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Mathematical expectation about discrete random variable with interval probability or fuzzy probability

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Abstract

The character and an algorithm about DRVIP(discrete random variable with interval probability) and the second kind DRVFP (discrete random variable with crisp event-fuzzy probability) are researched. Using the fuzzy resolution theorem, the solving mathematical expectation of a DRVFP can be translated into solving mathematical expectation of a series of RVIP. It is obvious that solving mathematical expectation of a DRVIP is a typical linear programming problem. A very functional calculating formula for solving mathematical expectation of DRVIP was obtained by using the Dantzig’s simplex method. The example indicates that the result obtained by using the functional calculating formula fits together completely with the result obtained by using the linear programming method, but the process using the formula deduced is simpler.

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Author information

Correspondence to Sheng-xie Xiao.

Additional information

Project supported by the National Natural Science Foundation of China ( No. 59878057) and the National Major Program of Science and Technology Foundation of China ( the Technological Action of West Development) (No. 2004BA901A02)

Communicated by CHEN Shang-lin

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Xiao, S., Lü, E. Mathematical expectation about discrete random variable with interval probability or fuzzy probability. Appl. Math. Mech.-Engl. Ed. 26, 1382–1390 (2005). https://doi.org/10.1007/BF03246243

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Keywords

  • interval number
  • fuzzy set
  • probability
  • random variable
  • mathematical expectation

Chinese Library Classification

  • O159

Document code

  • A

2000 Mathematics Subject Classification

  • 03E72
  • 62A01