• Shuming Wang
  • Junzo Watada


Randomness and fuzziness (or vagueness) are two major sources of uncertainty in the real world. Randomness relates to the stochastic variability of all possible outcomes of a situation and can be perfectly and mathematically described by probability theory with random variable. Fuzziness, on the other hand, stems from the imprecision of subjective human knowledge and exists objectively with a variety of manifestations in numbers of situations such as data capture and process, blurred boundaries of the parameters, expertise applications, and lack of precise knowledge. Fuzzy variable in the context of theory of fuzzy set and possibility (see [114, 117, 118, 171, 172]) is widely accepted as an effective mathematical approach to model the fuzzy uncertainty.


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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • Shuming Wang
    • 1
  • Junzo Watada
    • 1
  1. 1.Waseda UniversityKitakyushu-City 2-7Japan

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