clustering Periodic Patterns Using Fuzzy Statistical Parameters. International Journal of Innovative Computing Information and Control (IJICIC), 8, 2113-2124. [10] Baruah, H.K. (2010) The Randomness—Fuzziness Consistency Principle. International Journal of Energy, Information and Communications, 1, 37-48. [11] 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. [12] Loeve, M. (1977) Probability Theory I. Springer Verlag, New York.
[1] Zadeh, L.A. (1965) Fuzzy Sets as a Basis of Theory of Possibility. Fuzzy Sets and Systems, 1, 3-28.
http://dx.doi.org/10.1016/0165-0114(78)90029-5 [2] Chen, G.Q., Lee, S.C. and Yu, E.S.H. (1983) Application of Fuzzy Set Theory to Economics, In: Wang, P.P., Ed., Advances in Fuzzy Sets, Possibility Theory, and Application, Plenum Press, New York, 277-305.
http://dx.doi.org/10.1007/978-1-4613-3754-6_18 [3] Dubois, D. and Prade, H. (1983) Ranking Fuzzy Number in the Setting of Possibility Theory. Information Sciences, 3, 183-224.
http://dx.doi.org/10.1016/0020-0255(83)90025-7 [4] Prade, H. (1983) Fuzzy Programming: Why and How? Some Hints and Examples, in Advances in Fuzzy Sets, Possibility Theory and Application. [5] Baruah, H.K. (1999) Set Superimposition and Its Application to the Theory of Fuzzy Sets. Journal of the Assam Science Society, 40, 25-31. [6] Mazarbhuiya, F.A., Mahanta, A.K. and Baruah, H.K. (2003) Fuzzy Arithmetic without Using the Method of α-Cut. Bulletin of Pure and Applied Sciences, 22E, 45-54. [7] Mazarbhuiya, F.A., Mahanta, A.K. and Baruah, H.K. (2011) Solution of the Fuzzy Equation A+X= B Using the Method of Superimposition. Applied Mathematics, 2, 1039-1045.
http://dx.doi.org/10.4236/am.2011.28144 [8] Mahanta, A.K., Mazarbhuiya, F.A. and Baruah, H.K. (2008) Finding Calendar-Based Periodic Patterns. Pattern Recognition Letters, 29, Elsevier Publication, USA, 1274-1284. [9] Mazarbhuiya, F.A. and Abulaish, M. (2012) Clustering Periodic Patterns Using Fuzzy Statistical Parameters. International Journal of Innovative Computing Information and Control (IJICIC), 8, 2113-2124. [10] Baruah, H.K. (2010) The Randomness—Fuzziness Consistency Principle. International Journal of Energy, Information and Communications, 1, 37-48. [11] 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. [12] Loeve, M. (1977) Probability Theory I. Springer Verlag, New York.